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25
question
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result_float
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linear_formula
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6 values
math_qa__x0e51VtbYIlvYhZT
A store’s selling price of $2240 for a certain computer would yield a profit of 30 percent of the store’s cost for the computer. What selling price would yield a profit of 40 percent of the computer’s cost? Choose the correct choice from the following options: A) $ 2400 B) $ 2412 C) $ 2650 D) $ 2732 E) $ 2800
<gadget id="calculator">100 + 40</gadget> <output>140</output> <gadget id="calculator">100 + 30</gadget> <output>130</output> <gadget id="calculator">140 / 130</gadget> <output>14/13 = around 1.076923</output> <gadget id="calculator">2_240 * (14/13)</gadget> <output>31_360/13 = around 2_412.307692</output> <result>B</result>
B
2,412
A store’s selling price of $2240 for a certain computer would yield a profit of 30 percent of the store’s cost for the computer. What selling price would yield a profit of 40 percent of the computer’s cost?
{ "A": "$ 2400", "B": "$ 2412", "C": "$ 2650", "D": "$ 2732", "E": "$ 2800" }
multiply(2240, divide(add(const_100, 40), add(const_100, 30)))
add(n2,const_100)|add(n1,const_100)|divide(#0,#1)|multiply(n0,#2)|
"1.3 x = 2240 x = 2240 / 1.3 so , 1.4 x = 2240 * 1.4 / 1.3 = 2412 answer : - b"
gain
math_qa__L1oDdzuvxBx4bKno
Three table runners have a combined area of 220 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner? Choose the most appropriate option: A) 18 square inches B) 20 square inches C) 24 square inches D) 28 square inches E) 30 square inches
<gadget id="calculator">220 - 24</gadget> <output>196</output> <gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">175 * (4/5)</gadget> <output>140</output> <gadget id="calculator">196 - 140</gadget> <output>56</output> <gadget id="calculator">56 / 2</gadget> <output>28</output> <result>D</result>
D
28
Three table runners have a combined area of 220 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
{ "A": "18 square inches", "B": "20 square inches", "C": "24 square inches", "D": "28 square inches", "E": "30 square inches" }
divide(subtract(subtract(220, 24), multiply(175, divide(80, const_100))), const_2)
divide(n1,const_100)|subtract(n0,n3)|multiply(n2,#0)|subtract(#1,#2)|divide(#3,const_2)|
"total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 220 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 220 - 24 - 140 all three = 28 answer : d"
geometry
math_qa__GQ6X9dEHThNspA3e
The youngest of 4 children has siblings who are 2, 7, and 11 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 25, what is the age of the youngest sibling? Select: A) 17 B) 18 C) 19 D) 20 E) 21
<gadget id="calculator">4 * 25</gadget> <output>100</output> <gadget id="calculator">4 + 7</gadget> <output>11</output> <gadget id="calculator">11 + 11</gadget> <output>22</output> <gadget id="calculator">100 - 22</gadget> <output>78</output> <gadget id="calculator">78 / 4</gadget> <output>39/2 = around 19.5</output> <result>D</result>
D
20
The youngest of 4 children has siblings who are 2, 7, and 11 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 25, what is the age of the youngest sibling?
{ "A": "17", "B": "18", "C": "19", "D": "20", "E": "21" }
divide(subtract(multiply(const_4.0, 25), add(add(4, 7), 11)), 4)
add(n1,n2)|multiply(n0,n5)|add(n3,#0)|subtract(#1,#2)|divide(#3,n0)|
"x + ( x + 2 ) + ( x + 7 ) + ( x + 11 ) = 100 4 x + 20 = 100 4 x = 80 x = 20 the answer is d ."
general
math_qa__3DgMcNMzTZixO2Jy
A person walking at 10 Kmph reaches his office 10 minutes late. If he walks at 15 Kmph, he reaches there 10 minutes earlier. How far is the office from his house? Choose the correct choice from the following answers: A) 5 km B) 15 km C) 8 km D) 10 km E) 20 km
<gadget id="calculator">10 / 60</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">10 * (1/6)</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">15 * (1/6)</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(5/3) + (5/2)</gadget> <output>25/6 = around 4.166667</output> <gadget id="calculator">15 - 10</gadget> <output>5</output> <gadget id="calculator">(25/6) / 5</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">(5/6) + (1/6)</gadget> <output>1</output> <gadget id="calculator">1 * 10</gadget> <output>10</output> <result>D</result>
D
10
A person walking at 10 Kmph reaches his office 10 minutes late. If he walks at 15 Kmph, he reaches there 10 minutes earlier. How far is the office from his house?
{ "A": "5 km", "B": "15 km", "C": "8 km", "D": "10 km", "E": "20 km" }
multiply(add(divide(add(multiply(10, divide(10, const_60)), multiply(15, divide(10, const_60))), subtract(15, 10)), divide(10, const_60)), 10)
divide(n0,const_60)|subtract(n2,n0)|multiply(n0,#0)|multiply(n2,#0)|add(#2,#3)|divide(#4,#1)|add(#5,#0)|multiply(n0,#6)
formula = s 1 * s 2 / s 2 - s 1 * t 1 + t 2 / 60 = 10 * 15 / 5 * 20 / 60 = 30 * 20 / 60 = 10 km answer is d
physics
math_qa__zMdBgDgtdqWYyZsp
Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 18 machines produce in 6 minutes? Pick. A) 1344 B) 3360 C) 7560 D) 50400 E) 67200
<gadget id="calculator">18 / 8</gadget> <output>9/4 = around 2.25</output> <gadget id="calculator">560 * (9/4)</gadget> <output>1_260</output> <gadget id="calculator">1_260 * 6</gadget> <output>7_560</output> <result>C</result>
C
7,560
Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 18 machines produce in 6 minutes?
{ "A": "1344", "B": "3360", "C": "7560", "D": "50400", "E": "67200" }
multiply(multiply(560, divide(18, 8)), 6)
divide(n2,n0)|multiply(n1,#0)|multiply(n3,#1)|
"8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 18 machine produce 560 * 6 * ( 18 / 8 ) in 6 minutes 560 * 6 * 18 / 8 = 7560 answer is c ."
gain
math_qa__z9GuutgfqRAQFyqP
Two pipes A and B can fill a tank in 25 hours and 35 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? Choices: A) 20 hours B) 14 6 / 11 hours C) 10 hours D) 12 hours E) 8 hours
<gadget id="calculator">1 / 25</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">1 / 35</gadget> <output>1/35 = around 0.028571</output> <gadget id="calculator">(1/25) + (1/35)</gadget> <output>12/175 = around 0.068571</output> <gadget id="calculator">1 / (12/175)</gadget> <output>175/12 = around 14.583333</output> <result>B</result>
B
14
Two pipes A and B can fill a tank in 25 hours and 35 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
{ "A": "20 hours", "B": "14 6 / 11 hours", "C": "10 hours", "D": "12 hours", "E": "8 hours" }
divide(const_1, add(divide(const_1, 25), divide(const_1, 35)))
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)|
"part filled by a in 1 hour = 1 / 25 part filled by b in 1 hour = 1 / 30 part filled by ( a + b ) in 1 hour = 1 / 25 + 1 / 30 = 11 / 150 both the pipes together fill the tank in 150 / 11 = 14 6 / 11 hours answer is b"
physics
math_qa__F5V6nQWH1f722SHv
Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many W kilometers per hour did Tammy walk on the second day? Choose the correct option: A) 3 B) 3.5 C) 4 D) 4.5 E) 6
<gadget id="calculator">14 + 2</gadget> <output>16</output> <gadget id="calculator">16 / 2</gadget> <output>8</output> <gadget id="calculator">8 - 2</gadget> <output>6</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <gadget id="calculator">52 - 3</gadget> <output>49</output> <gadget id="calculator">6 + 8</gadget> <output>14</output> <gadget id="calculator">49 / 14</gadget> <output>7/2 = around 3.5</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(7/2) + (1/2)</gadget> <output>4</output> <result>C</result>
C
4
Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many W kilometers per hour did Tammy walk on the second day?
{ "A": "3", "B": "3.5", "C": "4", "D": "4.5", "E": "6" }
add(divide(subtract(52, divide(subtract(divide(add(14, 2), 2), 2), 2)), add(subtract(divide(add(14, 2), 2), 2), divide(add(14, 2), 2))), divide(const_1, 2))
add(n0,n1)|divide(const_1,n1)|divide(#0,n1)|subtract(#2,n1)|add(#2,#3)|divide(#3,n1)|subtract(n2,#5)|divide(#6,#4)|add(#7,#1)|
"ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
physics
math_qa__kUYyMa4x0c7zwsSI
an isosceles triangle with sides 13 13 10 and there is a circle inscribed it .find the radius of circle? Options. A) 1.32 B) 3.33 C) 3.58 D) 4.34 E) 5.18
<gadget id="calculator">(((13 + 13 + 10) / 2) * ((13 + 13 + 10) / 2 - 13) * ((13 + 13 + 10) / 2 - 13) * ((13 + 13 + 10) / 2 - 10)) ** (1/2)</gadget> <output>60</output> <gadget id="calculator">60 * 2</gadget> <output>120</output> <gadget id="calculator">13 + 13 + 10</gadget> <output>36</output> <gadget id="calculator">120 / 36</gadget> <output>10/3 = around 3.333333</output> <result>B</result>
B
3.33
an isosceles triangle with sides 13 13 10 and there is a circle inscribed it .find the radius of circle?
{ "A": "1.32", "B": "3.33", "C": "3.58", "D": "4.34", "E": "5.18" }
divide(multiply(triangle_area_three_edges(13, 13, 10), const_2), triangle_perimeter(13, 13, 10))
triangle_area_three_edges(n0,n0,n2)|triangle_perimeter(n0,n0,n2)|multiply(#0,const_2)|divide(#2,#1)
height of triangle = √ ( 13 ^ 2 - ( 10 / 2 ) ^ 2 ) = 12 area of triangle = r * s where , r = radius of inscribed circle & s = ( a + b + c ) / 2 area of triangle = 1 / 2 * b * h = 1 / 2 * 10 * 12 = 60 s = ( 13 + 13 + 10 ) / 2 = 18 r = area of triangle / s = 60 / 18 = 10 / 3 = 3.33 answer : b
geometry
math_qa__MYnJr6aGFh404yth
The diagonals of a rhombus are 10 cm and 15 cm. Find its area? Options: A) 75 B) 129 C) 150 D) 123 E) 117
<gadget id="calculator">(10 * 15) / 2</gadget> <output>75</output> <result>A</result>
A
75
The diagonals of a rhombus are 10 cm and 15 cm. Find its area?
{ "A": "75", "B": "129", "C": "150", "D": "123", "E": "117" }
rhombus_area(10, 15)
rhombus_area(n0,n1)|
"1 / 2 * 10 * 15 = 75 answer : a"
geometry
math_qa__AdrBSp6MoWkGKGrC
In a can, there is a mixture of milk and water in the ratio 1 : 5. If it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 3 : 5. Find the capacity of the can? Choose the correct choice from the following options A) 40 B) 44 C) 48 D) 8 E) 56
<gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 5</gadget> <output>3</output> <gadget id="calculator">3 - 1</gadget> <output>2</output> <gadget id="calculator">2 / 2</gadget> <output>1</output> <gadget id="calculator">5 * 1</gadget> <output>5</output> <gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 + 2</gadget> <output>8</output> <result>D</result>
D
8
In a can, there is a mixture of milk and water in the ratio 1 : 5. If it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 3 : 5. Find the capacity of the can?
{ "A": "40", "B": "44", "C": "48", "D": "8", "E": "56" }
add(add(multiply(5, divide(2, subtract(multiply(divide(3, 5), 5), 1))), divide(2, subtract(multiply(divide(3, 5), 5), 1))), 2)
divide(n3,n4)|multiply(n1,#0)|subtract(#1,n0)|divide(n2,#2)|multiply(n1,#3)|add(#3,#4)|add(n2,#5)|
"let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 1 / 6 ( t - 2 ) after adding milk , quantity of milk in the mixture = 3 / 8 t . 3 t / 8 - 2 = 1 / 6 = ( t - 2 ) 10 t = 96 - 16 = > t = 8 answer : d"
general
math_qa__kv4FUXlCnXrGRdVW
Each child has 6 crayons and 12 apples. If there are 12 children, how many crayons are there in total? Choose the correct choice from the following answers: A) 22 B) 65 C) 72 D) 78 E) 90
<gadget id="calculator">12 * 6</gadget> <output>72</output> <result>C</result>
C
72
Each child has 6 crayons and 12 apples. If there are 12 children, how many crayons are there in total?
{ "A": "22", "B": "65", "C": "72", "D": "78", "E": "90" }
multiply(12, 6)
multiply(n0,n2)|
6 * 12 = 72 . answer is c
general
math_qa__D9UJDLpv9jp98Nkg
A car takes 8 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? Select the correct option: A) 10 kmph B) 45 kmph C) 60 kmph D) 55 kmph E) 30 kmph
<gadget id="calculator">8 * 3</gadget> <output>24</output> <gadget id="calculator">24 / 2</gadget> <output>12</output> <gadget id="calculator">540 / 12</gadget> <output>45</output> <result>B</result>
B
45
A car takes 8 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
{ "A": "10 kmph", "B": "45 kmph", "C": "60 kmph", "D": "55 kmph", "E": "30 kmph" }
divide(540, divide(multiply(8, 3), 2))
multiply(n0,n2)|divide(#0,n3)|divide(n1,#1)|
"time = 8 distence = 540 3 / 2 of 8 hours = 8 * 3 / 2 = 12 hours required speed = 540 / 12 = 45 kmph b )"
physics
math_qa__e0V9ihqkPXUZu0Ku
Assisants are needed to prepare for preparation. Each helper can make either 2 large cakes or 35 small cakes/hour. The kitchen is available for 3hours and 20 large cakes and 700small cakes are needed. How many helpers are required? Choose one: A) 9 B) 10 C) 13 D) 16 E) 18
<gadget id="calculator">20 / 2</gadget> <output>10</output> <gadget id="calculator">700 / 35</gadget> <output>20</output> <gadget id="calculator">10 + 20</gadget> <output>30</output> <gadget id="calculator">30 / 3</gadget> <output>10</output> <result>B</result>
B
10
Assisants are needed to prepare for preparation. Each helper can make either 2 large cakes or 35 small cakes/hour. The kitchen is available for 3hours and 20 large cakes and 700small cakes are needed. How many helpers are required?
{ "A": "9", "B": "10", "C": "13", "D": "16", "E": "18" }
divide(add(divide(20, 2), divide(700, 35)), 3)
divide(n3,n0)|divide(n4,n1)|add(#0,#1)|divide(#2,n2)
20 large cakes will require the equivalent of 10 helpers working for one hour . 700 small cakes will require the equivalent of 20 helpers working for one hour . this means if only one hour were available we would need 30 helpers . but since three hours are available we can use 10 helpers . b
other
math_qa__SLVAu2ibUjom5tLH
If the perimeter of a rectangular park is 1000 m, its length when its breadth is 200 m is? Choose the most appropriate option. A) 50 B) 100 C) 200 D) 300 E) 400
<gadget id="calculator">1_000 / 2</gadget> <output>500</output> <gadget id="calculator">500 - 200</gadget> <output>300</output> <result>D</result>
D
300
If the perimeter of a rectangular park is 1000 m, its length when its breadth is 200 m is?
{ "A": "50", "B": "100", "C": "200", "D": "300", "E": "400" }
subtract(divide(1000, const_2), 200)
divide(n0,const_2)|subtract(#0,n1)|
2 ( l + 200 ) = 1000 = > l = 300 m answer : d
physics
math_qa__NAHPrlevUU0rk0fH
A boat running upstream takes 640 min to cover a certain distance, while it takes 280 min to cover the same distance running down stream. What is the ratio between the speed of the boat and speed of water current respectively? Answers A) 23 : 7 B) 22 : 9 C) 23 : 8 D) 23 : 9 E) 23 : 11
<gadget id="calculator">640 + 280</gadget> <output>920</output> <gadget id="calculator">920 / 2</gadget> <output>460</output> <gadget id="calculator">640 - 460</gadget> <output>180</output> <gadget id="calculator">460 / 180</gadget> <output>23/9 = around 2.555556</output> <result>D</result>
D
2.555556
A boat running upstream takes 640 min to cover a certain distance, while it takes 280 min to cover the same distance running down stream. What is the ratio between the speed of the boat and speed of water current respectively?
{ "A": "23 : 7", "B": "22 : 9", "C": "23 : 8", "D": "23 : 9", "E": "23 : 11" }
divide(divide(add(640, 280), const_2), subtract(640, divide(add(640, 280), const_2)))
add(n0,n1)|divide(#0,const_2)|subtract(n0,#1)|divide(#1,#2)
let the speed of the boat = x and speed of the current = y relative speed in upstream = x - y and in downstream = x + y let the distance ' d ' is to be covered in downstream and upstream , then time taken in upstream = d / ( x - y ) = 640 or d = 640 ( x - y ) - - - - ( i ) and time taken in downstream = d / ( x + y ) = 280 or d = 280 ( x + y ) - - - - ( ii ) comparing ( i ) & ( ii ) , 640 ( x - y ) = 280 ( x + y ) = > 16 ( x - y ) = 7 ( x + y ) = > 16 x - 16 y = 7 x - 7 y = > 9 x = 23 y = > x / y = 23 / 9 answer : d
physics
math_qa__9DusRWbIvEAbVhC3
f(1)=1,where f(x+y)=f(x)+f(y)+8xy-2.then f(7)=? Choices A) 162 B) 163 C) 164 D) 165 E) 166
<gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 + 8</gadget> <output>10</output> <gadget id="calculator">10 - 2</gadget> <output>8</output> <gadget id="calculator">8 + 1</gadget> <output>9</output> <gadget id="calculator">8 * 2</gadget> <output>16</output> <gadget id="calculator">9 + 16</gadget> <output>25</output> <gadget id="calculator">25 - 2</gadget> <output>23</output> <gadget id="calculator">23 + 1</gadget> <output>24</output> <gadget id="calculator">8 * 3</gadget> <output>24</output> <gadget id="calculator">24 + 24</gadget> <output>48</output> <gadget id="calculator">48 - 2</gadget> <output>46</output> <gadget id="calculator">46 + 1</gadget> <output>47</output> <gadget id="calculator">8 * 4</gadget> <output>32</output> <gadget id="calculator">47 + 32</gadget> <output>79</output> <gadget id="calculator">79 - 2</gadget> <output>77</output> <gadget id="calculator">77 + 1</gadget> <output>78</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">8 * 5</gadget> <output>40</output> <gadget id="calculator">78 + 40</gadget> <output>118</output> <gadget id="calculator">118 - 2</gadget> <output>116</output> <gadget id="calculator">116 + 1</gadget> <output>117</output> <gadget id="calculator">3 + 3</gadget> <output>6</output> <gadget id="calculator">8 * 6</gadget> <output>48</output> <gadget id="calculator">117 + 48</gadget> <output>165</output> <gadget id="calculator">165 - 2</gadget> <output>163</output> <result>B</result>
B
163
f(1)=1,where f(x+y)=f(x)+f(y)+8xy-2.then f(7)=?
{ "A": "162", "B": "163", "C": "164", "D": "165", "E": "166" }
subtract(add(add(subtract(add(add(subtract(add(add(subtract(add(add(subtract(add(add(subtract(add(add(1, 1), 8), 2), 1), multiply(8, const_2)), 2), 1), multiply(8, const_3)), 2), 1), multiply(8, const_4)), 2), 1), multiply(8, add(const_3, const_2))), 2), 1), multiply(8, add(const_3, const_3))), 2)
add(n0,n0)|add(const_2,const_3)|add(const_3,const_3)|multiply(n2,const_2)|multiply(n2,const_3)|multiply(n2,const_4)|add(n2,#0)|multiply(n2,#1)|multiply(n2,#2)|subtract(#6,n3)|add(n0,#9)|add(#10,#3)|subtract(#11,n3)|add(n0,#12)|add(#13,#4)|subtract(#14,n3)|add(n0,#15)|add(#16,#5)|subtract(#17,n3)|add(n0,#18)|add(#19,#7)|subtract(#20,n3)|add(n0,#21)|add(#22,#8)|subtract(#23,n3)
f ( 1 ) = 1 f ( 2 ) = f ( 1 + 1 ) = 1 + 1 + 8 - 2 = 8 f ( 3 ) = f ( 2 + 1 ) = 8 + 1 + ( 8 * 2 * 1 ) - 2 = 23 f ( 6 ) = f ( 3 + 3 ) = 23 + 23 + ( 8 * 3 * 3 ) - 2 = 116 f ( 7 ) = f ( 6 + 1 ) = 116 + 1 + ( 8 * 6 * 1 ) - 2 = 163 thus ans is 163 answer : b
general
math_qa__0H0BjzSQEmKBPhyk
What is the largest possible value of cc if 5c+(d−12)^2=235? Choose the correct choice from the following choices A) 17 B) 25 C) 35 D) 42 E) 47
<gadget id="calculator">235 / 5</gadget> <output>47</output> <result>E</result>
E
47
What is the largest possible value of cc if 5c+(d−12)^2=235?
{ "A": "17", "B": "25", "C": "35", "D": "42", "E": "47" }
divide(235, 5)
divide(n3,n0)
to maximize c , we should minimize ( d - 12 ) ^ 2 . ( d - 12 ) ^ 2 is a square of a number , thus its smallest possible value is 0 ( for d = 12 ) . in this case we ' d have 5 c + 0 = 235 - - > c = 47 . answer : e .
general
math_qa__NbnFyGTvqRDhKafn
At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? Choose the correct option: A) 404 B) 452 C) 444 D) 468 E) 422
<gadget id="calculator">112 / 2</gadget> <output>56</output> <gadget id="calculator">312 - 56</gadget> <output>256</output> <gadget id="calculator">222 - 56</gadget> <output>166</output> <gadget id="calculator">256 + 166</gadget> <output>422</output> <result>E</result>
E
422
At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
{ "A": "404", "B": "452", "C": "444", "D": "468", "E": "422" }
add(subtract(312, divide(112, const_2)), subtract(222, divide(112, const_2)))
divide(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|add(#1,#2)|
"312 + 222 - 112 ( since 112 is counted twice ) = 422 e is the answer"
other
math_qa__c5iEF4QKchKcmQ9J
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1700. The difference between the profit shares of A and C is? Choose the correct choice from the following choices: A) 288 B) 266 C) 155 D) 680 E) 441
<gadget id="calculator">12_000 / 10_000</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">8_000 / 10_000</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">(6/5) - (4/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 1_700</gadget> <output>680</output> <result>D</result>
D
680
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1700. The difference between the profit shares of A and C is?
{ "A": "288", "B": "266", "C": "155", "D": "680", "E": "441" }
multiply(subtract(divide(12000, 10000), divide(8000, 10000)), 1700)
divide(n2,n1)|divide(n0,n1)|subtract(#0,#1)|multiply(n3,#2)|
"ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1700 = > 5 parts out of 15 parts is rs . 1700 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1700 ) = rs . 680 answer : d"
gain
math_qa__IIqfUNfoUafrsvxP
If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 2 = ? Choose the correct option: A) 2 B) 4 C) 8 D) 16 E) 32
<gadget id="calculator">2 ** 4</gadget> <output>16</output> <gadget id="calculator">2 ** 2</gadget> <output>4</output> <gadget id="calculator">16 / 4</gadget> <output>4</output> <result>B</result>
B
4
If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 2 = ?
{ "A": "2", "B": "4", "C": "8", "D": "16", "E": "32" }
divide(power(2, divide(power(2, 4), power(2, 2))), power(2, 2))
power(n0,n2)|power(n0,n0)|power(n0,n4)|divide(#0,#1)|power(n0,#3)|divide(#4,#2)|
"4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 the answer is b ."
general
math_qa__afEHHeh18ICUfkEZ
A rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge. If the floor is 12 meters by 10 meters, what is the area of the rug in square meters? Pick: A) 30 B) 28 C) 36 D) 42 E) 24
<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">12 - 6</gadget> <output>6</output> <gadget id="calculator">10 - 6</gadget> <output>4</output> <gadget id="calculator">6 * 4</gadget> <output>24</output> <result>E</result>
E
24
A rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge. If the floor is 12 meters by 10 meters, what is the area of the rug in square meters?
{ "A": "30", "B": "28", "C": "36", "D": "42", "E": "24" }
rectangle_area(subtract(12, multiply(3, const_2)), subtract(10, multiply(3, const_2)))
multiply(n0,const_2)|subtract(n1,#0)|subtract(n2,#0)|rectangle_area(#1,#2)|
"a strip of 3 meters is covering the inner rectangular rug for all 4 sides . length of inner rug = 12 - ( 2 * 3 ) breadth of inner rug = 10 - ( 2 * 3 ) area of rug = 6 * 4 = 24 sq . mt â nswer : e"
geometry
math_qa__5R2vajUFK3exnpDe
On a trip, a cyclist averaged 8 miles per hour for the first 16 miles and 10 miles per hour for the remaining 16 miles. If the cyclist returned immediately via the same route and took a total of 6.8 hours for the round trip, what was the average speed (in miles per hour) for the return trip? Choose the correct answer: A) 9 B) 10 C) 11 D) 12 E) 13
<gadget id="calculator">16 + 16</gadget> <output>32</output> <gadget id="calculator">16 / 8</gadget> <output>2</output> <gadget id="calculator">16 / 10</gadget> <output>8/5 = around 1.6</output> <gadget id="calculator">2 + (8/5)</gadget> <output>18/5 = around 3.6</output> <gadget id="calculator">6.8 - (18/5)</gadget> <output>3.2</output> <gadget id="calculator">32 / 3.2</gadget> <output>10</output> <result>B</result>
B
10
On a trip, a cyclist averaged 8 miles per hour for the first 16 miles and 10 miles per hour for the remaining 16 miles. If the cyclist returned immediately via the same route and took a total of 6.8 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
{ "A": "9", "B": "10", "C": "11", "D": "12", "E": "13" }
divide(add(16, 16), subtract(6.8, add(divide(16, 8), divide(16, 10))))
add(n1,n3)|divide(n1,n0)|divide(n3,n2)|add(#1,#2)|subtract(n4,#3)|divide(#0,#4)|
"the time to go 32 miles was 16 / 8 + 16 / 10 = 2 + 1.6 = 3.6 hours . the average speed for the return trip was 32 miles / 3.2 hours = 10 mph . the answer is b ."
physics
math_qa__IqwQU6kLHgeqfOOR
One-third less than 20% of 180 is equal to: Pick one: A) 24 B) 30 C) 35 D) 40 E) 45
<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 180</gadget> <output>36</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 36</gadget> <output>12</output> <gadget id="calculator">36 - 12</gadget> <output>24</output> <result>A</result>
A
24
One-third less than 20% of 180 is equal to:
{ "A": "24", "B": "30", "C": "35", "D": "40", "E": "45" }
subtract(multiply(divide(20, const_100), 180), multiply(divide(const_1, const_3), multiply(divide(20, const_100), 180)))
divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)|
"lots of ways to tackle this . 20 % of 180 = 36 1 / 3 of 36 = 12 so , 1 / 3 , less than 36 is equal to 36 - 12 = 24 answer : a"
general
math_qa__JImvu9rBg8ibBeTT
The area of a square field is 576 km2. How long will it take for a horse to run around at the speed of 12 km/h ? Choices: A) 12 h B) 10 h C) 8 h D) 6 h E) none of these
<gadget id="calculator">576 ** (1/2)</gadget> <output>24</output> <gadget id="calculator">4 * 24</gadget> <output>96</output> <gadget id="calculator">96 / 12</gadget> <output>8</output> <result>C</result>
C
8
The area of a square field is 576 km2. How long will it take for a horse to run around at the speed of 12 km/h ?
{ "A": "12 h", "B": "10 h", "C": "8 h", "D": "6 h", "E": "none of these" }
divide(multiply(const_4, sqrt(576)), 12)
sqrt(n0)|multiply(#0,const_4)|divide(#1,n2)|
"area of field = 576 km 2 . then , each side of field = √ 576 = 24 km distance covered by the horse = perimeter of square field = 24 × 4 = 96 km ∴ time taken by horse = distances / peed = 96 / 12 = 8 h answer c"
geometry
math_qa__SBxJxFBWgAw1YwUR
A and B complete a work in 6 days. A can alone can do it in 10 days. If both can together can do the work in how many days? Choose one: A) 7 B) 3.75 C) 2 D) 1 E) 8
<gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">6 + 10</gadget> <output>16</output> <gadget id="calculator">60 / 16</gadget> <output>15/4 = around 3.75</output> <result>B</result>
B
3.75
A and B complete a work in 6 days. A can alone can do it in 10 days. If both can together can do the work in how many days?
{ "A": "7", "B": "3.75", "C": "2", "D": "1", "E": "8" }
divide(multiply(6, 10), add(6, 10))
add(n0,n1)|multiply(n0,n1)|divide(#1,#0)
1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer b
physics
math_qa__rTF6VshP25C0YJLz
Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)? Choose one. A) 670 B) 710 C) 750 D) 790 E) 830
<gadget id="calculator">12.5 * 40</gadget> <output>500</output> <gadget id="calculator">620 - 500</gadget> <output>120</output> <gadget id="calculator">120 / 0.16</gadget> <output>750</output> <result>C</result>
C
750
Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)?
{ "A": "670", "B": "710", "C": "750", "D": "790", "E": "830" }
divide(subtract(620, multiply(12.5, 40)), 0.16)
multiply(n0,n2)|subtract(n3,#0)|divide(#1,n1)
total pay = 40 * $ 12.50 + $ 0.16 * x = 620 x = 120 / 0.16 = 750 the answer is c .
physics
math_qa__mv2x5kNnovnQb7ax
What is the distance covered by a car if it travels with a speed of 160 kmh for 5 hours? Choose the correct choice. A) 350 km B) 400 km C) 800 km D) 600 km E) 650 km
<gadget id="calculator">160 * 5</gadget> <output>800</output> <result>C</result>
C
800
What is the distance covered by a car if it travels with a speed of 160 kmh for 5 hours?
{ "A": "350 km", "B": "400 km", "C": "800 km", "D": "600 km", "E": "650 km" }
multiply(160, 5)
multiply(n0,n1)
distance = time x speed 5 x 160 = 800 answer : c
physics
math_qa__c8x646SM4ORkdt6W
A cricketer scored 132 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets. Choose the correct choice from the following answers: A) 46.2 % B) 54.54 % C) 63 % D) 70 % E) none of these
<gadget id="calculator">12 * 4</gadget> <output>48</output> <gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">2 * 6</gadget> <output>12</output> <gadget id="calculator">48 + 12</gadget> <output>60</output> <gadget id="calculator">132 - 60</gadget> <output>72</output> <gadget id="calculator">72 / 132</gadget> <output>6/11 = around 0.545455</output> <gadget id="calculator">(6/11) * 100</gadget> <output>600/11 = around 54.545455</output> <result>B</result>
B
54.54
A cricketer scored 132 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
{ "A": "46.2 %", "B": "54.54 %", "C": "63 %", "D": "70 %", "E": "none of these" }
multiply(divide(subtract(132, add(multiply(12, const_4), multiply(2, multiply(2, const_3)))), 132), const_100)
multiply(n1,const_4)|multiply(n2,const_3)|multiply(n2,#1)|add(#0,#2)|subtract(n0,#3)|divide(#4,n0)|multiply(#5,const_100)|
"explanation : number of runs made by running = 132 - ( 12 x 4 + 2 x 6 ) = 132 - ( 60 ) = 72 now , we need to calculate 72 is what percent of 132 . = > 72 / 132 * 100 = 54.54 % answer : b"
general
math_qa__hCG9iz6BJpPSSXUI
The marks obtained by Polly and Sandy are in the ratio 4:5 and those obtained by Sandy and Willy are in the ratio of 5:2. The marks obtained by Polly and Willy are in the ratio of...? Choose the correct choice from the following answers. A) 2 : 1 B) 3 : 2 C) 4 : 3 D) 5 : 4 E) 6 : 5
<gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">20 / 10</gadget> <output>2</output> <result>A</result>
A
2
The marks obtained by Polly and Sandy are in the ratio 4:5 and those obtained by Sandy and Willy are in the ratio of 5:2. The marks obtained by Polly and Willy are in the ratio of...?
{ "A": "2 : 1", "B": "3 : 2", "C": "4 : 3", "D": "5 : 4", "E": "6 : 5" }
divide(multiply(4, 5), multiply(5, 2))
multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)|
"polly : sandy = 4 : 5 sandy : willy = 5 : 2 polly : sandy : willy = 4 : 5 : 2 polly : willy = 4 : 2 = 2 : 1 the answer is a ."
other
math_qa__Rm0C5vkajKqfhc85
A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $168, how many hours overtime did he work? Choose the correct choice: A) 8 B) 21 C) 14 D) 12 E) 15
<gadget id="calculator">3 * 40</gadget> <output>120</output> <gadget id="calculator">168 - 120</gadget> <output>48</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">48 / 6</gadget> <output>8</output> <result>A</result>
A
8
A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $168, how many hours overtime did he work?
{ "A": "8", "B": "21", "C": "14", "D": "12", "E": "15" }
divide(subtract(168, multiply(3, 40)), multiply(3, const_2))
multiply(n0,n1)|multiply(n0,const_2)|subtract(n2,#0)|divide(#2,#1)|
"answer is : b at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 168 - $ 120 = $ 48 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 48 / $ 6 = 8"
physics
math_qa__ehNIX7iTVIjDEBJw
If A is thrice as fast as B and together can do a work in 21 days. In how many days A alone can do the work? Choose the correct choice from the following answers: A) 36 B) 42 C) 28 D) 54 E) 45
<gadget id="calculator">21 * 4</gadget> <output>84</output> <gadget id="calculator">3 / 84</gadget> <output>1/28 = around 0.035714</output> <gadget id="calculator">1 / (1/28)</gadget> <output>28</output> <result>C</result>
C
28
If A is thrice as fast as B and together can do a work in 21 days. In how many days A alone can do the work?
{ "A": "36", "B": "42", "C": "28", "D": "54", "E": "45" }
inverse(divide(const_3, multiply(21, const_4)))
multiply(n0,const_4)|divide(const_3,#0)|inverse(#1)|
"a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 21 = 3 + 1 / 3 x = 4 / 3 x = 1 / 21 x = 21 * 4 / 3 = 28 answer : c"
physics
math_qa__JP0TbqBeLudUYkqz
If the number 98348*0 is exactly divisible by 72, then the minimum value of * is? Pick: A) 1 B) 2 C) 3 D) 4 E) 5
<gadget id="calculator">98_348 * 100</gadget> <output>9_834_800</output> <gadget id="calculator">9_834_800 % 72</gadget> <output>32</output> <gadget id="calculator">72 - 32</gadget> <output>40</output> <gadget id="calculator">40 / 10</gadget> <output>4</output> <result>D</result>
D
4
If the number 98348*0 is exactly divisible by 72, then the minimum value of * is?
{ "A": "1", "B": "2", "C": "3", "D": "4", "E": "5" }
divide(subtract(72, reminder(multiply(98348, const_100), 72)), const_10)
multiply(n0,const_100)|reminder(#0,n2)|subtract(n2,#1)|divide(#2,const_10)
72 = 8 * 9 divisibility 0 f 8 last 3 place should be divisible by 8 lly divisibility of 9 sum of digit should be divisible by 9 840 divisible by 8 nd 36 divisible by 9 answer : d
general
math_qa__kIpn6REssfh5k2QQ
A reduction of 12% in the price of oil enables a house wife to obtain 6kgs more for Rs.1200, what is the reduced price for kg? Choose the correct choice from the following answers: A) 24 B) 27 C) 40 D) 28 E) 20
<gadget id="calculator">1_200 * 12</gadget> <output>14_400</output> <gadget id="calculator">14_400 / 100</gadget> <output>144</output> <gadget id="calculator">144 / 6</gadget> <output>24</output> <result>A</result>
A
24
A reduction of 12% in the price of oil enables a house wife to obtain 6kgs more for Rs.1200, what is the reduced price for kg?
{ "A": "24", "B": "27", "C": "40", "D": "28", "E": "20" }
divide(divide(multiply(1200, 12), const_100), 6)
multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)|
"1200 * ( 12 / 100 ) = 144 - - - - 6 ? - - - - 1 = > rs . 24 answer : a"
gain
math_qa__ORuNDcN5OFPv6ddh
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm? Choose the correct choice from the following choices A) 600 B) 881 C) 767 D) 261 E) 121
<gadget id="calculator">2 * 10</gadget> <output>20</output> <gadget id="calculator">20 * 2</gadget> <output>40</output> <gadget id="calculator">(40 * 30) / 2</gadget> <output>600</output> <result>A</result>
A
600
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
{ "A": "600", "B": "881", "C": "767", "D": "261", "E": "121" }
rhombus_area(multiply(multiply(const_2, const_10), const_2), 30)
multiply(const_10,const_2)|multiply(#0,const_2)|rhombus_area(n1,#1)
consider the rhombus abcd . let the diagonals intersect at e . since diagonals bisect at right angles in a rhombus . be 2 + ae 2 = ab 2 252 = 152 + ae 2 ae = √ ( 625 - 225 ) = √ 400 = 20 , ac = 20 + 20 = 40 cm . area of a rhombus = 1 / 2 * d 1 d 2 = 1 / 2 * 40 * 30 = 600 sq . cm . answer : a
geometry
math_qa__8LQuCHaAdxspme3v
The average of temperatures at noontime from Monday to Friday is 40; the lowest one is 30, what is the possible maximum range of the temperatures? Choose the most appropriate option A) 20 B) 25 C) 50 D) 45 E) 75
<gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">40 * 5</gadget> <output>200</output> <gadget id="calculator">30 * 4</gadget> <output>120</output> <gadget id="calculator">200 - 120</gadget> <output>80</output> <gadget id="calculator">80 - 30</gadget> <output>50</output> <result>C</result>
C
50
The average of temperatures at noontime from Monday to Friday is 40; the lowest one is 30, what is the possible maximum range of the temperatures?
{ "A": "20", "B": "25", "C": "50", "D": "45", "E": "75" }
subtract(subtract(multiply(40, add(const_2, const_3)), multiply(30, const_4)), 30)
add(const_2,const_3)|multiply(n1,const_4)|multiply(n0,#0)|subtract(#2,#1)|subtract(#3,n1)|
"average = 40 , sum of temperatures = 40 * 5 = 200 as the min temperature is 30 , max would be 200 - 4 * 30 = 80 - - > the range = 80 ( max ) - 30 ( min ) = 50 answer : c"
general
math_qa__XhUPGY7z72KfSZYa
In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area Choose the correct choice from the following choices: A) 600 m 2 B) 540 m 2 C) 680 m 2 D) 574 m 2 E) none of these
<gadget id="calculator">30 * 20</gadget> <output>600</output> <result>A</result>
A
600
In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area
{ "A": "600 m 2", "B": "540 m 2", "C": "680 m 2", "D": "574 m 2", "E": "none of these" }
multiply(30, 20)
multiply(n0,n1)
in a parallelogram . area = diagonal × length of perpendicular on it . = 30 × 20 = 600 m 2 answer a
geometry
math_qa__8I3G2A6BJeKKUtih
Find large number from below question The difference of two numbers is 1370. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choose the correct choice: A) 1245 B) 1345 C) 1455 D) 1577 E) 1641
<gadget id="calculator">1_370 - 15</gadget> <output>1_355</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">1_355 / 5</gadget> <output>271</output> <gadget id="calculator">271 * 6</gadget> <output>1_626</output> <result>E</result>
E
1,641
Find large number from below question The difference of two numbers is 1370. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
{ "A": "1245", "B": "1345", "C": "1455", "D": "1577", "E": "1641" }
multiply(divide(subtract(1370, 15), subtract(6, const_1)), 6)
subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)|
"let the smaller number be x . then larger number = ( x + 1370 ) . x + 1370 = 6 x + 15 5 x = 1355 x = 271 large number = 271 + 1370 = 1641 e"
general
math_qa__nPQKU97yyxSjYPZI
A, B and C started a partnership business by investing Rs.8000, Rs.4000, Rs.2000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit? Choose the correct choice from the following A) 70000 B) 60000 C) 80000 D) 90000 E) 252000
<gadget id="calculator">8_000 / 2_000</gadget> <output>4</output> <gadget id="calculator">4 * 36_000</gadget> <output>144_000</output> <gadget id="calculator">4_000 / 2_000</gadget> <output>2</output> <gadget id="calculator">2 * 36_000</gadget> <output>72_000</output> <gadget id="calculator">144_000 + 72_000</gadget> <output>216_000</output> <gadget id="calculator">216_000 + 36_000</gadget> <output>252_000</output> <result>E</result>
E
252,000
A, B and C started a partnership business by investing Rs.8000, Rs.4000, Rs.2000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
{ "A": "70000", "B": "60000", "C": "80000", "D": "90000", "E": "252000" }
add(add(multiply(divide(8000, 2000), 36000), multiply(divide(4000, 2000), 36000)), 36000)
divide(n0,n2)|divide(n1,n2)|multiply(n3,#0)|multiply(n3,#1)|add(#2,#3)|add(n3,#4)|
"a : b : c = 8000 : 4000 : 2000 = 4 : 2 : 1 let total profit = p then p ã — 1 / 7 = 36000 p = ( 36000 ã — 7 ) / 1 = 252000 answer is e ."
gain
math_qa__kVvR5MQXhtxTRWTw
Find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm? Choose the correct option A) 180 cm 2 B) 150 cm 2 C) 168 cm 2 D) 198 cm 2 E) 987 cm 2
<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">6 + 9</gadget> <output>15</output> <gadget id="calculator">(1/2) * 15</gadget> <output>15/2 = around 7.5</output> <gadget id="calculator">(15/2) * 24</gadget> <output>180</output> <result>A</result>
A
180
Find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm?
{ "A": "180 cm 2", "B": "150 cm 2", "C": "168 cm 2", "D": "198 cm 2", "E": "987 cm 2" }
multiply(multiply(divide(const_1, const_2), add(6, 9)), 24)
add(n1,n2)|divide(const_1,const_2)|multiply(#0,#1)|multiply(n0,#2)|
"1 / 2 * 24 ( 9 + 6 ) = 180 cm 2 answer : a"
geometry
math_qa__n03L8RBkOeEmIUwX
The average monthly salary of 18 employees in an organisation is Rs. 2000. If the manager's salary is added, then the average salary increases by Rs. 200. What is the manager's monthly salary? Pick one. A) rs . 5800 B) rs . 3618 C) rs . 3600 D) rs . 3619 E) rs . 3610
<gadget id="calculator">2_000 + 200</gadget> <output>2_200</output> <gadget id="calculator">18 + 1</gadget> <output>19</output> <gadget id="calculator">2_200 * 19</gadget> <output>41_800</output> <gadget id="calculator">2_000 * 18</gadget> <output>36_000</output> <gadget id="calculator">41_800 - 36_000</gadget> <output>5_800</output> <result>A</result>
A
5,800
The average monthly salary of 18 employees in an organisation is Rs. 2000. If the manager's salary is added, then the average salary increases by Rs. 200. What is the manager's monthly salary?
{ "A": "rs . 5800", "B": "rs . 3618", "C": "rs . 3600", "D": "rs . 3619", "E": "rs . 3610" }
subtract(multiply(add(2000, 200), add(18, const_1)), multiply(2000, 18))
add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|
"manager ' s monthly salary = rs . ( 2200 * 19 - 2000 * 18 ) = rs . 5800 answer : a"
general
math_qa__y05P3txWCt8X7wBd
What is the leastvalue of x. So that 23x57 is divisible by 3? Select the correct option. A) 2 B) 5 C) 1 D) 6 E) 7
<gadget id="calculator">23 / 10</gadget> <output>23/10 = around 2.3</output> <gadget id="calculator">floor(23/10)</gadget> <output>2</output> <gadget id="calculator">23 % 10</gadget> <output>3</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">57 / 10</gadget> <output>57/10 = around 5.7</output> <gadget id="calculator">floor(57/10)</gadget> <output>5</output> <gadget id="calculator">5 + 5</gadget> <output>10</output> <gadget id="calculator">57 % 10</gadget> <output>7</output> <gadget id="calculator">10 + 7</gadget> <output>17</output> <gadget id="calculator">17 % 3</gadget> <output>2</output> <gadget id="calculator">3 - 2</gadget> <output>1</output> <result>C</result>
C
1
What is the leastvalue of x. So that 23x57 is divisible by 3?
{ "A": "2", "B": "5", "C": "1", "D": "6", "E": "7" }
subtract(3, reminder(add(add(add(floor(divide(23, const_10)), reminder(23, const_10)), floor(divide(57, const_10))), reminder(57, const_10)), 3))
divide(n0,const_10)|divide(n1,const_10)|reminder(n0,const_10)|reminder(n1,const_10)|floor(#0)|floor(#1)|add(#4,#2)|add(#6,#5)|add(#7,#3)|reminder(#8,n2)|subtract(n2,#9)
the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 7 = 17 + x least value of x may be 1 therefore 17 + 1 = 18 is divisible by 3 . c
general
math_qa__rl1tCgiyz6GSS8Ks
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 4000. The difference between the profit shares of A and C is? Pick one: A) 621 B) 276 C) 236 D) 1600 E) 211
<gadget id="calculator">12_000 / 10_000</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">8_000 / 10_000</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">(6/5) - (4/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 4_000</gadget> <output>1_600</output> <result>D</result>
D
1,600
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 4000. The difference between the profit shares of A and C is?
{ "A": "621", "B": "276", "C": "236", "D": "1600", "E": "211" }
multiply(subtract(divide(12000, 10000), divide(8000, 10000)), 4000)
divide(n2,n1)|divide(n0,n1)|subtract(#0,#1)|multiply(n3,#2)|
"explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 4000 = > 5 parts out of 15 parts is rs . 4000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 4000 ) = rs . 1600 answer : d"
gain
math_qa__KVAm2uOp91wpfmJf
In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 320 vote’s majority. What is the total number of votes polled? Choices A) 750 B) 700 C) 800 D) 850 E) none of these
<gadget id="calculator">100 * 320</gadget> <output>32_000</output> <gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">70 - 30</gadget> <output>40</output> <gadget id="calculator">32_000 / 40</gadget> <output>800</output> <result>C</result>
C
800
In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 320 vote’s majority. What is the total number of votes polled?
{ "A": "750", "B": "700", "C": "800", "D": "850", "E": "none of these" }
divide(multiply(const_100, 320), subtract(70, subtract(const_100, 70)))
multiply(n1,const_100)|subtract(const_100,n0)|subtract(n0,#1)|divide(#0,#2)|
"explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 320 ( 40 * 8 = 320 ) 100 % - - - - - > 800 ( 100 * 8 = 800 ) answer : option c"
gain
math_qa__zC7BAdj90YEnxvZ9
A train 280 m long, running with a speed of 72 km / hr will pass a tree in Choices: A) 14 sec B) 15 sec C) 16 sec D) 20 sec E) none
<gadget id="calculator">72 * 1_000</gadget> <output>72_000</output> <gadget id="calculator">280 / 72_000</gadget> <output>7/1_800 = around 0.003889</output> <gadget id="calculator">(7/1_800) * 3_600</gadget> <output>14</output> <result>A</result>
A
14
A train 280 m long, running with a speed of 72 km / hr will pass a tree in
{ "A": "14 sec", "B": "15 sec", "C": "16 sec", "D": "20 sec", "E": "none" }
multiply(divide(280, multiply(72, const_1000)), const_3600)
multiply(n1,const_1000)|divide(n0,#0)|multiply(#1,const_3600)|
"sol . speed = ( 72 x 5 / 18 ) m / sec . = 20 m / sec . time taken = ( 280 x 1 / 20 ) sec = 14 sec answer a"
physics
math_qa__hGnDLMMtcC9Ohqp8
A man swims downstream 24 km and upstream 12 km taking 6 hours each time, what is the speed of the man in still water? Options A) 5 B) 8 C) 10 D) 4 E) 3
<gadget id="calculator">12 / 6</gadget> <output>2</output> <gadget id="calculator">24 / 6</gadget> <output>4</output> <gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <result>E</result>
E
3
A man swims downstream 24 km and upstream 12 km taking 6 hours each time, what is the speed of the man in still water?
{ "A": "5", "B": "8", "C": "10", "D": "4", "E": "3" }
divide(add(divide(12, 6), divide(24, 6)), const_2)
divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)|
"24 - - - 6 ds = 4 ? - - - - 1 12 - - - - 6 us = 2 ? - - - - 1 m = ? m = ( 4 + 2 ) / 2 = 3 answer : e"
physics
math_qa__3RhXTPH6m3z3PJCM
S is a set of 45 consecutive multiples of 5. If the smallest number in S is 55, then the greatest number in S is Choose the correct choice from the following answers: A) 198 B) 275 C) 299 D) 402 E) 205
<gadget id="calculator">45 - 1</gadget> <output>44</output> <gadget id="calculator">44 * 5</gadget> <output>220</output> <gadget id="calculator">55 + 220</gadget> <output>275</output> <result>B</result>
B
275
S is a set of 45 consecutive multiples of 5. If the smallest number in S is 55, then the greatest number in S is
{ "A": "198", "B": "275", "C": "299", "D": "402", "E": "205" }
add(55, multiply(subtract(45, const_1), 5))
subtract(n0,const_1)|multiply(n1,#0)|add(n2,#1)|
"last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 45 consecutive multiples of 5 . if the smallest number in s is 55 , then the greatest number in s is first term = 55 ; total terms = 45 ; difference = 5 55 + ( 44 ) 5 = 275 ans b"
general
math_qa__lLd8fn1oZph9Bzjs
A can fill tank in 9 minutes, B can empty the tank in 18 minutes.. In what time the tank be filled, if both pipes work simultaneously? Choose the correct choice: A) 14 minutes B) 15 minutes C) 16 minutes D) 17 minutes E) 18 minutes
<gadget id="calculator">1 / 9</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">1 / 18</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">(1/9) - (1/18)</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">1 / (1/18)</gadget> <output>18</output> <result>E</result>
E
18
A can fill tank in 9 minutes, B can empty the tank in 18 minutes.. In what time the tank be filled, if both pipes work simultaneously?
{ "A": "14 minutes", "B": "15 minutes", "C": "16 minutes", "D": "17 minutes", "E": "18 minutes" }
divide(const_1, subtract(divide(const_1, 9), divide(const_1, 18)))
divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)
bigger no = 18 , ratio = 9 : 18 = 1 : 2 time taken to fill the tank = 18 / ( 2 - 1 ) = 18 minutes answer : e
physics
math_qa__URRJHaT1eZsD520m
If you spend 1/4 of your salary during the first week of the month and 20% of it during each of the coming 3 weeks, what part(fraction) of your salary will leave unspent at the end of the month? Choose one. A) 2 / 20 B) 3 / 20 C) 4 / 20 D) 5 / 20 E) none
<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 3</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(3/5) + (1/4)</gadget> <output>17/20 = around 0.85</output> <gadget id="calculator">1 - (17/20)</gadget> <output>3/20 = around 0.15</output> <result>B</result>
B
0.15
If you spend 1/4 of your salary during the first week of the month and 20% of it during each of the coming 3 weeks, what part(fraction) of your salary will leave unspent at the end of the month?
{ "A": "2 / 20", "B": "3 / 20", "C": "4 / 20", "D": "5 / 20", "E": "none" }
subtract(1, add(multiply(divide(20, const_100), 3), divide(1, 4)))
divide(n0,n1)|divide(n2,const_100)|multiply(n3,#1)|add(#0,#2)|subtract(n0,#3)
solution : 1 / 4 + 3 ( 20 / 100 ) = 1 / 4 + 3 / 5 = 5 + 12 / 20 = 17 / 20 the sallary that will be spent = 17 / 20 unspend will be = 1 − 17 / 20 = 20 − 17 / 20 = 3 / 20 answer b
gain
math_qa__G8sulO1NGJC4gPdO
A bag contains 6 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is Choose the correct choice from the following choices. A) 8 / 15 B) 2 / 5 C) 3 / 5 D) 11 / 15 E) 43 / 91
<gadget id="calculator">6 + 8</gadget> <output>14</output> <gadget id="calculator">8 / 14</gadget> <output>4/7 = around 0.571429</output> <gadget id="calculator">8 - 1</gadget> <output>7</output> <gadget id="calculator">14 - 1</gadget> <output>13</output> <gadget id="calculator">7 / 13</gadget> <output>7/13 = around 0.538462</output> <gadget id="calculator">(4/7) * (7/13)</gadget> <output>4/13 = around 0.307692</output> <gadget id="calculator">6 / 14</gadget> <output>3/7 = around 0.428571</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">5 / 13</gadget> <output>5/13 = around 0.384615</output> <gadget id="calculator">(3/7) * (5/13)</gadget> <output>15/91 = around 0.164835</output> <gadget id="calculator">(4/13) + (15/91)</gadget> <output>43/91 = around 0.472527</output> <result>E</result>
E
0.472527
A bag contains 6 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
{ "A": "8 / 15", "B": "2 / 5", "C": "3 / 5", "D": "11 / 15", "E": "43 / 91" }
add(multiply(divide(8, add(6, 8)), divide(subtract(8, const_1), subtract(add(6, 8), const_1))), multiply(divide(6, add(6, 8)), divide(subtract(6, const_1), subtract(add(6, 8), const_1))))
add(n0,n1)|subtract(n1,const_1)|subtract(n0,const_1)|divide(n1,#0)|divide(n0,#0)|subtract(#0,const_1)|divide(#1,#5)|divide(#2,#5)|multiply(#3,#6)|multiply(#4,#7)|add(#8,#9)|
"drawing two balls of same color from six green balls can be done in 6 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 6 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 43 / 91 answer : e"
other
math_qa__x4KVM80bLujyrj7B
A man’s current age is (2/5) of the age of his father. After 14 years, he will be (1/2) of the age of his father. What is the age of father at now? Choose the correct choice from the following: A) 40 B) 45 C) 38 D) 50 E) 70
<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">14 * (1/2)</gadget> <output>7</output> <gadget id="calculator">14 - 7</gadget> <output>7</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(1/2) - (2/5)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">7 / (1/10)</gadget> <output>70</output> <result>E</result>
E
70
A man’s current age is (2/5) of the age of his father. After 14 years, he will be (1/2) of the age of his father. What is the age of father at now?
{ "A": "40", "B": "45", "C": "38", "D": "50", "E": "70" }
divide(subtract(14, multiply(14, divide(1, 2))), subtract(divide(1, 2), divide(2, 5)))
divide(n3,n0)|divide(n0,n1)|multiply(n2,#0)|subtract(#0,#1)|subtract(n2,#2)|divide(#4,#3)
let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 14 ] = ( 1 / 2 ) ( a + 14 ) 2 ( 2 a + 70 ) = 5 ( a + 14 ) a = 70 e
general
math_qa__PfHG3dQM77yhO7F6
At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 5 charts have been brought to the meeting, how many people are present? Select. A) 5 B) 7 C) 8 D) 9 E) 10
<gadget id="calculator">5 + 10</gadget> <output>15</output> <gadget id="calculator">2 + 1</gadget> <output>3</output> <gadget id="calculator">15 / 3</gadget> <output>5</output> <result>A</result>
A
5
At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 5 charts have been brought to the meeting, how many people are present?
{ "A": "5", "B": "7", "C": "8", "D": "9", "E": "10" }
divide(add(5, 10), add(2, 1))
add(n4,n5)|add(n0,n1)|divide(#0,#1)|
"say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 5 add both : 3 a + 3 b = 15 so a + b = 5 total number of people = 5 a"
general
math_qa__qQh2A46r9Mf8RidV
A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17. What was the number erased? Choose the correct choice from the following answers. A) seven 7 B) 8 C) 9 D) 15 E) 17
<gadget id="calculator">7 / 17</gadget> <output>7/17 = around 0.411765</output> <gadget id="calculator">35 + (7/17)</gadget> <output>602/17 = around 35.411765</output> <gadget id="calculator">(602/17) * 2</gadget> <output>1_204/17 = around 70.823529</output> <gadget id="calculator">floor(1_204/17)</gadget> <output>70</output> <gadget id="calculator">70 / 2</gadget> <output>35</output> <gadget id="calculator">70 - 1</gadget> <output>69</output> <gadget id="calculator">35 * 69</gadget> <output>2_415</output> <gadget id="calculator">69 - 1</gadget> <output>68</output> <gadget id="calculator">(602/17) * 68</gadget> <output>2_408</output> <gadget id="calculator">2_415 - 2_408</gadget> <output>7</output> <result>A</result>
A
7
A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17. What was the number erased?
{ "A": "seven 7", "B": "8", "C": "9", "D": "15", "E": "17" }
subtract(multiply(divide(floor(multiply(add(35, divide(7, 17)), const_2)), const_2), subtract(floor(multiply(add(35, divide(7, 17)), const_2)), 1)), multiply(add(35, divide(7, 17)), subtract(subtract(floor(multiply(add(35, divide(7, 17)), const_2)), 1), 1)))
divide(n2,n3)|add(n1,#0)|multiply(#1,const_2)|floor(#2)|divide(#3,const_2)|subtract(#3,n0)|multiply(#4,#5)|subtract(#5,n0)|multiply(#1,#7)|subtract(#6,#8)|
"2 ) the average of the new group of numbers is 35 7 / 17 . the denominator of that fraction tells us that the total number of terms in the new list must be a multiple of 17 : 17 , 34 , 51 , 68 , 85 , etc . 3 ) since we ' re removing 1 number from a list of consecutive positive integers , we could quickly limit down the possible number of terms in the original list : if new = 17 , old = 18 , but the numbers from 1 to 18 would not have an average in the mid - 30 s ( it would be much smaller ) . eliminate this option . if new = 34 , old = 35 , but we run into the same problem . the average wo n ' t match here either . eliminate this option . if new = 51 , old = 52 , same problem here . eliminate this option . if new = 68 , old = 69 . . . . here we have a group of numbers that might just be what we ' re looking for . in theold group , the average is themiddle term = 35 , which is really close to the new average once we remove a number . now , we just have to figure out which of the 5 answers was removed ( and that changed the new average to 35 7 / 17 ) . there are a couple of ways to do this math , but i ' m going to use the answers to save myself some steps : sum of 1 to 69 , inclusive = 69 ( 35 ) = 2415 remove answer b . . . . 2415 - 8 = 2407 new average = 2407 / 68 = 35 27 / 68 now , we can compare 27 / 68 to 7 / 17 27 / 68 and 28 / 68 this is really close , but is not the answer . eliminate b . the answer is either a or c . since 28 / 68 is a bigger fraction than 27 / 68 , we need the sum ( of the 68 integers ) to be bigger . . . which means we need to remove a smaller number . final answer : a"
general
math_qa__mfRM6Fk6nSG9FZh2
manoj borrowed rs . 3900 from anwar at 6 % p . a . simple interest for 3 years . he then added some more money to the borrowed sum and lent it to ramu for the same time at 9 % p . a . simple interest . if manoj gains rs . 824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction , then what is the sum lent by him to ramu ? Select: A) 22877 B) 5655 C) 2778 D) 6787 E) 1771
<gadget id="calculator">9 / 100</gadget> <output>9/100 = around 0.09</output> <gadget id="calculator">(9/100) * 3</gadget> <output>27/100 = around 0.27</output> <gadget id="calculator">3_900 * (27/100)</gadget> <output>1_053</output> <gadget id="calculator">6 / 100</gadget> <output>3/50 = around 0.06</output> <gadget id="calculator">(3/50) * 3</gadget> <output>9/50 = around 0.18</output> <gadget id="calculator">3_900 * (9/50)</gadget> <output>702</output> <gadget id="calculator">1_053 - 702</gadget> <output>351</output> <gadget id="calculator">824.85 - 351</gadget> <output>473.85</output> <gadget id="calculator">473.85 / (27/100)</gadget> <output>1_755</output> <gadget id="calculator">3_900 + 1_755</gadget> <output>5_655</output> <result>B</result>
B
5,655
manoj borrowed rs . 3900 from anwar at 6 % p . a . simple interest for 3 years . he then added some more money to the borrowed sum and lent it to ramu for the same time at 9 % p . a . simple interest . if manoj gains rs . 824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction , then what is the sum lent by him to ramu ?
{ "A": "22877", "B": "5655", "C": "2778", "D": "6787", "E": "1771" }
add(3900, divide(subtract(824.85, subtract(multiply(3900, multiply(divide(9, const_100), const_3)), multiply(3900, multiply(divide(6, const_100), const_3)))), multiply(divide(9, const_100), const_3)))
divide(n3,const_100)|divide(n1,const_100)|multiply(#0,const_3)|multiply(#1,const_3)|multiply(n0,#2)|multiply(n0,#3)|subtract(#4,#5)|subtract(n4,#6)|divide(#7,#2)|add(n0,#8)
let the sum lent by manoj to ramu be rs . p . amount gained by manoj = p . 3.9 / 100 = 3900 . 3.6 / 100 = rs . 824.85 27 p = 70200 = 82485 p = ( 82485 + 70200 ) / 27 = 3055 + 2600 = rs . 5655 answer : b
gain
math_qa__mWUqNzAkoqsKkWdT
The arithmetic mean and standard deviation of a certain normal distribution are 10.5 and 1, respectively. What value is exactly 2 standard deviations less than the mean? Choose the correct choice from the following answers: A) 6 B) 8.5 C) 11.5 D) 12 E) 12.5
<gadget id="calculator">2 * 1</gadget> <output>2</output> <gadget id="calculator">10.5 - 2</gadget> <output>8.5</output> <result>B</result>
B
8.5
The arithmetic mean and standard deviation of a certain normal distribution are 10.5 and 1, respectively. What value is exactly 2 standard deviations less than the mean?
{ "A": "6", "B": "8.5", "C": "11.5", "D": "12", "E": "12.5" }
subtract(10.5, multiply(2, 1))
multiply(n1,n2)|subtract(n0,#0)|
"mean = 10.5 two standard deviations is 1 + 1 = 2 there could be two calues for this . mean + two standard deviations = 12.5 mean - two standard deviations = 8.5 answer choice has 8.5 and so b is the answer ."
general
math_qa__iZjWC69tuANagctY
What is the measure of the angle E made by the diagonals of the any adjacent sides of a cube. Choose the correct choice A) 30 B) 45 C) 60 D) 75 E) 90
<gadget id="calculator">180 / 3</gadget> <output>60</output> <result>C</result>
C
60
What is the measure of the angle E made by the diagonals of the any adjacent sides of a cube.
{ "A": "30", "B": "45", "C": "60", "D": "75", "E": "90" }
divide(const_180, const_3)
divide(const_180,const_3)
c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . . c
geometry
math_qa__JlCdiGhs2x0vFsof
If Albert’s monthly earnings rise by 20%, he would earn $560. If, instead, his earnings rise by only 21%, how much (in $) would he earn this month? Answers A) 643 B) 652 C) 660 D) 564 E) 693
<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 + (1/5)</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">560 / (6/5)</gadget> <output>1_400/3 = around 466.666667</output> <gadget id="calculator">21 / 100</gadget> <output>21/100 = around 0.21</output> <gadget id="calculator">1 + (21/100)</gadget> <output>121/100 = around 1.21</output> <gadget id="calculator">(1_400/3) * (121/100)</gadget> <output>1_694/3 = around 564.666667</output> <result>D</result>
D
564
If Albert’s monthly earnings rise by 20%, he would earn $560. If, instead, his earnings rise by only 21%, how much (in $) would he earn this month?
{ "A": "643", "B": "652", "C": "660", "D": "564", "E": "693" }
multiply(divide(560, add(const_1, divide(20, const_100))), add(const_1, divide(21, const_100)))
divide(n2,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|divide(n1,#3)|multiply(#2,#4)|
"= 560 / 1.2 ∗ 1.21 = 564 = 564 answer is d"
gain
math_qa__VyjOQpds6zWjUniz
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 30%. Their gross income from sales for one month increases by what percent? Choose the correct choice A) 9 % B) 11 % C) 13 % D) 15 % E) 17 %
<gadget id="calculator">30 - 10</gadget> <output>20</output> <gadget id="calculator">30 / 10</gadget> <output>3</output> <gadget id="calculator">20 - 3</gadget> <output>17</output> <result>E</result>
E
17
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 30%. Their gross income from sales for one month increases by what percent?
{ "A": "9 %", "B": "11 %", "C": "13 %", "D": "15 %", "E": "17 %" }
subtract(subtract(30, 10), divide(30, 10))
divide(n1,n0)|subtract(n1,n0)|subtract(#1,#0)
let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.3 x = 1.17 * ( p * x ) , an increase of 17 % . the answer is e .
gain
math_qa__GnkTSRiLYh9OV9pO
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is? Options: A) 52 : 56 B) 52 : 53 C) 52 : 50 D) 22 : 56 E) 52 : 51
<gadget id="calculator">100 + 4</gadget> <output>104</output> <gadget id="calculator">100 + 6</gadget> <output>106</output> <gadget id="calculator">104 / 106</gadget> <output>52/53 = around 0.981132</output> <result>B</result>
B
0.981132
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is?
{ "A": "52 : 56", "B": "52 : 53", "C": "52 : 50", "D": "22 : 56", "E": "52 : 51" }
divide(add(const_100, 4), add(const_100, 6))
add(n0,const_100)|add(n1,const_100)|divide(#0,#1)|
"let c . p . of the article be rs . x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 answer : b"
gain
math_qa__lvo394QZrXxpDmNY
Lovely shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys? Choose the correct choice from the following choices: A) 0.8 B) 0.75 C) 8 / 9 D) 5 / 7 E) 6 / 8
<gadget id="calculator">21 - 12</gadget> <output>9</output> <gadget id="calculator">9 / 12</gadget> <output>3/4 = around 0.75</output> <result>D</result>
D
0.714286
Lovely shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
{ "A": "0.8", "B": "0.75", "C": "8 / 9", "D": "5 / 7", "E": "6 / 8" }
divide(subtract(21, 12), 12)
subtract(n4,n1)|divide(#0,n1)
the approach of plugging in the numbers is a fine approach . but , in this case , the answer was the first option and thus , by plugging in a number in the ration given , we arrived at the answer quickly ! however , what if the correct ratio was option d or c ? in any case , the algebraic solution is n ' t that complex if you realize a key concept : the number 7 can be factored out of the second equation ! here ' s the working : lovely shop runs a sale on goldfish and platys . 13 x + 12 y = 5.60 < < < < < equation 1 14 x + 21 y = 8.05 < < < < < equation 2 2 x + 3 y = 1.15 [ factor out 7 from equation 2 ] < < < < < equation 3 8 x + 12 y = 4.6 [ multiply equation 3 with 4 ] 5 x = 1.0 [ equation 1 - equation 2 ] x = 0.2 3 y = 1.15 - 0.4 = 0.75 [ substitute for x in equation 1 ] y = 0.25 x / y = 0.2 / 0.25 = 20 / 25 = 4 / 5 = 0.8 [ answer a ] the whole thing must have taken me about 45 s : d
other
math_qa__Ou7dtx8H4dWGeYUe
A football team lost 5 yards and then gained 9. What is the team's progress? Choose the correct option: A) 1 B) 3 C) 2 D) 4 E) 5
<gadget id="calculator">9 - 5</gadget> <output>4</output> <result>D</result>
D
4
A football team lost 5 yards and then gained 9. What is the team's progress?
{ "A": "1", "B": "3", "C": "2", "D": "4", "E": "5" }
subtract(9, 5)
subtract(n1,n0)|
"for lost , use negative . for gain , use positive . progress = - 5 + 9 = 4 yards correct answer is d ) 4"
gain
math_qa__Mwr6Ws81rxqFGeZk
in expressing a length 810472 km as nearly as possible with 3 significant digits , find the percentage error . Options: A) 0.034 B) 0.024 C) 0.352 D) 0.063 E) 0.026
<gadget id="calculator">3 * 10</gadget> <output>30</output> <gadget id="calculator">30 + 4</gadget> <output>34</output> <gadget id="calculator">34 / 100</gadget> <output>17/50 = around 0.34</output> <gadget id="calculator">(17/50) / 10</gadget> <output>17/500 = around 0.034</output> <result>A</result>
A
0.034
in expressing a length 810472 km as nearly as possible with 3 significant digits , find the percentage error .
{ "A": "0.034", "B": "0.024", "C": "0.352", "D": "0.063", "E": "0.026" }
divide(divide(add(multiply(3, const_10), const_4), const_100), const_10)
multiply(n1,const_10)|add(#0,const_4)|divide(#1,const_100)|divide(#2,const_10)
error = ( 81.5 – 81.472 ) km = 0.028 . required percentage = [ ( 0.028 / 81.472 ) * 100 ] % = 0.034 % . answer a .
general
math_qa__aqSUvgqrKRmSqO8t
There are 5 more women than there are men on a local co-ed softball team. If there are a total of 15 players on the team, what is the ratio of men to women? Choices: A) 10 / 16 B) 6 / 16 C) 5 / 10 D) 6 / 10 E) 4 / 10
<gadget id="calculator">15 - 5</gadget> <output>10</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 + 5</gadget> <output>10</output> <gadget id="calculator">5 / 10</gadget> <output>1/2 = around 0.5</output> <result>C</result>
C
0.5
There are 5 more women than there are men on a local co-ed softball team. If there are a total of 15 players on the team, what is the ratio of men to women?
{ "A": "10 / 16", "B": "6 / 16", "C": "5 / 10", "D": "6 / 10", "E": "4 / 10" }
divide(divide(subtract(15, 5), add(const_1, const_1)), add(divide(subtract(15, 5), add(const_1, const_1)), 5))
add(const_1,const_1)|subtract(n1,n0)|divide(#1,#0)|add(n0,#2)|divide(#2,#3)
w = m + 5 w + m = 15 m + 5 + m = 15 2 m = 10 m = 5 w = 10 ratio : 5 : 10 ans : c
general
math_qa__GRhahEXuftBaJ7Hc
A can do a work in 3days. B can do in 6days. If both A&B are working together in how many days they can finish the work? Select the correct option: A) 1 B) 3 C) 2 D) 4 E) 5
<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/3) + (1/6)</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 / (1/2)</gadget> <output>2</output> <result>C</result>
C
2
A can do a work in 3days. B can do in 6days. If both A&B are working together in how many days they can finish the work?
{ "A": "1", "B": "3", "C": "2", "D": "4", "E": "5" }
divide(const_1, add(divide(const_1, 3), divide(const_1, 6)))
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)|
"1 day work of a = 1 / 3 1 day work of b = 1 / 6 1 day work of a & b = 1 / 3 + 1 / 6 = 1 / 2 a & b finish the work in 2 days answer is c"
physics
math_qa__vl5a5ISbG8M5Ic2a
The population of a village is 6000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years? Answers: A) 5000 B) 4860 C) 5400 D) 4800 E) 5120
<gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">90 / 100</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">(9/10) ** 2</gadget> <output>81/100 = around 0.81</output> <gadget id="calculator">6_000 * (81/100)</gadget> <output>4_860</output> <result>B</result>
B
4,860
The population of a village is 6000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
{ "A": "5000", "B": "4860", "C": "5400", "D": "4800", "E": "5120" }
multiply(6000, power(divide(subtract(const_100, 10), const_100), 2))
subtract(const_100,n1)|divide(#0,const_100)|power(#1,n2)|multiply(n0,#2)
formula : ( after = 100 denominator ago = 100 numerator ) 6000 ã — 90 / 100 ã — 90 / 100 = 4860 b
gain
math_qa__28IcbIH4EALiGYGZ
Excluding the stoppages, the speed of a bus is 64 km/hr and including the stoppages the speed of the bus is 48km/hr. For how many minutes does the bus stop per hour? Choose the correct choice from the following. A) 15 min B) 10 min C) 12 min D) 20 min E) 18 min
<gadget id="calculator">48 / 64</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) * 60</gadget> <output>45</output> <gadget id="calculator">60 - 45</gadget> <output>15</output> <result>A</result>
A
15
Excluding the stoppages, the speed of a bus is 64 km/hr and including the stoppages the speed of the bus is 48km/hr. For how many minutes does the bus stop per hour?
{ "A": "15 min", "B": "10 min", "C": "12 min", "D": "20 min", "E": "18 min" }
subtract(const_60, multiply(divide(48, 64), const_60))
divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)|
"speed of the bus without stoppage = 64 km / hr speed of the bus with stoppage = 48 km / hr difference in speed = 16 km / hr so , the time taken in the stoppages = time taken to cover 16 km = ( 16 / 64 ) hr = 1 / 4 hr = 15 min answer : a"
physics
math_qa__T59A5ZMvF0scvFlR
an analysis of the monthly incentives received by 5 salesmen : the mean and median of the incentives is $ 7000 . the only mode among the observations is $ 12000 . incentives paid to each salesman were in full thousands . what is the difference z between the highest and the lowest incentive received by the 5 salesmen in the month ? Choose the correct choice from the following answers A) $ 4000 B) $ 5000 C) $ 9000 D) $ 11000 E) $ 13000
<gadget id="calculator">12_000 - 1_000</gadget> <output>11_000</output> <result>D</result>
D
11,000
an analysis of the monthly incentives received by 5 salesmen : the mean and median of the incentives is $ 7000 . the only mode among the observations is $ 12000 . incentives paid to each salesman were in full thousands . what is the difference z between the highest and the lowest incentive received by the 5 salesmen in the month ?
{ "A": "$ 4000", "B": "$ 5000", "C": "$ 9000", "D": "$ 11000", "E": "$ 13000" }
subtract(12000, const_1000)
subtract(n2,const_1000)
break down the question in to steps : step # 1 : incentives received by 5 salesmen - - > abcde step # 2 : mean and median of the incentives is $ 7000 : via number properties - - > total incentives = 7000 * 5 = 35000 ab 7000 de step # 3 : only mode among the observations is $ 12000 : mode is the value that appears most often in a set of data . therefore 12000 must occur more then once and since 12000 is larger than the mean ( 7000 ) the most it can occur is twice in our list . if we place the numbers in ascending order we haveab 70001200012000 step # 4 : what is the difference z between the highest and the lowest incentive : - the total paid has to equal mean * # of numbers = 7000 * 5 = 35 000 . - the three values we have so far ( 12000 12000 and 7000 ) equal 31000 . - therefore the first two numbers ( ab ) must equal 4000 - there is only one mode which is 12000 , therefore 4000 must be equal to a set of two numbers that are not the and a < b if a = 1000 b = 3000 - - > difference between the highest and the lowest incentive = 12000 - 1000 = 11000 no other options for a or b to fit the criteria final list : 1000300070001200012000 answer d
general
math_qa__ZkvY3hgpx8Knl0rd
If the numbers 1 to 97 are written on 97 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite? Choose the correct option A) 1 / 50 B) 1 / 25 C) 1 / 97 D) 1 E) 2
<gadget id="calculator">1 / 97</gadget> <output>1/97 = around 0.010309</output> <result>C</result>
C
0.010309
If the numbers 1 to 97 are written on 97 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
{ "A": "1 / 50", "B": "1 / 25", "C": "1 / 97", "D": "1", "E": "2" }
divide(1, 97)
divide(n0,n1)|
"there are 25 primes , 71 composite numbers from 1 to 97 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 97 . answer : c"
other
math_qa__op7w5bPvv2UoAsNY
3.5 can be expressed in terms of percentage as? Choices: A) 0.35 % B) 3.5 % C) 35 % D) 350 % E) 0.0035 %
<gadget id="calculator">3.5 * 100</gadget> <output>350</output> <result>D</result>
D
350
3.5 can be expressed in terms of percentage as?
{ "A": "0.35 %", "B": "3.5 %", "C": "35 %", "D": "350 %", "E": "0.0035 %" }
multiply(3.5, const_100)
multiply(n0,const_100)|
"answer : option d 3.5 = 35 / 10 = ( 35 / 10 * 100 ) = 350 %"
general
math_qa__hYBVDBY28NcAHoCg
A rectangular photograph is surrounded by a border that is 2 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 94) square inches. What is the perimeter of the photograph, in inches? Choose the correct choice from the following options: A) 34 B) 36 C) 23 D) 40 E) 42
<gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">8 ** 2</gadget> <output>64</output> <gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">64 - 16</gadget> <output>48</output> <gadget id="calculator">94 - 48</gadget> <output>46</output> <gadget id="calculator">46 / 2</gadget> <output>23</output> <result>C</result>
C
23
A rectangular photograph is surrounded by a border that is 2 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 94) square inches. What is the perimeter of the photograph, in inches?
{ "A": "34", "B": "36", "C": "23", "D": "40", "E": "42" }
divide(subtract(94, subtract(power(multiply(4, const_2), const_2), power(multiply(2, const_2), const_2))), const_2)
multiply(n1,const_2)|multiply(n0,const_2)|power(#0,const_2)|power(#1,const_2)|subtract(#2,#3)|subtract(n2,#4)|divide(#5,const_2)|
"let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 4 ) ( b + 4 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 94 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 94 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 4 ) ( b + 4 ) = ( l + 8 ) ( b + 8 ) - 94 lb + 4 l + 4 b + 16 = lb + 8 l + 8 b + 64 - 94 simplify 4 l + 4 b = 46 - - - - - - > 2 ( l + b ) = 23 ( check eq ( 1 ) ) answer is c"
geometry
math_qa__d7JKmNaJSq5ajTzu
An inspector rejects 15% of the meters as defective. How many will he examine to reject 10? Choose the correct choice from the following: A) 100 B) 66.7 C) 250 D) 200 E) 160
<gadget id="calculator">10 * 100</gadget> <output>1_000</output> <gadget id="calculator">1_000 / 15</gadget> <output>200/3 = around 66.666667</output> <result>B</result>
B
66.7
An inspector rejects 15% of the meters as defective. How many will he examine to reject 10?
{ "A": "100", "B": "66.7", "C": "250", "D": "200", "E": "160" }
divide(multiply(10, const_100), 15)
multiply(n1,const_100)|divide(#0,n0)|
"then , 10 % of x = 15 ( 15 / 100 ) x = 10 x = ( 10 * 100 * ) / 15 = 66.7 answer is b"
gain
math_qa__eG1YmvHHggKmVtJG
The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 35 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average? Choose the correct answer: A) 16 B) 17 C) 19 D) 22 E) 26
<gadget id="calculator">16 * 10</gadget> <output>160</output> <gadget id="calculator">160 - 25</gadget> <output>135</output> <gadget id="calculator">135 + 35</gadget> <output>170</output> <gadget id="calculator">170 / 10</gadget> <output>17</output> <result>B</result>
B
17
The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 35 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
{ "A": "16", "B": "17", "C": "19", "D": "22", "E": "26" }
divide(add(subtract(multiply(16, 10), 25), 35), 10)
multiply(n0,n1)|subtract(#0,n3)|add(n2,#1)|divide(#2,n0)
the total sum of the numbers should be increased by 10 . then the average will increase by 10 / 10 = 1 . the correct average is 17 . the answer is b .
general
math_qa__PkoauHUM8fwszvh6
There are 600 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%? Select the correct option A) 100 B) 200 C) 250 D) 300 E) 400
<gadget id="calculator">99 / 100</gadget> <output>99/100 = around 0.99</output> <gadget id="calculator">600 * (99/100)</gadget> <output>594</output> <gadget id="calculator">98 / 100</gadget> <output>49/50 = around 0.98</output> <gadget id="calculator">600 * (49/50)</gadget> <output>588</output> <gadget id="calculator">594 - 588</gadget> <output>6</output> <gadget id="calculator">1 - (49/50)</gadget> <output>1/50 = around 0.02</output> <gadget id="calculator">6 / (1/50)</gadget> <output>300</output> <result>D</result>
D
300
There are 600 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
{ "A": "100", "B": "200", "C": "250", "D": "300", "E": "400" }
divide(subtract(multiply(600, divide(99, const_100)), multiply(600, divide(98, const_100))), subtract(const_1, divide(98, const_100)))
divide(n1,const_100)|divide(n2,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(const_1,#1)|subtract(#2,#3)|divide(#5,#4)|
"there are 594 managers and 6 others . the 6 others would compose 2 % of the total number of people if there were 300 people in the room . thus 300 managers must leave . the answer is d ."
gain
math_qa__oWlWt5kQmcwHjXYY
When 3 fair coins are tossed together, what is the probability of getting 2 tails? Choose the correct choice from the following choices: A) 1 / 2 B) 1 / 3 C) 1 / 4 D) 3 / 4 E) 2 / 3
<gadget id="calculator">2 ** 3</gadget> <output>8</output> <gadget id="calculator">4 / 8</gadget> <output>1/2 = around 0.5</output> <result>A</result>
A
0.5
When 3 fair coins are tossed together, what is the probability of getting 2 tails?
{ "A": "1 / 2", "B": "1 / 3", "C": "1 / 4", "D": "3 / 4", "E": "2 / 3" }
divide(const_4, power(const_2, 3))
power(const_2,n0)|divide(const_4,#0)
we can get 2 tails in 3 c 2 ways . we can get 3 tails in exactly one way . also , there are a total out 8 possible outcomes . thus , the required probability = ( 3 + 1 ) / 8 = 1 / 2 answer : a
probability
math_qa__4Q16lu33VonogWBq
The ratio of two cow A,B milk is 5:3.3kg milk of cow A get distributed and 1kg milk of cow B get distributed.now,8kg milk of cow B left.Now what is the ratio of cow A and B left milk? Choose the correct option: A) 3 : 2 B) 4 : 3 C) 5 : 4 D) 6 : 5 E) 5 : 3
<gadget id="calculator">5 / 3.3</gadget> <output>1.515152</output> <gadget id="calculator">1.515152 * 8</gadget> <output>12.121216</output> <gadget id="calculator">12.121216 / 8</gadget> <output>1.515152</output> <result>A</result>
A
1.5
The ratio of two cow A,B milk is 5:3.3kg milk of cow A get distributed and 1kg milk of cow B get distributed.now,8kg milk of cow B left.Now what is the ratio of cow A and B left milk?
{ "A": "3 : 2", "B": "4 : 3", "C": "5 : 4", "D": "6 : 5", "E": "5 : 3" }
divide(multiply(divide(5, 3.3), 8), 8)
divide(n0,n1)|multiply(n3,#0)|divide(#1,n3)
left milk of cow b = 3 x - 1 = 8,3 x = 9 , x = 3 . left milk of cow a = 15 - 3 = 12 12 / 8 = 3 : 2 . answer a
other
math_qa__bsNKLEEdZzawweF7
A tank is filled by 3 pipes A,B,C in 8 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ? Choose the correct answer A) 25 hr B) 35 hr C) 56 hr D) 20 hr E) 50 hr
<gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">6 + 1</gadget> <output>7</output> <gadget id="calculator">7 * 8</gadget> <output>56</output> <result>C</result>
C
56
A tank is filled by 3 pipes A,B,C in 8 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
{ "A": "25 hr", "B": "35 hr", "C": "56 hr", "D": "20 hr", "E": "50 hr" }
multiply(add(add(multiply(const_2, const_2), const_2), const_1), 8)
multiply(const_2,const_2)|add(#0,const_2)|add(#1,const_1)|multiply(n1,#2)|
"suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 8 7 / x = 1 / 8 x = 56 hours answer is c"
physics
math_qa__u8KqT9nxH6GDBUMc
A car travels at a speed of 75 miles per hour. How far will it travel in 5 hours? Choose the correct choice from the following. A) 425 miles B) 625 miles C) 325 miles D) 375 miles E) 625 miles
<gadget id="calculator">75 * 5</gadget> <output>375</output> <result>D</result>
D
375
A car travels at a speed of 75 miles per hour. How far will it travel in 5 hours?
{ "A": "425 miles", "B": "625 miles", "C": "325 miles", "D": "375 miles", "E": "625 miles" }
multiply(75, 5)
multiply(n0,n1)|
"during each hour , the car travels 65 miles . for 5 hours it will travel 75 + 75 + 75 + 75 + 75 = 5 * 65 = 375 miles correct answer d"
physics
math_qa__c1jZdZo2dpPumJYi
Angelina walked 150 meters from her home to the grocery at a constant speed. She then walked 200 meters to the gym at double the speed. She spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym? Choose the correct choice from the following choices: A) 2 B) 3 C) 4 D) 10 E) 12
<gadget id="calculator">200 / 2</gadget> <output>100</output> <gadget id="calculator">150 - 100</gadget> <output>50</output> <gadget id="calculator">50 / 10</gadget> <output>5</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <result>D</result>
D
10
Angelina walked 150 meters from her home to the grocery at a constant speed. She then walked 200 meters to the gym at double the speed. She spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
{ "A": "2", "B": "3", "C": "4", "D": "10", "E": "12" }
multiply(divide(subtract(150, divide(200, const_2)), 10), const_2)
divide(n1,const_2)|subtract(n0,#0)|divide(#1,n2)|multiply(#2,const_2)
let the speed be x . . . so time taken from home to grocery = 150 / x . . the speed to gym = 2 x . . so time taken = 200 / 2 x = 100 / x . . its given 150 / x - 100 / x = 10 50 / x = 10 x = 5 m / secs . . so grocery to gym = 2 * 5 = 10 m / s . . . answer : d
physics
math_qa__11BYqQ15Z1hVRndX
A cylinder of height h is 5/6 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h? Choose the correct choice from the following answers A) 25 % B) 50 % C) 60 % D) 72 % E) 100 %
<gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">5 / 6</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">(3/5) / (5/6)</gadget> <output>18/25 = around 0.72</output> <gadget id="calculator">(18/25) * 100</gadget> <output>72</output> <result>D</result>
D
72
A cylinder of height h is 5/6 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
{ "A": "25 %", "B": "50 %", "C": "60 %", "D": "72 %", "E": "100 %" }
multiply(divide(divide(3, 5), divide(5, 6)), const_100)
divide(n3,n4)|divide(n0,n1)|divide(#0,#1)|multiply(#2,const_100)|
"basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 5 / 6 new cylinder 3 / 5 so 3 / 5 / 5 / 6 = 3 / 5 * 6 / 5 = 0.72 or 72 % . answer d"
gain
math_qa__iJwjWOeS4GcGjGbf
A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is ? Pick: A) 285 B) 227 C) 271 D) 187 E) 199
<gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">30 / 7</gadget> <output>30/7 = around 4.285714</output> <gadget id="calculator">floor(30/7)</gadget> <output>4</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 * 510</gadget> <output>2_550</output> <gadget id="calculator">30 - 5</gadget> <output>25</output> <gadget id="calculator">25 * 240</gadget> <output>6_000</output> <gadget id="calculator">2_550 + 6_000</gadget> <output>8_550</output> <gadget id="calculator">8_550 / 30</gadget> <output>285</output> <result>A</result>
A
285
A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is ?
{ "A": "285", "B": "227", "C": "271", "D": "187", "E": "199" }
divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 510), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30)
add(const_3,const_4)|divide(n2,#0)|floor(#1)|add(#2,const_1)|multiply(n0,#3)|subtract(n2,#3)|multiply(n1,#5)|add(#4,#6)|divide(#7,n2)|
"since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a"
general
math_qa__bbRi2diBeNOviUaG
A train running at the speed of 30 km/hr crosses a pole in 9 seconds. Find the length of the train? Choose the most appropriate option: A) 75 B) 65 C) 25 D) 288 E) 212
<gadget id="calculator">30 * 1_000</gadget> <output>30_000</output> <gadget id="calculator">30_000 / 3_600</gadget> <output>25/3 = around 8.333333</output> <gadget id="calculator">(25/3) * 9</gadget> <output>75</output> <result>A</result>
A
75
A train running at the speed of 30 km/hr crosses a pole in 9 seconds. Find the length of the train?
{ "A": "75", "B": "65", "C": "25", "D": "288", "E": "212" }
multiply(divide(multiply(30, const_1000), const_3600), 9)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
"speed = 30 * ( 5 / 18 ) m / sec = 25 / 3 m / sec length of train ( distance ) = speed * time ( 25 / 3 ) * 9 = 75 meter answer : a"
physics
math_qa__0Hdj8tLAiJoUx8nw
If 8 men or 12 women can do a piece of work in 15 days, in how many days can the same work be done by 6 men and 11 women? Pick one A) 9 days B) 11 days C) 13 days D) 15 days E) 17 days
<gadget id="calculator">8 * 15</gadget> <output>120</output> <gadget id="calculator">6 / 120</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">12 * 15</gadget> <output>180</output> <gadget id="calculator">11 / 180</gadget> <output>11/180 = around 0.061111</output> <gadget id="calculator">(1/20) + (11/180)</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">1 / (1/9)</gadget> <output>9</output> <result>A</result>
A
9
If 8 men or 12 women can do a piece of work in 15 days, in how many days can the same work be done by 6 men and 11 women?
{ "A": "9 days", "B": "11 days", "C": "13 days", "D": "15 days", "E": "17 days" }
inverse(add(divide(6, multiply(8, 15)), divide(11, multiply(12, 15))))
multiply(n0,n2)|multiply(n1,n2)|divide(n3,#0)|divide(n4,#1)|add(#2,#3)|inverse(#4)|
"8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 15 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 15 = 1 / 180 so , 20 women work = 20 / 180 = 1 / 9 ans : 9 days answer : a"
physics
math_qa__HGmaRkvh6E7FRgph
A train 200 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? Choose the correct choice: A) 443 m B) 354 m C) 450 m D) 350 m E) 300 m
<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">72 * (5/18)</gadget> <output>20</output> <gadget id="calculator">25 * 20</gadget> <output>500</output> <gadget id="calculator">500 - 200</gadget> <output>300</output> <result>E</result>
E
300
A train 200 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
{ "A": "443 m", "B": "354 m", "C": "450 m", "D": "350 m", "E": "300 m" }
subtract(multiply(25, multiply(72, const_0_2778)), 200)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
"e 300 e = 72 * 5 / 18 = 25 = 500 â € “ 200 = 300"
physics
math_qa__0ScG62LXBqwpisMF
The length of a train and that of a platform are equal. If with a speed of 126 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Options: A) 227 B) 299 C) 1050 D) 750 E) 211
<gadget id="calculator">126 * 1_000</gadget> <output>126_000</output> <gadget id="calculator">60 / 1</gadget> <output>60</output> <gadget id="calculator">126_000 / 60</gadget> <output>2_100</output> <gadget id="calculator">2_100 / 2</gadget> <output>1_050</output> <result>C</result>
C
1,050
The length of a train and that of a platform are equal. If with a speed of 126 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
{ "A": "227", "B": "299", "C": "1050", "D": "750", "E": "211" }
divide(divide(multiply(126, const_1000), divide(const_60, const_1)), const_2)
divide(const_60,const_1)|multiply(n0,const_1000)|divide(#1,#0)|divide(#2,const_2)|
"speed = [ 126 * 5 / 18 ] m / sec = 35 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 35 è x = 35 * 60 / 2 = 1050 answer : c"
physics
math_qa__pUzMOTuKcBRkGqu9
Laura took out a charge account at the General Store and agreed to pay 7% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments? Choose the correct choice from the following answers A) $ 2.10 B) $ 37.10 C) $ 37.45 D) $ 38.10 E) $ 38.80
<gadget id="calculator">7 / 100</gadget> <output>7/100 = around 0.07</output> <gadget id="calculator">(7/100) * 35</gadget> <output>49/20 = around 2.45</output> <gadget id="calculator">(49/20) + 35</gadget> <output>749/20 = around 37.45</output> <result>C</result>
C
37.45
Laura took out a charge account at the General Store and agreed to pay 7% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
{ "A": "$ 2.10", "B": "$ 37.10", "C": "$ 37.45", "D": "$ 38.10", "E": "$ 38.80" }
add(multiply(divide(7, const_100), 35), 35)
divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)|
"principal that is amount taken by laura at year beginning = 35 $ rate of interest = 7 % interest = ( 7 / 100 ) * 35 = 2.45 $ total amount that laura owes a year later = 35 + 2.45 = 37.45 $ answer c"
general
math_qa__bNDBK6w7FLOnNWOw
A dishonest dealer professes to sell goods at the cost price but uses a weight of 852 grams per kg, what is his percent? Answers: A) 22 % B) 25 % C) 17.37 % D) 99 % E) 12 %
<gadget id="calculator">100 / 852</gadget> <output>25/213 = around 0.117371</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">100 * 10</gadget> <output>1_000</output> <gadget id="calculator">(25/213) * 1_000</gadget> <output>25_000/213 = around 117.370892</output> <gadget id="calculator">(25_000/213) - 100</gadget> <output>3_700/213 = around 17.370892</output> <result>C</result>
C
17.37
A dishonest dealer professes to sell goods at the cost price but uses a weight of 852 grams per kg, what is his percent?
{ "A": "22 %", "B": "25 %", "C": "17.37 %", "D": "99 %", "E": "12 %" }
subtract(multiply(divide(const_100, 852), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)
add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)|
"852 - - - 148 100 - - - ? = > 17.37 % answer : c"
gain
math_qa__9yKd16WNN8gnpDPM
A man walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 60 miles? Choose one. A) 300 B) 318 C) 322 D) 324 E) 390
<gadget id="calculator">6 * 4</gadget> <output>24</output> <gadget id="calculator">60 / 10</gadget> <output>6</output> <gadget id="calculator">6 * 60</gadget> <output>360</output> <gadget id="calculator">24 + 360</gadget> <output>384</output> <result>E</result>
E
390
A man walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 60 miles?
{ "A": "300", "B": "318", "C": "322", "D": "324", "E": "390" }
add(multiply(6, const_4), multiply(divide(60, 10), const_60))
divide(n2,n0)|multiply(n1,const_4)|multiply(#0,const_60)|add(#1,#2)|
"to cover 60 miles the man needs ( time ) = ( distance ) / ( rate ) = 60 / 10 = 6 hours = 360 minutes . he will also rest 5 times ( after 10 , 20 , 30,40 and 50 miles ) , so total resting time = 5 * 6 = 30 minutes . total time = 360 + 30 = 390 minutes . answer : e ."
physics
math_qa__unU05k7czYgMN8Qe
The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 15. Find the sum : Select the correct option. A) 4500 B) 7500 C) 5000 D) 6000 E) none of these
<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">1 + (1/20)</gadget> <output>21/20 = around 1.05</output> <gadget id="calculator">(21/20) ** 2</gadget> <output>441/400 = around 1.1025</output> <gadget id="calculator">2 * (1/20)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 + (1/10)</gadget> <output>11/10 = around 1.1</output> <gadget id="calculator">(441/400) - (11/10)</gadget> <output>1/400 = around 0.0025</output> <gadget id="calculator">15 / (1/400)</gadget> <output>6_000</output> <result>D</result>
D
6,000
The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 15. Find the sum :
{ "A": "4500", "B": "7500", "C": "5000", "D": "6000", "E": "none of these" }
divide(15, subtract(power(add(const_1, divide(5, const_100)), 2), add(const_1, multiply(2, divide(5, const_100)))))
divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|add(#2,const_1)|power(#1,n1)|subtract(#4,#3)|divide(n2,#5)|
"sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 15 , the sum = 400 × 15 = 6000 answer d"
gain
math_qa__xuCyQoJRIYc2X44V
A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle? Pick one A) 9 : 8 B) 15 : 8 C) 27 : 8 D) 8 : 9 E) 8 : 15
<gadget id="calculator">3 * 10</gadget> <output>30</output> <gadget id="calculator">30 - 3</gadget> <output>27</output> <gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">27 / 8</gadget> <output>27/8 = around 3.375</output> <result>C</result>
C
3.375
A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?
{ "A": "9 : 8", "B": "15 : 8", "C": "27 : 8", "D": "8 : 9", "E": "8 : 15" }
divide(subtract(multiply(const_3, const_10), const_3), multiply(const_4, const_2))
multiply(const_10,const_3)|multiply(const_2,const_4)|subtract(#0,const_3)|divide(#2,#1)
let x be side of square perimeter of square = 4 x = perimeter of triangle = 3 * side of triangle so side of eq . triangle = ( 4 / 3 ) * x diameter of circle circumscribing the square = sqrt ( 2 ) * x area of circle circumscribing the square = pi * ( sqrt ( 2 ) * x ) ^ 2 / 4 = ( pi / 2 ) * x ^ 2 - - - - ( 1 ) to find radius of the circle inscribed in the triangle area of triangle = r * s = sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 now s = ( 4 / 3 ) * x + ( 4 / 3 ) * x + ( 4 / 3 ) * x / 2 = 2 x so sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 = r * 2 x gives r = { 2 / 3 * ( 3 ^ 1 / 2 ) } * x area of the circle inscribed in the triangle = pi * [ { 2 / 3 * ( 3 ^ 1 / 2 ) } * x ] ^ 2 = pi * ( 4 / 27 ) * x ^ 2 - - - - - - - ( 2 ) so reqd ratio = eqn ( 1 ) / eqn ( 2 ) = [ ( pi / 2 ) * x ^ 2 ] / [ pi * ( 4 / 27 ) * x ^ 2 ] = 27 / 8 so reqd ratio = 27 : 8 answer : c
geometry
math_qa__nYB93N5EQhJhaeIy
10 is subtracted from 50% of a number, the result is 25. Find the number? Options: A) 75 B) 70 C) 35 D) 170 E) 50
<gadget id="calculator">10 + 25</gadget> <output>35</output> <gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">35 / (1/2)</gadget> <output>70</output> <result>B</result>
B
70
10 is subtracted from 50% of a number, the result is 25. Find the number?
{ "A": "75", "B": "70", "C": "35", "D": "170", "E": "50" }
divide(add(10, 25), divide(50, const_100))
add(n0,n2)|divide(n1,const_100)|divide(#0,#1)|
"( 50 / 100 ) * x â € “ 10 = 25 5 x = 350 x = 70 answer : b"
gain
math_qa__19dK1I3GY6Syj2fe
A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? Pick A) 5.2 hrs B) 2.9 hrs C) 1.9 hrs D) 7.5 hrs E) 1.4 hrs
<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/3) - (1/5)</gadget> <output>2/15 = around 0.133333</output> <gadget id="calculator">1 / (2/15)</gadget> <output>15/2 = around 7.5</output> <result>D</result>
D
7.5
A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
{ "A": "5.2 hrs", "B": "2.9 hrs", "C": "1.9 hrs", "D": "7.5 hrs", "E": "1.4 hrs" }
divide(const_1, subtract(divide(const_1, 3), divide(const_1, 5)))
divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)|
"net part filled in 1 hour = ( 1 / 3 - 1 / 5 ) = 2 / 15 the cistern will be filled in 15 / 2 hrs i . e . , 7.5 hrs . answer : d"
physics
math_qa__QDu3mSKh1xweDdzB
The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made? Options. A) 328897 B) 120000 C) 877888 D) 277768 E) 188871
<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 - (1/5)</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">(4/5) * (4/5)</gadget> <output>16/25 = around 0.64</output> <gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">100 ** (1/2)</gadget> <output>10</output> <gadget id="calculator">10_000 * 10</gadget> <output>100_000</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 * 100</gadget> <output>500</output> <gadget id="calculator">500 * 100</gadget> <output>50_000</output> <gadget id="calculator">100_000 + 50_000</gadget> <output>150_000</output> <gadget id="calculator">(16/25) * 150_000</gadget> <output>96_000</output> <gadget id="calculator">20 + 2</gadget> <output>22</output> <gadget id="calculator">22 * 100</gadget> <output>2_200</output> <gadget id="calculator">2_200 * 10</gadget> <output>22_000</output> <gadget id="calculator">96_000 + 22_000</gadget> <output>118_000</output> <result>B</result>
B
120,000
The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?
{ "A": "328897", "B": "120000", "C": "877888", "D": "277768", "E": "188871" }
add(multiply(multiply(subtract(1, divide(20, const_100)), subtract(1, divide(20, const_100))), add(multiply(multiply(const_100, const_100), sqrt(const_100)), multiply(multiply(divide(sqrt(const_100), const_2), const_100), const_100))), multiply(multiply(add(20, const_2), const_100), sqrt(const_100)))
add(n0,const_2)|divide(n0,const_100)|multiply(const_100,const_100)|sqrt(const_100)|divide(#3,const_2)|multiply(#2,#3)|multiply(#0,const_100)|subtract(n1,#1)|multiply(#4,const_100)|multiply(#7,#7)|multiply(#6,#3)|multiply(#8,const_100)|add(#5,#11)|multiply(#12,#9)|add(#13,#10)|
"the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 24,000 is made = 96,000 + 24,000 = rs . 1 , 20,000 answer : b"
gain
math_qa__goe00zeA1MyWo8sV
A tank can supply water to a village for 100 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 75 days only. For how many days will the supply last if the leak drains out 20 liters per day? Select: A) 50 B) 60 C) 65 D) 70 E) 72
<gadget id="calculator">10 * 75</gadget> <output>750</output> <gadget id="calculator">100 - 75</gadget> <output>25</output> <gadget id="calculator">750 / 25</gadget> <output>30</output> <gadget id="calculator">30 * 100</gadget> <output>3_000</output> <gadget id="calculator">20 + 30</gadget> <output>50</output> <gadget id="calculator">3_000 / 50</gadget> <output>60</output> <result>B</result>
B
60
A tank can supply water to a village for 100 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 75 days only. For how many days will the supply last if the leak drains out 20 liters per day?
{ "A": "50", "B": "60", "C": "65", "D": "70", "E": "72" }
divide(multiply(divide(multiply(10, 75), subtract(100, 75)), 100), add(20, divide(multiply(10, 75), subtract(100, 75))))
multiply(n1,n2)|subtract(n0,n2)|divide(#0,#1)|add(n3,#2)|multiply(n0,#2)|divide(#4,#3)|
"losing 10 liters per day results in a loss of 750 liters in 75 days . so , those 750 liters were for 25 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 100 = 3000 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 3000 / 50 = 60 days . the answer is b ."
physics
math_qa__GkoLGrQXdVSPvjlR
A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? Choose the most appropriate option A) 300 m B) 278 m C) 350 m D) 228 m E) 282 m
<gadget id="calculator">300 / 18</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">(50/3) * 36</gadget> <output>600</output> <gadget id="calculator">600 - 300</gadget> <output>300</output> <result>A</result>
A
300
A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
{ "A": "300 m", "B": "278 m", "C": "350 m", "D": "228 m", "E": "282 m" }
subtract(multiply(divide(300, 18), 36), 300)
divide(n0,n2)|multiply(n1,#0)|subtract(#1,n0)|
"speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 36 = 50 / 3 3 ( x + 300 ) = 1800 è x = 300 m . answer : a"
physics
math_qa__7pRvMnunvrnLKzGa
The ratio of pens to pencils is 5 to 6. There are 9 more pencils than pens. How many pencils are there? Choose one: A) 36 B) 42 C) 48 D) 54 E) 60
<gadget id="calculator">9 * 5</gadget> <output>45</output> <gadget id="calculator">45 + 9</gadget> <output>54</output> <result>D</result>
D
54
The ratio of pens to pencils is 5 to 6. There are 9 more pencils than pens. How many pencils are there?
{ "A": "36", "B": "42", "C": "48", "D": "54", "E": "60" }
add(multiply(9, 5), 9)
multiply(n0,n2)|add(n2,#0)
let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 9 x = 9 the number of pencils is 54 . the answer is d .
other
math_qa__F8rmhaEvXd34TT8N
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle. Pick one: A) 5 B) 10 C) 15 D) 20 E) 25
<gadget id="calculator">70 / 2</gadget> <output>35</output> <gadget id="calculator">35 * 35</gadget> <output>1_225</output> <gadget id="calculator">4 * 300</gadget> <output>1_200</output> <gadget id="calculator">1_225 - 1_200</gadget> <output>25</output> <gadget id="calculator">25 ** (1/2)</gadget> <output>5</output> <gadget id="calculator">35 - 5</gadget> <output>30</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <result>C</result>
C
15
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle.
{ "A": "5", "B": "10", "C": "15", "D": "20", "E": "25" }
divide(subtract(divide(70, const_2), sqrt(subtract(multiply(divide(70, const_2), divide(70, const_2)), multiply(const_4, 300)))), const_2)
divide(n1,const_2)|multiply(n0,const_4)|multiply(#0,#0)|subtract(#2,#1)|sqrt(#3)|subtract(#0,#4)|divide(#5,const_2)|
"l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c"
geometry
math_qa__urrSe8IeO2Miqdnv
If the average of 10 digits is 80 and the average of 6 of them is 58, calculate the average of the remaining 4 numbers? Answers. A) 119 B) 117 C) 116 D) 113 E) 115
<gadget id="calculator">10 * 80</gadget> <output>800</output> <gadget id="calculator">6 * 58</gadget> <output>348</output> <gadget id="calculator">800 - 348</gadget> <output>452</output> <gadget id="calculator">452 / 4</gadget> <output>113</output> <result>D</result>
D
113
If the average of 10 digits is 80 and the average of 6 of them is 58, calculate the average of the remaining 4 numbers?
{ "A": "119", "B": "117", "C": "116", "D": "113", "E": "115" }
divide(subtract(multiply(10, 80), multiply(6, 58)), 4)
multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)|
"explanation : total of the 10 digits - 10 * 80 = 800 total of the 6 digits - 6 * 58 = 348 total of the remaining 4 digits - 800 - 348 = 452 average of the remaining 4 numbers = 452 / 4 = 113 answer : d"
general
math_qa__GFKcckjZAPOGXPtR
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Choose the correct choice from the following answers: A) 11 B) 12 C) 13 D) 15 E) 14
<gadget id="calculator">39 * 12</gadget> <output>468</output> <gadget id="calculator">468 * 5</gadget> <output>2_340</output> <gadget id="calculator">30 * 6</gadget> <output>180</output> <gadget id="calculator">2_340 / 180</gadget> <output>13</output> <result>C</result>
C
13
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
{ "A": "11", "B": "12", "C": "13", "D": "15", "E": "14" }
divide(multiply(multiply(39, 12), 5), multiply(30, 6))
multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)|
"first codition = total hours to complete the work = 39 persons * 12 days * 5 hr second codition = total hours to complete the work = 30 persons * x days * 6 hr since the work is still the same so 39 * 12 * 5 = 30 * x * 6 x = 13 answer : c"
physics
math_qa__F0Z3VZJmOzzNsQQ8
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 300 resolutions. Choose the correct choice from the following choices. A) 421 m B) 422 m C) 423 m D) 424 m E) 425 m
<gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">7 * 3</gadget> <output>21</output> <gadget id="calculator">21 + 1</gadget> <output>22</output> <gadget id="calculator">22 / 7</gadget> <output>22/7 = around 3.142857</output> <gadget id="calculator">(22/7) * 22.4</gadget> <output>70.4</output> <gadget id="calculator">70.4 * 2</gadget> <output>140.8</output> <gadget id="calculator">140.8 * 300</gadget> <output>42_240</output> <gadget id="calculator">42_240 / 100</gadget> <output>2_112/5 = around 422.4</output> <result>B</result>
B
422
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 300 resolutions.
{ "A": "421 m", "B": "422 m", "C": "423 m", "D": "424 m", "E": "425 m" }
divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 300), const_100)
add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)|
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 300 resolutions . = 300 * 2 * 22 / 7 * 22.4 = 42200 cm = 422 m answer : b"
physics
math_qa__z3eojepIpz18AMgm
An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets liquid in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank. Answers: A) 8600 litres B) 12800 litres C) 12100 litres D) 11200 litres E) 13200 litres
<gadget id="calculator">8 * 60</gadget> <output>480</output> <gadget id="calculator">10 + 6</gadget> <output>16</output> <gadget id="calculator">480 * 16</gadget> <output>7_680</output> <gadget id="calculator">7_680 / 6</gadget> <output>1_280</output> <gadget id="calculator">1_280 * 10</gadget> <output>12_800</output> <result>B</result>
B
12,800
An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets liquid in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.
{ "A": "8600 litres", "B": "12800 litres", "C": "12100 litres", "D": "11200 litres", "E": "13200 litres" }
multiply(divide(multiply(multiply(8, const_60), add(10, 6)), 6), 10)
add(n0,n2)|multiply(n1,const_60)|multiply(#0,#1)|divide(#2,n2)|multiply(n0,#3)|
"let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 10 hours = ( x - 480 ) * ( 10 + 6 ) hours 10 x = ( x - 480 ) * 16 - - > x = 1280 - - > capacity = 10 x = 12800 liters . answer : b"
physics
math_qa__ADDj5yMVnTGtaQaG
Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet? Choose the correct choice from the following. A) 15 B) 18 C) 21 D) 24 E) 27
<gadget id="calculator">45 / 60</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) * 4</gadget> <output>3</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">60 / 60</gadget> <output>1</output> <gadget id="calculator">1 - (3/4)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">7 / (1/4)</gadget> <output>28</output> <gadget id="calculator">28 - 4</gadget> <output>24</output> <result>D</result>
D
24
Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet?
{ "A": "15", "B": "18", "C": "21", "D": "24", "E": "27" }
subtract(divide(add(multiply(divide(45, 60), 4), 4), subtract(divide(60, 60), divide(45, 60))), 4)
divide(n3,n2)|divide(n2,n2)|multiply(n0,#0)|subtract(#1,#0)|add(n0,#2)|divide(#4,#3)|subtract(#5,n0)|
"let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him y : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
physics