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Calc-math_qa

like 4

math_qa__qV3bM0mc5XADcqqk

The diagonals of a rhombus are 11 cm and 20 cm. Find its area? Choose the correct choice from the following choices. A) 329 B) 288 C) 150 D) 238 E) 110

<gadget id="calculator">(11 * 20) / 2</gadget> <output>110</output> <result>E</result>

E

The diagonals of a rhombus are 11 cm and 20 cm. Find its area?

rhombus_area(11, 20)

rhombus_area(n0,n1)|

"1 / 2 * 11 * 20 = 110 answer : e"

geometry

math_qa__Mo6mlfZEEAhce28I

A man can row his boat with the stream at 36 km/h and against the stream in 8 km/h. The man's rate is? Choose one A) 1 kmph B) 6 kmph C) 7 kmph D) 14 kmph E) 9 kmph

<gadget id="calculator">36 - 8</gadget> <output>28</output> <gadget id="calculator">28 / 2</gadget> <output>14</output> <result>D</result>

D

A man can row his boat with the stream at 36 km/h and against the stream in 8 km/h. The man's rate is?

divide(subtract(36, 8), const_2)

subtract(n0,n1)|divide(#0,const_2)|

"explanation : ds = 36 us = 8 s = ? s = ( 36 - 8 ) / 2 = 14 kmph answer : d"

gain

math_qa__bCfMg8pmYAbRYh0B

Ashok secured average of 75 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? Choose the correct choice from the following choices: A) 38 B) 27 C) 99 D) 17 E) 80

<gadget id="calculator">75 * 6</gadget> <output>450</output> <gadget id="calculator">74 * 5</gadget> <output>370</output> <gadget id="calculator">450 - 370</gadget> <output>80</output> <result>E</result>

E

Ashok secured average of 75 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?

subtract(multiply(75, 6), multiply(74, 5))

multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|

"explanation : number of subjects = 6 average of marks in 6 subjects = 75 therefore total marks in 6 subjects = 75 * 6 = 450 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 450 – 370 = 80 answer : e"

general

math_qa__gniiTIQCKZ1NUpNP

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 5 m, the volume of the box (in m3) is: Pick: A) 4940 B) 5120 C) 6420 D) 8960 E) 7960

<gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">48 - 10</gadget> <output>38</output> <gadget id="calculator">36 - 10</gadget> <output>26</output> <gadget id="calculator">38 * 26 * 5</gadget> <output>4_940</output> <result>A</result>

A

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 5 m, the volume of the box (in m3) is:

volume_rectangular_prism(subtract(48, multiply(5, const_2)), subtract(36, multiply(5, const_2)), 5)

multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|volume_rectangular_prism(n2,#1,#2)|

"clearly , l = ( 48 - 10 ) m = 38 m , b = ( 36 - 10 ) m = 26 m , h = 8 m . volume of the box = ( 38 x 26 x 5 ) m 3 = 4940 m 3 . answer : option a"

geometry

math_qa__S4VpZ8KjqjkrmH26

A rectangular lawn of dimensions 80 m * 60 m has two roads each 15 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? Choose the correct choice from the following answers: A) 3820 B) 930 C) 9309 D) 3900 E) 5625

<gadget id="calculator">80 + 60</gadget> <output>140</output> <gadget id="calculator">140 - 15</gadget> <output>125</output> <gadget id="calculator">125 * 15</gadget> <output>1_875</output> <gadget id="calculator">1_875 * 3</gadget> <output>5_625</output> <result>E</result>

E

A rectangular lawn of dimensions 80 m * 60 m has two roads each 15 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?

multiply(multiply(subtract(add(80, 60), 15), 15), 3)

add(n0,n1)|subtract(#0,n2)|multiply(n2,#1)|multiply(n3,#2)|

"explanation : area = ( l + b – d ) d ( 80 + 60 – 15 ) 15 = > 1875 m 2 1875 * 3 = rs . 5625 answer : option e"

geometry

math_qa__WbCMc4BQq2j7H1CK

A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 4 metres apart, how many poles will be needed ? Choose the most appropriate option A) 55 B) 70 C) 57 D) 58 E) none of these

<gadget id="calculator">2 * (90 + 50)</gadget> <output>280</output> <gadget id="calculator">280 / 4</gadget> <output>70</output> <result>B</result>

B

A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 4 metres apart, how many poles will be needed ?

divide(rectangle_perimeter(90, 50), 4)

rectangle_perimeter(n0,n1)|divide(#0,n2)

solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 4 ] = 70 m answer b

physics

math_qa__VWrBuQ361XdX4S18

If the capacity of a cylindrical tank is 1848 m3 and the diameter of its base is 14 m, then find the depth of the tank. Pick one: A) 10 B) 11 C) 12 D) 13 E) none of them

<gadget id="calculator">14 / 2</gadget> <output>7</output> <gadget id="calculator">pi * (7 ** 2)</gadget> <output>49*pi = around 153.93804</output> <gadget id="calculator">1_848 / (49*pi)</gadget> <output>264/(7*pi) = around 12.00483</output> <result>C</result>

C

If the capacity of a cylindrical tank is 1848 m3 and the diameter of its base is 14 m, then find the depth of the tank.

divide(1848, circle_area(divide(14, const_2)))

divide(n2,const_2)|circle_area(#0)|divide(n0,#1)

let the depth of the tank be h meters . then , ∏ x 72 x h = 1848  h = ( 1848 x ( 7 / 22 ) x ( 1 / 49 ) = 12 m answer is c

physics

math_qa__UeI9UIn3MXO9rB4o

If a train, travelling at a speed of 160 kmph, crosses a pole in 18 sec, then the length of train is? Choose the correct choice from the following answers: A) 800 B) 125 C) 288 D) 266 E) 121

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">160 * (5/18)</gadget> <output>400/9 = around 44.444444</output> <gadget id="calculator">(400/9) * 18</gadget> <output>800</output> <result>A</result>

A

If a train, travelling at a speed of 160 kmph, crosses a pole in 18 sec, then the length of train is?

multiply(multiply(160, const_0_2778), 18)

multiply(n0,const_0_2778)|multiply(n1,#0)|

"d = 160 * 5 / 18 * 18 = 800 m answer : a"

physics

math_qa__tfTMl4Ilh23kjlAG

A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 45 paise per sq m is Choose the correct choice: A) rs . 234.80 B) rs . 334.80 C) rs . 434.80 D) rs . 534.80 E) none of these

<gadget id="calculator">45 / 100</gadget> <output>9/20 = around 0.45</output> <gadget id="calculator">25 * 12</gadget> <output>300</output> <gadget id="calculator">25 * 6</gadget> <output>150</output> <gadget id="calculator">2 * 150</gadget> <output>300</output> <gadget id="calculator">12 * 6</gadget> <output>72</output> <gadget id="calculator">72 * 2</gadget> <output>144</output> <gadget id="calculator">300 + 144</gadget> <output>444</output> <gadget id="calculator">300 + 444</gadget> <output>744</output> <gadget id="calculator">(9/20) * 744</gadget> <output>1_674/5 = around 334.8</output> <result>B</result>

B

A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 45 paise per sq m is

multiply(divide(45, const_100), add(multiply(25, 12), add(multiply(const_2, multiply(25, 6)), multiply(multiply(12, 6), const_2))))

divide(n3,const_100)|multiply(n0,n2)|multiply(n1,n2)|multiply(n0,n1)|multiply(#1,const_2)|multiply(#2,const_2)|add(#4,#5)|add(#6,#3)|multiply(#7,#0)|

"explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 45 / 100 ) = rs . 334.80 answer : b"

physics

math_qa__68uCvLIzAnUP1IZE

A man rows his boat 120 km downstream and 60 km upstream, taking 2 hours each time. Find the speed of the stream? Choose one. A) 6 B) 15 C) 17 D) 18 E) 2

<gadget id="calculator">120 / 2</gadget> <output>60</output> <gadget id="calculator">60 / 2</gadget> <output>30</output> <gadget id="calculator">60 - 30</gadget> <output>30</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <result>B</result>

B

A man rows his boat 120 km downstream and 60 km upstream, taking 2 hours each time. Find the speed of the stream?

divide(subtract(divide(120, 2), divide(60, 2)), const_2)

divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)|

"speed downstream = d / t = 120 / ( 2 ) = 60 kmph speed upstream = d / t = 60 / ( 2 ) = 30 kmph the speed of the stream = ( 60 - 30 ) / 2 = 15 kmph answer : b"

physics

math_qa__Xbkyh8e3K901XJt5

There are 14 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks? Choices: A) 1 / 5 B) 11 / 22 C) 81 / 724 D) 91 / 946 E) 101 / 987

<gadget id="calculator">14 + 20</gadget> <output>34</output> <gadget id="calculator">34 + 10</gadget> <output>44</output> <gadget id="calculator">14 / 44</gadget> <output>7/22 = around 0.318182</output> <gadget id="calculator">14 - 1</gadget> <output>13</output> <gadget id="calculator">44 - 1</gadget> <output>43</output> <gadget id="calculator">13 / 43</gadget> <output>13/43 = around 0.302326</output> <gadget id="calculator">(7/22) * (13/43)</gadget> <output>91/946 = around 0.096195</output> <result>D</result>

D

There are 14 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?

multiply(divide(14, add(add(14, 20), 10)), divide(subtract(14, const_1), subtract(add(add(14, 20), 10), const_1)))

add(n0,n1)|subtract(n0,const_1)|add(n2,#0)|divide(n0,#2)|subtract(#2,const_1)|divide(#1,#4)|multiply(#3,#5)|

"14 / 44 * 13 / 43 = 91 / 946 the answer is d ."

other

math_qa__e98REkCER09kgu8a

If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is? Answers: A) 3377 B) 2688 C) 2688 D) 8436 E) 1268

<gadget id="calculator">100 + 4</gadget> <output>104</output> <gadget id="calculator">104 / 100</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">(26/25) * (26/25)</gadget> <output>676/625 = around 1.0816</output> <gadget id="calculator">7_500 * (676/625)</gadget> <output>8_112</output> <result>D</result>

D

If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is?

multiply(7500, multiply(divide(add(const_100, 4), const_100), divide(add(const_100, 4), const_100)))

add(n1,const_100)|divide(#0,const_100)|multiply(#1,#1)|multiply(n0,#2)

a = 7500 ( 26 / 25 ) ^ 3 = 8436 answer : d

gain

math_qa__UXCPuOCjKJRMkFxf

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 21 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel? Choose the correct choice from the following choices. A) 54 B) 66 C) 68 D) 60 E) 63

<gadget id="calculator">36 / 2</gadget> <output>18</output> <gadget id="calculator">18 / 6</gadget> <output>3</output> <gadget id="calculator">21 * 3</gadget> <output>63</output> <result>E</result>

E

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 21 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?

multiply(21, divide(divide(36, 2), 6))

divide(n1,n3)|divide(#0,n0)|multiply(n2,#1)|

"e 63 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 21 mph = 63 miles"

physics

math_qa__LPgHTQzHLV0EaA5Q

The sum of number of boys and girls in a school is 400. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is? Select the correct option. A) 50 B) 40 C) 60 D) 80 E) 70

<gadget id="calculator">400 / 100</gadget> <output>4</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">400 / 5</gadget> <output>80</output> <result>D</result>

D

The sum of number of boys and girls in a school is 400. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?

divide(400, add(divide(400, const_100), const_1))

divide(n0,const_100)|add(#0,const_1)|divide(n0,#1)|

"we have x + x % of 400 = 400 x + x / 100 * 400 = 400 5 * x = 400 x = 80 answer is d"

general

math_qa__Iy00nUM6FcBzKh2L

A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 15% so that the customer could not buy the required amount of the product. The customer managed to buy only 60% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? Choose the most appropriate option: A) 27 % B) 29 % C) 31 % D) 33 % E) 35 %

<gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">(3/20) + 1</gadget> <output>23/20 = around 1.15</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(23/20) * (3/5)</gadget> <output>69/100 = around 0.69</output> <gadget id="calculator">1 - (69/100)</gadget> <output>31/100 = around 0.31</output> <gadget id="calculator">(31/100) * 100</gadget> <output>31</output> <result>C</result>

C

A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 15% so that the customer could not buy the required amount of the product. The customer managed to buy only 60% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?

multiply(subtract(const_1, multiply(add(divide(15, const_100), const_1), divide(60, const_100))), const_100)

divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(#2,#1)|subtract(const_1,#3)|multiply(#4,const_100)|

"let x be the amount of money paid for the first purchase . the second time , the customer paid 0.6 ( 1.15 x ) = 0.69 x . the difference is 31 % . the answer is c ."

general

math_qa__GLwzlrJVXUTmK6FE

If xy=1, x/y=36, for positive numbers x and y, y=? Choose the correct choice from the following A) 1 / 2 B) 2 C) 1 / 3 D) 3 E) 1 / 6

<gadget id="calculator">1 / 36</gadget> <output>1/36 = around 0.027778</output> <gadget id="calculator">(1/36) ** (1/2)</gadget> <output>1/6 = around 0.166667</output> <result>E</result>

E

If xy=1, x/y=36, for positive numbers x and y, y=?

sqrt(divide(1, 36))

divide(n0,n1)|sqrt(#0)|

"very easy question . 2 variables and 2 easy equations . xy = 1 - - - > x = 1 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 1 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 1 / 36 - - - > y = 1 / 6 or - 1 / 6 the question states that x and y are positive integers . therefore , y = 1 / 6 is the answer . answer e ."

general

math_qa__LQlzM1us1jL6nzjm

For covering 88km a wheel revolve 1000 times.what is the radius of wheel? Pick: A) 14 m B) 24 m C) 28 m D) 40 m E) none of the above

<gadget id="calculator">88 / 1_000</gadget> <output>11/125 = around 0.088</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">(11/125) * 7</gadget> <output>77/125 = around 0.616</output> <gadget id="calculator">(77/125) / 2</gadget> <output>77/250 = around 0.308</output> <gadget id="calculator">10 * 2</gadget> <output>20</output> <gadget id="calculator">20 + 2</gadget> <output>22</output> <gadget id="calculator">(77/250) / 22</gadget> <output>7/500 = around 0.014</output> <gadget id="calculator">(7/500) * 1_000</gadget> <output>14</output> <gadget id="calculator">14 * 2</gadget> <output>28</output> <result>C</result>

C

For covering 88km a wheel revolve 1000 times.what is the radius of wheel?

multiply(multiply(divide(divide(multiply(divide(88, 1000), add(const_3, const_4)), const_2), add(multiply(const_10, const_2), const_2)), const_1000), const_2)

add(const_3,const_4)|divide(n0,n1)|multiply(const_10,const_2)|add(#2,const_2)|multiply(#0,#1)|divide(#4,const_2)|divide(#5,#3)|multiply(#6,const_1000)|multiply(#7,const_2)

distance travel in 1 round = 88000 / 1000 m = 88 m perimeter = 88 m , 2 π r = 882 r = [ 88 * 7 / 22 ] = 28 m hence , diameter = 28 m answer c

general

math_qa__R418GPSAIn82h1JN

A car covers a distance of 642 km in 6 ½ hours. Find its speed? Pick one: A) 104 kmph B) 176 kmph C) 298 kmph D) 186 kmph E) 107 kmph

<gadget id="calculator">642 / 6</gadget> <output>107</output> <result>E</result>

E

A car covers a distance of 642 km in 6 ½ hours. Find its speed?

divide(642, 6)

divide(n0,n1)

642 / 6 = 107 kmph answer : e

physics

math_qa__PZ8MHYxqR3Fqriad

I sold a book at a profit of 12%. Had I sold it for $18 more, 18% would have been gained. Find the cost price? Choose the correct option A) $ 100 B) $ 250 C) $ 300 D) $ 200 E) $ 180

<gadget id="calculator">18 * 12</gadget> <output>216</output> <gadget id="calculator">18 - 12</gadget> <output>6</output> <gadget id="calculator">216 / 6</gadget> <output>36</output> <gadget id="calculator">36 * 100</gadget> <output>3_600</output> <gadget id="calculator">3_600 / 12</gadget> <output>300</output> <result>C</result>

C

I sold a book at a profit of 12%. Had I sold it for $18 more, 18% would have been gained. Find the cost price?

divide(multiply(divide(multiply(18, 12), subtract(18, 12)), const_100), 12)

multiply(n0,n1)|subtract(n2,n0)|divide(#0,#1)|multiply(#2,const_100)|divide(#3,n0)|

"118 % of cost - 112 % of cost = $ 18 6 % of cost = $ 18 cost = 18 * 100 / 6 = $ 300 answer is c"

gain

math_qa__0r5mDstvVpsCJ2h9

The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 21 minutes is: Choose the correct answer: A) 9.75 B) 5.75 C) 8.75 D) 6.75 E) 5.15

<gadget id="calculator">21 / 60</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">20 + 5</gadget> <output>25</output> <gadget id="calculator">(7/20) * 25</gadget> <output>35/4 = around 8.75</output> <result>C</result>

C

The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 21 minutes is:

multiply(divide(21, const_60), add(20, 5))

add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)|

"explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 21 / 60 ) ) km = 8.75 km . answer : c"

physics

math_qa__MoAVE3Ko6eGOkRy2

If the price of an article went up by 25%, then by what percent should it be brought down to bring it back to its original price? Choose the most appropriate option: A) 20 % B) 2 / 8 % C) 2 / 1 % D) 1 / 3 % E) 2 / 7 %

<gadget id="calculator">100 + 25</gadget> <output>125</output> <gadget id="calculator">25 / 125</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 100</gadget> <output>20</output> <result>A</result>

A

If the price of an article went up by 25%, then by what percent should it be brought down to bring it back to its original price?

multiply(divide(25, add(const_100, 25)), const_100)

add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100)

let the price of the article be rs . 100 . 25 % of 100 = 25 . new price = 100 + 25 = rs . 125 required percentage = ( 125 - 100 ) / 125 * 100 = 25 / 125 * 100 = 20 % . answer : a

gain

math_qa__4wgGTlkKjCgyFtRT

A retailer buys 40 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? Choose the correct choice from the following choices. A) 5 B) 10 C) 15 D) 20 E) none of them

<gadget id="calculator">1 / 100</gadget> <output>1/100 = around 0.01</output> <gadget id="calculator">1 - (1/100)</gadget> <output>99/100 = around 0.99</output> <gadget id="calculator">36 / 40</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">(99/100) - (9/10)</gadget> <output>9/100 = around 0.09</output> <gadget id="calculator">(9/100) / (9/10)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">100 * (1/10)</gadget> <output>10</output> <result>B</result>

B

A retailer buys 40 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?

multiply(const_100, divide(subtract(subtract(1, divide(1, const_100)), divide(36, 40)), divide(36, 40)))

divide(n2,const_100)|divide(n1,n0)|subtract(n2,#0)|subtract(#2,#1)|divide(#3,#1)|multiply(#4,const_100)|

"let the market price of each pen be rs 1 then , c . p of 40 pens = rs 36 s . p of 40 pens = 99 % of rs 40 = rs 39.60 profit % = ( ( 3.60 * 100 ) / 36 ) % = 10 % answer is b ."

gain

math_qa__W5e2UjenfawCogz7

Given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km? Choose the correct answer. A) 22754.3 B) 22254.2 C) 25754.2 D) 22753.2 E) 22254.2

<gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">11 * 2</gadget> <output>22</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">22 / 7</gadget> <output>22/7 = around 3.142857</output> <gadget id="calculator">(22/7) * 2</gadget> <output>44/7 = around 6.285714</output> <gadget id="calculator">(44/7) * 3.62</gadget> <output>22.754286</output> <gadget id="calculator">22.754286 * 1_000</gadget> <output>22_754.286</output> <result>A</result>

A

Given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km?

multiply(multiply(multiply(divide(multiply(add(const_10, const_1), const_2), add(const_3, const_4)), const_2), 3.62), const_1000)

add(const_1,const_10)|add(const_3,const_4)|multiply(#0,const_2)|divide(#2,#1)|multiply(#3,const_2)|multiply(n0,#4)|multiply(#5,const_1000)

2 * 22 / 7 * 3.62 * x = 22754.3 x = 1000 answer : a

physics

math_qa__gNAbToYagumHRvhv

Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15? Choose the correct option A) 2 B) 3 C) 5 D) 7 E) 8

<gadget id="calculator">427_398 / 15</gadget> <output>142_466/5 = around 28_493.2</output> <gadget id="calculator">floor(142_466/5)</gadget> <output>28_493</output> <gadget id="calculator">28_493 * 15</gadget> <output>427_395</output> <gadget id="calculator">427_398 - 427_395</gadget> <output>3</output> <result>B</result>

B

Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?

subtract(427398, multiply(floor(divide(427398, 15)), 15))

divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)|

"on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted b"

general

math_qa__PNi460JdhKATzsFc

If 15 students in a class average 73% on an exam and 10 students average 88% on the same exam, what is the average in percent for all 25 students? Choose the correct choice from the following: A) 77 % B) 78 % C) 79 % D) 80 % E) 81 %

<gadget id="calculator">15 * 73</gadget> <output>1_095</output> <gadget id="calculator">10 * 88</gadget> <output>880</output> <gadget id="calculator">1_095 + 880</gadget> <output>1_975</output> <gadget id="calculator">1_975 / 25</gadget> <output>79</output> <result>C</result>

C

If 15 students in a class average 73% on an exam and 10 students average 88% on the same exam, what is the average in percent for all 25 students?

divide(add(multiply(15, 73), multiply(10, 88)), 25)

multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|divide(#2,n4)|

"( 15 * 73 + 10 * 88 ) / 25 = 79 % the answer is c ."

general

math_qa__P1pUVV2A2vKlTEAC

If the price of a TV is first decreased by 10% and then increased by 30%, then the net change in the price will be : Answers: A) 4 % increase B) 17 % increase C) 10 % decrease D) 6 % increase E) none of these

<gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">100 + 30</gadget> <output>130</output> <gadget id="calculator">90 * 130</gadget> <output>11_700</output> <gadget id="calculator">11_700 / 100</gadget> <output>117</output> <gadget id="calculator">117 - 100</gadget> <output>17</output> <result>B</result>

B

If the price of a TV is first decreased by 10% and then increased by 30%, then the net change in the price will be :

subtract(divide(multiply(subtract(const_100, 10), add(const_100, 30)), const_100), const_100)

add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(#3,const_100)|

"explanation : solution : let the original price be rs . 100 . new final price = 130 % of ( 10 % of 100 ) = rs . 130 / 100 * 90 / 100 * 100 = rs . 117 . . ' . increase = 17 % answer : b"

general

math_qa__gv3nVx19upbonIOn

If the true discount on a sum due 2 years hence at 14% per annum be Rs.168,the sum due is : Select: A) rs . 768 B) rs . 968 C) rs . 1960 D) rs . 2400 E) none

<gadget id="calculator">100 * 168</gadget> <output>16_800</output> <gadget id="calculator">14 * 2</gadget> <output>28</output> <gadget id="calculator">16_800 / 28</gadget> <output>600</output> <gadget id="calculator">600 + 168</gadget> <output>768</output> <result>A</result>

A

If the true discount on a sum due 2 years hence at 14% per annum be Rs.168,the sum due is :

add(divide(multiply(const_100, 168), multiply(14, 2)), 168)

multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|add(n2,#2)

solution p . w = 100 xt . d . / r x t = 100 x 168 / 14 x 2 = 600 . ∴ sum = ( p . w . + td . ) = rs . 768 . answer a

gain

math_qa__YlSVDJUof6HE7N6H

A soft drink company had 6000 small and 10000 big bottles in storage. If 12% of small15% of big bottles have been sold, then the total bottles remaining in storage is Choose the correct choice from the following answers: A) 15360 B) 13780 C) 15060 D) 14930 E) 16075

<gadget id="calculator">6_000 + 10_000</gadget> <output>16_000</output> <gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">6_000 * (3/25)</gadget> <output>720</output> <gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">(3/20) * 10_000</gadget> <output>1_500</output> <gadget id="calculator">720 + 1_500</gadget> <output>2_220</output> <gadget id="calculator">16_000 - 2_220</gadget> <output>13_780</output> <result>B</result>

B

A soft drink company had 6000 small and 10000 big bottles in storage. If 12% of small15% of big bottles have been sold, then the total bottles remaining in storage is

subtract(add(6000, 10000), add(multiply(6000, divide(12, const_100)), multiply(divide(15, const_100), 10000)))

add(n0,n1)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n1,#2)|add(#3,#4)|subtract(#0,#5)|

"6000 + 10000 - ( 0.12 * 6000 + 0.15 * 10000 ) = 13780 . answer : b ."

general

math_qa__whh2xO166VqwKihS

In a race where 18 cars are running, the chance that car X will win is 1/8, that Y will win is 1/12 and that Z will win is 1/6. Assuming that a dead heat is impossible, find the chance that one of them will win. Choose the correct answer: A) 1 / 140 B) 1 / 180 C) 3 / 12 D) 3 / 8 E) 57 / 120

<gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(1/8) + (1/12)</gadget> <output>5/24 = around 0.208333</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(5/24) + (1/6)</gadget> <output>3/8 = around 0.375</output> <result>D</result>

D

In a race where 18 cars are running, the chance that car X will win is 1/8, that Y will win is 1/12 and that Z will win is 1/6. Assuming that a dead heat is impossible, find the chance that one of them will win.

add(add(divide(1, 8), divide(1, 12)), divide(1, 6))

divide(n1,n2)|divide(n1,n4)|divide(n1,n6)|add(#0,#1)|add(#3,#2)|

"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 8 + 1 / 12 + 1 / 6 = 3 / 8 answer : d"

general

math_qa__yzSGYngfFWWpais2

The average marks of 25 students in a class is 100. But a student mark is wrongly noted as 60 instead of 10 then find the correct average marks? Answers A) 78 B) 82 C) 98 D) 91 E) 85

<gadget id="calculator">100 * 25</gadget> <output>2_500</output> <gadget id="calculator">2_500 - 60</gadget> <output>2_440</output> <gadget id="calculator">2_440 + 10</gadget> <output>2_450</output> <gadget id="calculator">2_450 / 25</gadget> <output>98</output> <result>C</result>

C

The average marks of 25 students in a class is 100. But a student mark is wrongly noted as 60 instead of 10 then find the correct average marks?

divide(add(subtract(multiply(100, 25), 60), 10), 25)

multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0)|

"correct avg marks = 100 + ( 10 - 60 ) / 25 avg = 100 - 2 = 98 answer is c"

general

math_qa__mcSEkHe54bVPwTgN

What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345? Choose the correct choice: A) 2345 B) 4500 C) 5000 D) 6000 E) 7000

<gadget id="calculator">2 * 1_000</gadget> <output>2_000</output> <gadget id="calculator">3 * 100</gadget> <output>300</output> <gadget id="calculator">2_000 + 300</gadget> <output>2_300</output> <gadget id="calculator">10 * 4</gadget> <output>40</output> <gadget id="calculator">2_300 + 40</gadget> <output>2_340</output> <gadget id="calculator">5 + 2_340</gadget> <output>2_345</output> <result>A</result>

A

What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345?

add(5, add(add(multiply(2, const_1000), multiply(3, const_100)), multiply(const_10, 4)))

multiply(n0,const_1000)|multiply(n1,const_100)|multiply(n2,const_10)|add(#0,#1)|add(#3,#2)|add(n3,#4)

2000 + 300 + 40 + 5 = 2345 answer a

general

math_qa__O2OYb5pZnmqyNWEO

If p and q are positive integers each greater than 1, and 17(p+1)=28(q+1), what is the least possible value of p+q? Pick one. A) 36 B) 42 C) 44 D) 43 E) none

<gadget id="calculator">28 + 17</gadget> <output>45</output> <gadget id="calculator">45 - 2</gadget> <output>43</output> <result>D</result>

D

If p and q are positive integers each greater than 1, and 17(p+1)=28(q+1), what is the least possible value of p+q?

subtract(add(28, 17), const_2)

add(n1,n3)|subtract(#0,const_2)|

"17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 28 / 17 - - > the least positive value of p + 1 is 28 , so the least value of p is 27 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 27 + 16 = 43 . answer : d"

general

math_qa__ugLFaZsWlaBbDq66

What is the area of square field whose side of length 8 m? Choose the correct choice from the following answers. A) 225 B) 64 C) 772 D) 882 E) 21

<gadget id="calculator">8 ** 2</gadget> <output>64</output> <result>B</result>

B

What is the area of square field whose side of length 8 m?

square_area(8)

square_area(n0)|

"8 * 8 = 64 sq m answer : b"

geometry

math_qa__oZARPCjD7csgVoST

A thief is spotted by a policeman from a distance of 225 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken? Choose the correct choice from the following choices A) 350 m B) 200 m C) 400 m D) 900 m E) none of them

<gadget id="calculator">225 * 8</gadget> <output>1_800</output> <gadget id="calculator">10 - 8</gadget> <output>2</output> <gadget id="calculator">1_800 / 2</gadget> <output>900</output> <result>D</result>

D

A thief is spotted by a policeman from a distance of 225 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?

divide(multiply(225, 8), subtract(10, 8))

multiply(n0,n1)|subtract(n2,n1)|divide(#0,#1)|

"relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 225 m / 1000 ) x 1 / 2 hr = 9 / 80 hr . in 9 / 80 hrs , the thief covers a distance of 8 x 9 / 80 km = 9 / 10 km = 900 m answer is d ."

physics

math_qa__WHwcz4d5IiAIpRD9

Mary works 9 hours per day on Monday, Wednesday and Friday, and 5 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $407 per week. How much does she earn in dollars per hour? Select the correct option: A) 12 B) 10 C) 9 D) 8 E) 11

<gadget id="calculator">9 * 3</gadget> <output>27</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">27 + 10</gadget> <output>37</output> <gadget id="calculator">407 / 37</gadget> <output>11</output> <result>E</result>

E

Mary works 9 hours per day on Monday, Wednesday and Friday, and 5 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $407 per week. How much does she earn in dollars per hour?

divide(407, add(multiply(9, const_3), multiply(5, const_2)))

multiply(n0,const_3)|multiply(n1,const_2)|add(#0,#1)|divide(n2,#2)

so , she works 27 hours in 3 days so , she works 10 hours in 2 days so in a week she works 37 hours ( 27 + 10 ) and earns $ 407 so , hourly wage is 407 / 37 = > 11 hence answer will be ( e ) 11

physics

math_qa__scnbgoxA8Cb8y5ic

When a number is divided by 4 &then multiply by 12 the answer is 9 what is the no.? Choose the correct choice from the following options: A) 3 B) 5 C) 5.6 D) 5.7 E) 6.5

<gadget id="calculator">9 / 12</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) * 4</gadget> <output>3</output> <result>A</result>

A

When a number is divided by 4 &then multiply by 12 the answer is 9 what is the no.?

multiply(divide(9, 12), 4)

divide(n2,n1)|multiply(n0,#0)

if $ x $ is the number , x / 4 * 12 = 9 = > 3 x = 9 = > x = 3 a

general

math_qa__w5VstXJ3tr917xlB

A toy store's revenue in November was 3/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January? Select A) 1 / 4 B) 1 / 2 C) 2 / 3 D) 2 E) 4

<gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) + 1</gadget> <output>7/4 = around 1.75</output> <gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(7/4) * (3/5)</gadget> <output>21/20 = around 1.05</output> <gadget id="calculator">(21/20) / 2</gadget> <output>21/40 = around 0.525</output> <gadget id="calculator">1 / (21/40)</gadget> <output>40/21 = around 1.904762</output> <result>D</result>

D

A toy store's revenue in November was 3/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

divide(const_1, divide(multiply(add(divide(3, 4), const_1), divide(3, 5)), const_2))

divide(n0,n3)|divide(n0,n1)|add(#0,const_1)|multiply(#2,#1)|divide(#3,const_2)|divide(const_1,#4)

let dec rev = 100 then nov rev is 3 / 5 ( 100 ) = > 60 therefore jan rev = 3 / 4 ( nov rev ) = 3 / 4 ( 60 ) = > 45 hence dec rev = x * ( nov rev + jan rev ) / 2 100 = x * ( 60 + 45 ) / 2 x = 100 / 52.5 = > 1.90 = 2 ans ) d

general

math_qa__4BT0By4RdYqZtn58

Calculate the average of first 18 even numbers is? Select. A) 21 B) 29 C) 19 D) 14 E) 10

<gadget id="calculator">18 + 1</gadget> <output>19</output> <result>C</result>

C

Calculate the average of first 18 even numbers is?

add(18, const_1)

add(n0,const_1)

explanation : sum of 10 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : option c

general

math_qa__KxLEbaE4kQKAR6Sx

An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 22 gallons of ethanol, how many gallons of fuel A were added? Choose the correct choice from the following answers: A) 160 B) 150 C) 250 D) 80 E) 50

<gadget id="calculator">16 / 100</gadget> <output>4/25 = around 0.16</output> <gadget id="calculator">200 * (4/25)</gadget> <output>32</output> <gadget id="calculator">32 - 22</gadget> <output>10</output> <gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">(4/25) - (3/25)</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">10 / (1/25)</gadget> <output>250</output> <result>C</result>

C

An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 22 gallons of ethanol, how many gallons of fuel A were added?

divide(subtract(multiply(200, divide(16, const_100)), 22), subtract(divide(16, const_100), divide(12, const_100)))

divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|subtract(#0,#1)|subtract(#2,n3)|divide(#4,#3)|

"say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 22 gallons then 0.12 a + 0.16 ( 200 - a ) = 22 - - > a = 250 . answer : c ."

gain

math_qa__s1w69cYZmOsXXSZp

In a class of 36 students 26 play football and play 20 long tennis, if 17 play above, many play neither? Select. A) 7 B) 8 C) 10 D) 12 E) 14

<gadget id="calculator">26 + 20</gadget> <output>46</output> <gadget id="calculator">46 - 17</gadget> <output>29</output> <gadget id="calculator">36 - 29</gadget> <output>7</output> <result>A</result>

A

In a class of 36 students 26 play football and play 20 long tennis, if 17 play above, many play neither?

subtract(36, subtract(add(26, 20), 17))

add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)|

"26 + 20 - 17 = 29 36 - 29 = 7 play neither answer is a"

other

math_qa__59x1XnTkOBZifdPQ

Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2? Choose the correct choice from the following options A) 7 B) 8 C) 9 D) 10 E) 11

<gadget id="calculator">3 + 3</gadget> <output>6</output> <gadget id="calculator">6 + 2</gadget> <output>8</output> <result>B</result>

B

Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2?

add(add(3, 3), 2)

add(n0,n0)|add(n3,#0)|

"p is a positiveeveninteger with apositive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 2 is 6 + 2 = 8 . answer : b ."

general

math_qa__oBcjZLBkLreXx0cr

Dan's age after 18 years will be 5 times his age 6 years ago. What is the present age of Dan? Choose the correct choice from the following answers. A) 8 B) 10 C) 12 D) 14 E) 16

<gadget id="calculator">6 * 5</gadget> <output>30</output> <gadget id="calculator">18 + 30</gadget> <output>48</output> <gadget id="calculator">5 - 1</gadget> <output>4</output> <gadget id="calculator">48 / 4</gadget> <output>12</output> <result>C</result>

C

Dan's age after 18 years will be 5 times his age 6 years ago. What is the present age of Dan?

divide(add(18, multiply(6, 5)), subtract(5, const_1))

multiply(n1,n2)|subtract(n1,const_1)|add(n0,#0)|divide(#2,#1)|

"let dan ' s present age be x . x + 18 = 5 ( x - 6 ) 4 x = 48 x = 12 the answer is c ."

general

math_qa__sjJh8141bywHCy8r

If 5% more is gained by selling an article for Rs. 420 than by selling it for Rs. 380, the cost of the article is? Pick. A) 500 B) 688 C) 200 D) 121 E) 800

<gadget id="calculator">420 - 380</gadget> <output>40</output> <gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">40 / (1/20)</gadget> <output>800</output> <result>E</result>

E

If 5% more is gained by selling an article for Rs. 420 than by selling it for Rs. 380, the cost of the article is?

divide(subtract(420, 380), divide(5, const_100))

divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)

let c . p . be rs . x . then , 5 % of x = 420 - 380 = 40 x / 20 = 40 = > x = 800 answer : e

gain

math_qa__WrFyMYxuf4hqpJFO

Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 72% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere? Choose the correct choice from the following choices. A) 7 B) 11 C) 13 D) 14 E) 38

<gadget id="calculator">72 / 100</gadget> <output>18/25 = around 0.72</output> <gadget id="calculator">39 * (18/25)</gadget> <output>702/25 = around 28.08</output> <gadget id="calculator">(702/25) / 2</gadget> <output>351/25 = around 14.04</output> <result>D</result>

D

Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 72% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

divide(multiply(39, divide(72, const_100)), const_2)

divide(n1,const_100)|multiply(n0,#0)|divide(#1,const_2)|

"maximum number of points on the surface is 72 % * 39 = 28.08 . . . or 28 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 28 points , so at best we can form 14 pairs ( 28 ) . so , answer is ( d )"

geometry

math_qa__qK2ZVaXVRvHe4p6f

The proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? Answers: A) 40.9 % B) 41.9 % C) 42.9 % D) 43.9 % E) 44.9 %

<gadget id="calculator">4 + 5</gadget> <output>9</output> <gadget id="calculator">5 + 6</gadget> <output>11</output> <gadget id="calculator">11 + 9</gadget> <output>20</output> <gadget id="calculator">9 / 20</gadget> <output>9/20 = around 0.45</output> <gadget id="calculator">(9/20) * 100</gadget> <output>45</output> <result>E</result>

E

The proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?

multiply(divide(add(4, 5), add(add(5, 6), add(4, 5))), const_100)

add(n1,n3)|add(n0,n2)|add(#1,#0)|divide(#0,#2)|multiply(#3,const_100)|

"let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 4 / 9 ) ( v / 2 ) + ( 5 / 11 ) ( v / 2 ) = 2 v / 9 + 5 v / 22 = 89 v / 198 . the concentration of alcohol is 89 / 198 = 44.9 % the answer is e ."

general

math_qa__nO78ZzeDwuNMgW8m

A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 24 inches and the width of the wall is 42 inches, what is the length of the wall, in inches? Select the correct option A) 21.4 B) 23.4 C) 25.4 D) 26.4 E) 27.4

<gadget id="calculator">24 ** 2</gadget> <output>576</output> <gadget id="calculator">2 * 576</gadget> <output>1_152</output> <gadget id="calculator">1_152 / 42</gadget> <output>192/7 = around 27.428571</output> <result>E</result>

E

A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 24 inches and the width of the wall is 42 inches, what is the length of the wall, in inches?

divide(multiply(const_2, square_area(24)), 42)

square_area(n0)|multiply(#0,const_2)|divide(#1,n1)|

"since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 24 ^ 2 = 576 . area of rectangle is double of that 2 * 576 = 1152 . now a = lw and we need find w so a / l = w ; 1152 / 42 = 27.4 answer ! answer : e"

geometry

math_qa__tT1NfoEBTA0P0Orz

If 22 men do a work in 55 days, in how many days will 10 men do it? Select. A) 121 B) 123 C) 119 D) 125 E) 127

<gadget id="calculator">22 * 55</gadget> <output>1_210</output> <gadget id="calculator">1_210 / 10</gadget> <output>121</output> <result>A</result>

A

If 22 men do a work in 55 days, in how many days will 10 men do it?

divide(multiply(22, 55), 10)

multiply(n0,n1)|divide(#0,n2)|

"22 * 55 = 10 * x x = 121 days answer : a"

physics

math_qa__lrEcm12Gdon06NAm

The sum of digits of a two digit number is 10,The difference between the digits is 6. Find the number Choose the correct option: A) 85 B) 94 C) 82 D) 72 E) none

<gadget id="calculator">10 + 6</gadget> <output>16</output> <gadget id="calculator">16 / 2</gadget> <output>8</output> <gadget id="calculator">8 * 10</gadget> <output>80</output> <gadget id="calculator">10 - 8</gadget> <output>2</output> <gadget id="calculator">80 + 2</gadget> <output>82</output> <result>C</result>

C

The sum of digits of a two digit number is 10,The difference between the digits is 6. Find the number

add(multiply(divide(add(10, 6), const_2), 10), subtract(10, divide(add(10, 6), const_2)))

add(n0,n1)|divide(#0,const_2)|multiply(n0,#1)|subtract(n0,#1)|add(#2,#3)

description : = > x + y = 10 , x - y = 6 adding these 2 x = 16 = > x = 8 , y = 2 . thus the number is 82 answer c

general

math_qa__dXCVZPa27naVS0Q5

Tough and Tricky questions: Word Problems. A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to decrease his average weekly income to $400 over the 7-week period? Select the correct option A) $ 350 B) $ 400 C) $ 365 D) $ 385 E) $ 375

<gadget id="calculator">7 * 400</gadget> <output>2_800</output> <gadget id="calculator">406 + 413</gadget> <output>819</output> <gadget id="calculator">819 + 420</gadget> <output>1_239</output> <gadget id="calculator">1_239 + 436</gadget> <output>1_675</output> <gadget id="calculator">1_675 + 395</gadget> <output>2_070</output> <gadget id="calculator">2_800 - 2_070</gadget> <output>730</output> <gadget id="calculator">730 / 2</gadget> <output>365</output> <result>C</result>

C

Tough and Tricky questions: Word Problems. A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to decrease his average weekly income to $400 over the 7-week period?

divide(subtract(multiply(7, 400), add(add(add(add(406, 413), 420), 436), 395)), const_2)

add(n1,n2)|multiply(n6,n7)|add(n3,#0)|add(n4,#2)|add(n5,#3)|subtract(#1,#4)|divide(#5,const_2)

official solution : ( c ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 400 over 7 weeks , the salesman would need to earn : $ 400 × 7 = $ 2800 . subtract $ 2070 from $ 2800 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 7 weeks : $ 2800 – $ 2070 = $ 730 . dividing $ 730 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 730 / 2 = $ 365 . the correct answer is choice ( c ) .

general

math_qa__WrMFWPlewYB7cC0R

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 40 miles? Pick A) 258 B) 318 C) 322 D) 324 E) 330

<gadget id="calculator">6 * 4</gadget> <output>24</output> <gadget id="calculator">40 / 10</gadget> <output>4</output> <gadget id="calculator">4 * 60</gadget> <output>240</output> <gadget id="calculator">24 + 240</gadget> <output>264</output> <result>A</result>

A

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 40 miles?

add(multiply(6, const_4), multiply(divide(40, 10), const_60))

divide(n2,n0)|multiply(n1,const_4)|multiply(#0,const_60)|add(#1,#2)|

"to cover 40 miles the man needs ( time ) = ( distance ) / ( rate ) = 40 / 10 = 4 hours = 240 minutes . he will also rest 3 times ( after 10 , 20 , and 30 miles ) , so total resting time = 3 * 6 = 18 minutes . total time = 240 + 18 = 258 minutes . answer : a ."

physics

math_qa__qasfVCfFOVn7l1Bi

While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 4 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files? Answers: A) 2 B) 2.4 C) 2.7 D) 3 E) 3.5

<gadget id="calculator">240 / 12</gadget> <output>20</output> <gadget id="calculator">240 / 4</gadget> <output>60</output> <gadget id="calculator">20 + 60</gadget> <output>80</output> <gadget id="calculator">240 / 80</gadget> <output>3</output> <result>D</result>

D

While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 4 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?

divide(240, add(divide(240, 12), divide(240, 4)))

divide(n0,n1)|divide(n0,n3)|add(#0,#1)|divide(n0,#2)|

"both computers together process files at a rate of 240 / 12 + 240 / 4 = 20 + 60 = 80 files per hour . the time required to process 240 files is 240 / 80 = 3 hours the answer is d ."

physics

math_qa__TeD8A11HD6cFvGC5

Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 72th number in this set? Options. A) 573 B) 608 C) 613 D) 616 E) 621

<gadget id="calculator">72 - 1</gadget> <output>71</output> <gadget id="calculator">71 * 8</gadget> <output>568</output> <gadget id="calculator">568 + 5</gadget> <output>573</output> <result>A</result>

A

Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 72th number in this set?

add(multiply(subtract(72, const_1), 8), 5)

subtract(n2,const_1)|multiply(n0,#0)|add(n1,#1)

the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 72 th number = 8 * ( 72 - 1 ) + 5 = 573 answer = a

general

math_qa__mU3agAVdpsahXe7U

How many positive integers will divide evenly into 190? Choices: A) 4 B) 6 C) 8 D) 12 E) 16

<gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">4 * 2</gadget> <output>8</output> <result>C</result>

C

How many positive integers will divide evenly into 190?

multiply(multiply(add(const_1, const_1), add(const_1, const_1)), add(const_1, const_1))

add(const_1,const_1)|multiply(#0,#0)|multiply(#0,#1)

the question is asking how many factors 190 has . 190 = 2 * 5 * 19 the number of factors is 2 ^ 3 = 8 the answer is c .

general

math_qa__vfFRyO6atIsTgXsg

Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 50 milliliters of solution X to create a solution that is 25 percent alcohol by volume? Choices. A) 150 B) 500 / 3 C) 400 D) 480 E) 600

<gadget id="calculator">25 - 10</gadget> <output>15</output> <gadget id="calculator">30 - 25</gadget> <output>5</output> <gadget id="calculator">15 / 5</gadget> <output>3</output> <gadget id="calculator">3 * 50</gadget> <output>150</output> <result>A</result>

A

Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 50 milliliters of solution X to create a solution that is 25 percent alcohol by volume?

multiply(divide(subtract(25, 10), subtract(30, 25)), 50)

subtract(n3,n0)|subtract(n1,n3)|divide(#0,#1)|multiply(n2,#2)|

"we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 50 then y = 150 answer : a"

general

math_qa__3xogW6Kc1GMwdDtz

The diameter of a garden roller is 1.4 m and it is 3 m long. How much area will it cover in 5 revolutions ? (use π = 22⁄7) Pick one A) 60 m 2 B) 64 m 2 C) 68 m 2 D) 66 m 2 E) none of these

<gadget id="calculator">22 / 7</gadget> <output>22/7 = around 3.142857</output> <gadget id="calculator">3 * (22/7)</gadget> <output>66/7 = around 9.428571</output> <gadget id="calculator">1.4 / 3</gadget> <output>0.466667</output> <gadget id="calculator">(66/7) * 0.466667</gadget> <output>4.400003</output> <gadget id="calculator">4.400003 * 3</gadget> <output>13.200009</output> <gadget id="calculator">5 * 13.200009</gadget> <output>66.000045</output> <result>D</result>

D

The diameter of a garden roller is 1.4 m and it is 3 m long. How much area will it cover in 5 revolutions ? (use π = 22⁄7)

multiply(5, multiply(multiply(multiply(3, divide(22, 7)), divide(1.4, 3)), 3))

divide(n0,n1)|divide(n3,n4)|multiply(#1,n1)|multiply(#0,#2)|multiply(n1,#3)|multiply(n2,#4)|

"required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 ⠁ „ 7 ã — 0.7 ã — 3 = 66 m 2 answer d"

physics

math_qa__rnrBqiLDfPV0nZyI

shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60000 chips ? Pick one A) 14 B) 20 C) 22 D) 24 E) 15

<gadget id="calculator">5_000 + 12_000</gadget> <output>17_000</output> <gadget id="calculator">17_000 + 15_000</gadget> <output>32_000</output> <gadget id="calculator">32_000 + 16_000</gadget> <output>48_000</output> <gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">6 + 2</gadget> <output>8</output> <gadget id="calculator">8 + 4</gadget> <output>12</output> <gadget id="calculator">48_000 / 12</gadget> <output>4_000</output> <gadget id="calculator">60_000 / 4_000</gadget> <output>15</output> <result>E</result>

E

shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60000 chips ?

divide(60000, divide(add(add(add(5000, 12000), 15000), 16000), add(add(add(2, 4), 2), 4)))

add(n2,n5)|add(n1,n4)|add(n8,#0)|add(n1,#1)|add(n11,#2)|add(n4,#3)|divide(#4,#5)|divide(n16,#6)

for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e

general

math_qa__H6Lgn1nNAQbTuOjw

3/4 of 1/2 of 2/5 of 5020 = ? Pick: A) 392 B) 229 C) 753 D) 493 E) 540

<gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(3/4) * (1/2)</gadget> <output>3/8 = around 0.375</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(3/8) * (2/5)</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">(3/20) * 5_020</gadget> <output>753</output> <result>C</result>

C

3/4 of 1/2 of 2/5 of 5020 = ?

multiply(multiply(multiply(divide(3, 4), divide(1, 2)), divide(2, 5)), 5020)

divide(n3,n5)|divide(n0,n1)|divide(n2,n3)|multiply(#1,#2)|multiply(#0,#3)|multiply(n6,#4)|

"c 753 ? = 5020 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 753"

general

math_qa__3rXiGzOE5Z58vgJO

A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 360 m long platform? Pick one: A) 19 B) 27 C) 29 D) 48 E) 28

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">(5/18) * 36</gadget> <output>10</output> <gadget id="calculator">10 * 12</gadget> <output>120</output> <gadget id="calculator">360 + 120</gadget> <output>480</output> <gadget id="calculator">480 / 10</gadget> <output>48</output> <result>D</result>

D

A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 360 m long platform?

divide(add(360, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36))

multiply(n0,const_0_2778)|multiply(n1,#0)|add(n2,#1)|divide(#2,#0)|

"let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 360 ) / 36 * 5 / 18 = 48 min . answer : d"

physics

math_qa__7IqnfQSO5CCZSjSf

an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many t ways can the assembly line be arranged ? Pick one: A) 120 B) 240 C) 360 D) 480 E) 720

<gadget id="calculator">factorial(4)</gadget> <output>24</output> <gadget id="calculator">factorial(6)</gadget> <output>720</output> <gadget id="calculator">720 / 24</gadget> <output>30</output> <gadget id="calculator">factorial(2)</gadget> <output>2</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <gadget id="calculator">24 * 15</gadget> <output>360</output> <result>C</result>

C

an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many t ways can the assembly line be arranged ?

multiply(factorial(const_4), divide(divide(factorial(6), factorial(const_4)), factorial(const_2)))

factorial(n0)|factorial(const_4)|factorial(const_2)|divide(#0,#1)|divide(#3,#2)|multiply(#4,#1)

c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want t = 6 c ! / 2 - > 720 / 2 = 360

general

math_qa__BZYiU5y0y9IzGUbU

The average marks of a class of 30 students is 30 and that of another class of 50 students is 60. Find the average marks of all the students? Pick one: A) 52.5 B) 52.9 C) 52.1 D) 48.75 E) 42.5

<gadget id="calculator">30 * 30</gadget> <output>900</output> <gadget id="calculator">50 * 60</gadget> <output>3_000</output> <gadget id="calculator">900 + 3_000</gadget> <output>3_900</output> <gadget id="calculator">30 + 50</gadget> <output>80</output> <gadget id="calculator">3_900 / 80</gadget> <output>195/4 = around 48.75</output> <result>D</result>

D

The average marks of a class of 30 students is 30 and that of another class of 50 students is 60. Find the average marks of all the students?

divide(add(multiply(30, 30), multiply(50, 60)), add(30, 50))

add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)|

"sum of the marks for the class of 30 students = 30 * 30 = 900 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 900 + 3000 = 3900 average marks of all the students = 3900 / 80 = 48.75 answer : d"

general

math_qa__kRl3OuUw0IBmI8hU

An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that the drawn ball are 2 blue and 1 red? Choose the most appropriate option: A) 25 / 323 B) 21 / 969 C) 28 / 989 D) 74 / 879 E) 23 / 589

<gadget id="calculator">binomial(6, 2)</gadget> <output>15</output> <gadget id="calculator">binomial(5, 1)</gadget> <output>5</output> <gadget id="calculator">15 * 5</gadget> <output>75</output> <gadget id="calculator">5 + 6</gadget> <output>11</output> <gadget id="calculator">11 + 8</gadget> <output>19</output> <gadget id="calculator">binomial(19, 3)</gadget> <output>969</output> <gadget id="calculator">75 / 969</gadget> <output>25/323 = around 0.077399</output> <result>A</result>

A

An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that the drawn ball are 2 blue and 1 red?

divide(multiply(choose(6, 2), choose(5, 1)), choose(add(add(5, 6), 8), 3))

add(n0,n1)|choose(n1,n4)|choose(n0,n5)|add(n2,#0)|multiply(#1,#2)|choose(#3,n3)|divide(#4,#5)|

"sample space = no . of ways 3 balls were drawn from urn = 19 c 3 = 969 no . ways 2 blue balls and 1 red were drawn from bag = 6 c 2 * 5 c 1 = 75 probability = 75 / 969 = 25 / 323 ans - a"

probability

math_qa__igDvgNzszrq72Tbs

John Purchased 1300 large bottles at $1.89 per bottle and 750 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle? Choose the correct option. A) $ 1.63 B) $ 1.64 C) $ 1.68 D) $ 1.70 E) $ 1.76

<gadget id="calculator">1_300 * 1.89</gadget> <output>2_457</output> <gadget id="calculator">750 * 1.38</gadget> <output>1_035</output> <gadget id="calculator">2_457 + 1_035</gadget> <output>3_492</output> <gadget id="calculator">1_300 + 750</gadget> <output>2_050</output> <gadget id="calculator">3_492 / 2_050</gadget> <output>1_746/1_025 = around 1.703415</output> <result>D</result>

D

John Purchased 1300 large bottles at $1.89 per bottle and 750 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle?

divide(add(multiply(1300, 1.89), multiply(750, 1.38)), add(1300, 750))

add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)|

"( 1300 * 1.89 + 750 * 1.38 ) / ( 1300 + 750 ) = ~ 1.70 option ( d )"

general

math_qa__OMqwrAJ9Bs5WaXAg

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours Q will it take if Jim types the report and Mary edits it immediately after he is done? Pick: A) 41.4 B) 34.1 C) 13.4 D) 12.4 E) 10.8

<gadget id="calculator">1 / 12.5</gadget> <output>0.08</output> <gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">0.08 - (1/30)</gadget> <output>0.046667</output> <gadget id="calculator">1 / 0.046667</gadget> <output>21.428418</output> <gadget id="calculator">1 / 7.5</gadget> <output>0.133333</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">0.133333 - (1/12)</gadget> <output>0.05</output> <gadget id="calculator">1 / 0.05</gadget> <output>20</output> <gadget id="calculator">21.428418 + 20</gadget> <output>41.428418</output> <result>A</result>

A

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours Q will it take if Jim types the report and Mary edits it immediately after he is done?

add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12))))

divide(const_1,n0)|divide(const_1,n2)|divide(const_1,n1)|divide(const_1,n3)|subtract(#0,#1)|subtract(#2,#3)|inverse(#4)|inverse(#5)|add(#6,#7)

break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many q hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a .

physics

math_qa__6sTLm2xwwMGhOST7

A sports equipment store sold ping pong rackets for a total of $735. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold? Options. A) 50 B) 100 C) 490 D) 500 E) 75

<gadget id="calculator">735 / 9.8</gadget> <output>75</output> <result>E</result>

E

A sports equipment store sold ping pong rackets for a total of $735. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold?

divide(735, 9.8)

divide(n0,n1)|

"average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 735 x = 75 pairs were sold . answer : e"

general

math_qa__bpStm643M4QON2eW

The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? Choose the correct choice from the following answers. A) 150 B) 185 C) 190 D) 210 E) 220

<gadget id="calculator">200 - 15</gadget> <output>185</output> <result>B</result>

B

The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?

subtract(200, 15)

subtract(n1,n2)|

"185 answer is b"

general

math_qa__1X4EqgqGsW7wbcZf

If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is? Pick one: A) 150 m B) 899 m C) 200 m D) 166 m E) 187 m

<gadget id="calculator">600 / 2</gadget> <output>300</output> <gadget id="calculator">300 - 150</gadget> <output>150</output> <result>A</result>

A

If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is?

subtract(divide(600, const_2), 150)

divide(n0,const_2)|subtract(#0,n1)|

"2 ( l + 150 ) = 600 = > l = 150 m answer : a"

physics

math_qa__5HuBrgGRKvM2QWNB

A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a trolley that is running with a speed of 12 km/hr in the direction opposite to that in which the train is going? Choose the correct option A) 4.31 B) 6.75 C) 7.92 D) 5.5 E) 6.5

<gadget id="calculator">60 + 12</gadget> <output>72</output> <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">110 / 20</gadget> <output>11/2 = around 5.5</output> <result>D</result>

D

A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a trolley that is running with a speed of 12 km/hr in the direction opposite to that in which the train is going?

divide(110, multiply(add(60, 12), const_0_2778))

add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)

speed of train relative to trolley = 60 + 12 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the trolley = 110 * 1 / 20 = 5.5 sec . answer : d

physics

math_qa__vUNzQcuSheFJxjo3

In a certain Parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle? Pick one. A) 75 B) 80 C) 85 D) 90 E) 95

<gadget id="calculator">3_600 / 10</gadget> <output>360</output> <gadget id="calculator">10 * 2</gadget> <output>20</output> <gadget id="calculator">360 - 20</gadget> <output>340</output> <gadget id="calculator">340 / 4</gadget> <output>85</output> <result>C</result>

C

In a certain Parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle?

divide(subtract(divide(const_3600, const_10), multiply(10, const_2)), const_4)

divide(const_3600,const_10)|multiply(n0,const_2)|subtract(#0,#1)|divide(#2,const_4)|

"in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 10 ) = 180 - - > x = 85 . answer : c ."

geometry

math_qa__37YD9vOR8OtDM1oq

The average of 10 numbers was calculated as 18. It is discovered later on that while calculating the average, one number, namely 66, was incorrectly read as 26. What is the correct average? Choose the correct choice A) 20 B) 21 C) 22 D) 23 E) 24

<gadget id="calculator">10 * 18</gadget> <output>180</output> <gadget id="calculator">66 - 26</gadget> <output>40</output> <gadget id="calculator">180 + 40</gadget> <output>220</output> <gadget id="calculator">220 / 10</gadget> <output>22</output> <result>C</result>

C

The average of 10 numbers was calculated as 18. It is discovered later on that while calculating the average, one number, namely 66, was incorrectly read as 26. What is the correct average?

divide(add(multiply(10, 18), subtract(66, 26)), 10)

multiply(n0,n1)|subtract(n2,n3)|add(#0,#1)|divide(#2,n0)|

"10 * 18 - 26 + 66 = 220 220 / 10 = 22 the answer is c ."

general

math_qa__TwTJgB5j1ecS2EAI

Each child has 5 crayons and 14 apples. If there are 10 children, how many crayons are there in total? Pick one. A) 22 B) 65 C) 12 D) 36 E) 50

<gadget id="calculator">10 * 5</gadget> <output>50</output> <result>E</result>

E

Each child has 5 crayons and 14 apples. If there are 10 children, how many crayons are there in total?

multiply(10, 5)

multiply(n0,n2)|

5 * 10 = 50 . answer is e .

general

math_qa__roycKpkqIEkhn43g

What is the area of square field whose side of length 7 m? Select: A) 225 B) 662 C) 772 D) 882 E) 49

<gadget id="calculator">7 ** 2</gadget> <output>49</output> <result>E</result>

E

What is the area of square field whose side of length 7 m?

square_area(7)

square_area(n0)|

"7 * 7 = 49 sq m answer : e"

geometry

math_qa__bb8Iiy08sLUZBfnu

how many integers between 1 and 1050 are divisible by 10 , 25 , and 35 ? Choose the most appropriate option: A) 4 B) 5 C) 6 D) 7 E) 3

<gadget id="calculator">lcm(10, 25)</gadget> <output>50</output> <gadget id="calculator">lcm(50, 35)</gadget> <output>350</output> <gadget id="calculator">1_050 / 350</gadget> <output>3</output> <result>E</result>

E

how many integers between 1 and 1050 are divisible by 10 , 25 , and 35 ?

divide(1050, lcm(lcm(10, 25), 35))

lcm(n2,n3)|lcm(n4,#0)|divide(n1,#1)

prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e

general

math_qa__b7n4Z7xPi5hbSKp9

A cycle is bought for Rs.900 and sold for Rs.1440, find the gain percent? Select A) 39 % B) 20 % C) 23 % D) 74 % E) 60 %

<gadget id="calculator">1_440 - 900</gadget> <output>540</output> <gadget id="calculator">540 / 900</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 100</gadget> <output>60</output> <result>E</result>

E

A cycle is bought for Rs.900 and sold for Rs.1440, find the gain percent?

multiply(divide(subtract(1440, 900), 900), const_100)

subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|

"900 - - - - 540 100 - - - - ? = > 60 % answer : e"

gain

math_qa__3pdFcy4HbAWRUqf9

A and B can finish a work in 7 days and 8 days respectively.if both do work one day and leave one day.and A start the work then in how much days work will finish? Choose the correct choice from the following answers A) 52 / 7 B) 8 C) 14 / 2 D) 6 E) 43 / 6

<gadget id="calculator">1 / 7</gadget> <output>1/7 = around 0.142857</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">1 - (1/8)</gadget> <output>7/8 = around 0.875</output> <gadget id="calculator">(1/7) / (7/8)</gadget> <output>8/49 = around 0.163265</output> <gadget id="calculator">1 / (8/49)</gadget> <output>49/8 = around 6.125</output> <gadget id="calculator">1 + (49/8)</gadget> <output>57/8 = around 7.125</output> <result>A</result>

A

A and B can finish a work in 7 days and 8 days respectively.if both do work one day and leave one day.and A start the work then in how much days work will finish?

add(const_1, inverse(divide(divide(const_1, 7), subtract(const_1, divide(const_1, 8)))))

divide(const_1,n0)|divide(const_1,n1)|subtract(const_1,#1)|divide(#0,#2)|inverse(#3)|add(#4,const_1)

( a + b ) work in 2 days = [ 1 / 7 + 1 / 8 ] = 15 / 56 ( a + b ) work in 6 days = 45 / 56 now , the turn of a , work of a in 1 day = 1 / 7 . till now completed work = [ 45 / 56 + 1 / 7 ] = 53 / 56 , remaining work = [ 1 - 53 / 56 ] = 3 / 56 now , turn of b , 1 / 8 work b do in 1 day so , 3 / 56 part of work b do = [ 8 * 3 / 56 ] = 3 / 7 days total time taken = 6 + 1 + 3 / 7 = 52 / 7 days answer a

physics

math_qa__1CcqRv3NFT85pILv

5 pumps, working 9 hours a day, can empty a tank in 3 days. How many hours a day should 6 pumps work in order to empty the tank in 1 day? Choose the correct choice from the following options. A) 20 hours B) 22.5 hours C) 23 hours D) 23.5 hours E) 24 hours

<gadget id="calculator">5 * 9</gadget> <output>45</output> <gadget id="calculator">45 * 3</gadget> <output>135</output> <gadget id="calculator">135 / 6</gadget> <output>45/2 = around 22.5</output> <result>B</result>

B

5 pumps, working 9 hours a day, can empty a tank in 3 days. How many hours a day should 6 pumps work in order to empty the tank in 1 day?

divide(multiply(multiply(5, 9), 3), 6)

multiply(n0,n1)|multiply(n2,#0)|divide(#1,n3)|

"let the required hours needed be x more pumps , less hours ( indirect proportion ) more days , less hours ( indirect proportion ) hence we can write as ( pumps ) 5 : 6 } : : x : 9 ( days ) 3 : 1 = > 5 * 3 * 9 = 6 * 1 * x = > x = 45 / 2 = > 22.5 answer : b"

physics

math_qa__SgxGhv5Va46mdVZH

If the average (arithmetic mean) of (2a+16) and (3a-8) is 79, what is the value of a? Choices. A) 25 B) 30 C) 28 D) 36 E) 42

<gadget id="calculator">79 * 2</gadget> <output>158</output> <gadget id="calculator">16 - 8</gadget> <output>8</output> <gadget id="calculator">158 - 8</gadget> <output>150</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">150 / 5</gadget> <output>30</output> <result>B</result>

B

If the average (arithmetic mean) of (2a+16) and (3a-8) is 79, what is the value of a?

divide(subtract(multiply(79, 2), subtract(16, 8)), add(2, 3))

add(n0,n2)|multiply(n0,n4)|subtract(n1,n3)|subtract(#1,#2)|divide(#3,#0)|

"( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 79 a = 30 the answer is b ."

general

math_qa__8eg1SpxFfrWB9cAy

We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out? Choose the correct choice from the following answers: A) 5 B) 6 C) 7 D) 8 E) 9

<gadget id="calculator">3 - 2</gadget> <output>1</output> <gadget id="calculator">3 * 12</gadget> <output>36</output> <gadget id="calculator">2 * 18</gadget> <output>36</output> <gadget id="calculator">36 + 36</gadget> <output>72</output> <gadget id="calculator">504 / 72</gadget> <output>7</output> <gadget id="calculator">1 * 7</gadget> <output>7</output> <result>C</result>

C

We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out?

multiply(subtract(3, 2), divide(504, add(multiply(3, 12), multiply(2, 18))))

multiply(n0,n2)|multiply(n1,n3)|subtract(n2,n3)|add(#0,#1)|divide(n4,#3)|multiply(#4,#2)|

"let x be the number of canoes . then 2 x / 3 is the number of kayaks . 12 x + ( 2 x / 3 ) * 18 = 504 12 x + 12 x = 504 24 x = 504 x = 21 ( canoes ) 2 x / 3 = 14 ( kayaks ) there were 21 - 14 = 7 more canoes rented out . the answer is c ."

general

math_qa__zji6owisK1HyT67x

The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ? Choose the correct choice: A) 96 B) 106 C) 122 D) 116 E) 122

<gadget id="calculator">20 + 1</gadget> <output>21</output> <gadget id="calculator">4 + 32</gadget> <output>36</output> <gadget id="calculator">21 * 36</gadget> <output>756</output> <gadget id="calculator">20 * 32</gadget> <output>640</output> <gadget id="calculator">756 - 640</gadget> <output>116</output> <result>D</result>

D

The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?

subtract(multiply(add(20, const_1), add(4, 32)), multiply(20, 32))

add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|

"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 4 = 36 runs total runs = new avg x new no . of innings = 36 * 21 = 756 runs made in the 11 th inning = 756 - 640 = 116 answer : d"

general

math_qa__LMVcaWXYB4JUlFbS

A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability R that a + b is prime? Choose the correct choice from the following answers A) 0 B) 1 / 12 C) 5 / 12 D) 7 / 18 E) 4 / 9

<gadget id="calculator">12 + 3</gadget> <output>15</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/6) ** 2</gadget> <output>1/36 = around 0.027778</output> <gadget id="calculator">15 * (1/36)</gadget> <output>5/12 = around 0.416667</output> <result>C</result>

C

A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability R that a + b is prime?

multiply(add(const_12, const_3), power(divide(1, 6), const_2))

add(const_12,const_3)|divide(n0,n1)|power(#1,const_2)|multiply(#0,#2)

total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes r = 15 / 36 . answer : c .

general

math_qa__17IFYAgdVcAii6tX

X can do a piece of work in 8hours. Y and Z together can do it in 6 hours, while X and Z together can do it in 4 hours. How long will Y alone take to do it? Choices: A) 24 hours B) 20 hours C) 34 hours D) 12 hours E) 10 hours

<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/4) - (1/8)</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/6) - (1/8)</gadget> <output>1/24 = around 0.041667</output> <gadget id="calculator">1 / (1/24)</gadget> <output>24</output> <result>A</result>

A

X can do a piece of work in 8hours. Y and Z together can do it in 6 hours, while X and Z together can do it in 4 hours. How long will Y alone take to do it?

inverse(subtract(inverse(6), subtract(inverse(4), inverse(8))))

inverse(n1)|inverse(n2)|inverse(n0)|subtract(#1,#2)|subtract(#0,#3)|inverse(#4)

x ' s 1 hour work = 1 / 8 ( y + z ) ' s 1 hour work = 1 / 6 ( x + z ) ' s 1 hour work = 1 / 4 ( x + y + z ) ' s 1 hour work = ( 1 / 8 + 1 / 6 ) = 7 / 24 y ' s 1 hour ' s work = ( 7 / 24 - 1 / 4 ) = 1 / 24 y alone will take 24 hours to do the work . correct option is a

physics

math_qa__iEDsCThYMhfNbFIa

A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.13000 after a year? Options: A) 3630 B) 3900 C) 8828 D) 2387 E) 2813

<gadget id="calculator">6_300 + 4_200</gadget> <output>10_500</output> <gadget id="calculator">10_500 + 10_500</gadget> <output>21_000</output> <gadget id="calculator">6_300 / 21_000</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) * 13_000</gadget> <output>3_900</output> <result>B</result>

B

A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.13000 after a year?

multiply(divide(6300, add(add(6300, 4200), 10500)), 13000)

add(n0,n1)|add(n2,#0)|divide(n0,#1)|multiply(n3,#2)|

"6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 13000 = 3900 answer : b"

gain

math_qa__SUS8CmVXIgL9Yluv

If two students starting from same point, walking in the opposite directions with 6km/hr and 9km/hr as average speeds respectively. Then the distance between them after 4 hours is? Choose the correct choice from the following options A) 65 km B) 55 km C) 15 km D) 60 km E) 75 km

<gadget id="calculator">6 * 4</gadget> <output>24</output> <gadget id="calculator">9 * 4</gadget> <output>36</output> <gadget id="calculator">24 + 36</gadget> <output>60</output> <result>D</result>

D

If two students starting from same point, walking in the opposite directions with 6km/hr and 9km/hr as average speeds respectively. Then the distance between them after 4 hours is?

add(multiply(6, 4), multiply(9, 4))

multiply(n0,n2)|multiply(n1,n2)|add(#0,#1)

explanation : total distance = distance traveled by person a + distance traveled by person b = ( 6 × 4 ) + ( 9 × 4 ) = 24 + 36 = 60 km answer : d

physics

math_qa__eDUk0uDUo50KSNFo

Dacid obtained 51, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Choose the correct choice from the following. A) 29 B) 38 C) 39 D) 70 E) 75

<gadget id="calculator">51 + 65</gadget> <output>116</output> <gadget id="calculator">116 + 82</gadget> <output>198</output> <gadget id="calculator">198 + 67</gadget> <output>265</output> <gadget id="calculator">265 + 85</gadget> <output>350</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">350 / 5</gadget> <output>70</output> <result>D</result>

D

Dacid obtained 51, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?

divide(add(add(add(add(51, 65), 82), 67), 85), divide(const_10, const_2))

add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|

"average = ( 51 + 65 + 82 + 67 + 85 ) / 5 = 70 answer : d"

general

math_qa__OlzSKTFG0OG345K0

In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 23 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. Select A) 9 / 8 B) 4 / 1 C) 2 / 3 D) 3 / 4 E) 3 / 2

<gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">45 / 5</gadget> <output>9</output> <gadget id="calculator">45 - 9</gadget> <output>36</output> <gadget id="calculator">9 + 23</gadget> <output>32</output> <gadget id="calculator">36 / 32</gadget> <output>9/8 = around 1.125</output> <result>A</result>

A

In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 23 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.

divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 23))

add(n1,n2)|divide(n0,#0)|add(n3,#1)|subtract(n0,#1)|divide(#3,#2)|

"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 23 ) = 36 / 32 = 9 / 8 . answer : a ."

general

math_qa__r3XlyXREmHlLgzA2

70 percent of the members of a study group are women, and 40 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer? Choose one: A) 0.28 B) 0.27 C) 0.25 D) 0.32 E) 0.35

<gadget id="calculator">5 * 5</gadget> <output>25</output> <gadget id="calculator">25 * 4</gadget> <output>100</output> <gadget id="calculator">70 / 100</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(7/10) * (2/5)</gadget> <output>7/25 = around 0.28</output> <result>A</result>

A

70 percent of the members of a study group are women, and 40 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?

multiply(divide(70, multiply(multiply(const_5, const_5), const_4)), divide(40, multiply(multiply(const_5, const_5), const_4)))

multiply(const_5,const_5)|multiply(#0,const_4)|divide(n0,#1)|divide(n1,#1)|multiply(#2,#3)|

"say there are 100 people in that group , then there would be 0.7 * 0.40 * 100 = 28 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 28 / 100 . answer : a"

gain

math_qa__yopqOFBSKUCAJrq7

The cost price of a radio is Rs.1500 and it was sold for Rs.1260, find the loss %? Choose the correct answer. A) 18 B) 16 C) 26 D) 17 E) 11

<gadget id="calculator">1_500 - 1_260</gadget> <output>240</output> <gadget id="calculator">240 / 1_500</gadget> <output>4/25 = around 0.16</output> <gadget id="calculator">(4/25) * 100</gadget> <output>16</output> <result>B</result>

B

The cost price of a radio is Rs.1500 and it was sold for Rs.1260, find the loss %?

multiply(divide(subtract(1500, 1260), 1500), const_100)

subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|

"explanation : 1500 - - - - 240 100 - - - - ? = > 16 % answer : b"

gain

math_qa__FPM4wz01NPWDbNyp

Find the area of a cuboid of length 12cm , breadth 6 cm . and height 10cm. Choose the correct choice from the following: A) 400 cm cube B) 410 cm cube C) 720 cm cube D) 730 cm cube E) 480 cm cube

<gadget id="calculator">12 * 6</gadget> <output>72</output> <gadget id="calculator">72 * 10</gadget> <output>720</output> <result>C</result>

C

Find the area of a cuboid of length 12cm , breadth 6 cm . and height 10cm.

multiply(multiply(12, 6), 10)

multiply(n0,n1)|multiply(n2,#0)|

"area of a cuboid = lxbxh = 12 cm x 6 cm x 10 cm = 720 cm cube answer : c"

physics

math_qa__WxUQmF4vDDq4kzVu

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. 1900. The difference between the profit shares of A and C is? Choose the correct choice from the following answers A) 288 B) 760 C) 155 D) 600 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_900</gadget> <output>760</output> <result>B</result>

B

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. 1900. The difference between the profit shares of A and C is?

multiply(subtract(divide(12000, 10000), divide(8000, 10000)), 1900)

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 . 1900 = > 5 parts out of 15 parts is rs . 1900 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1900 ) = rs . 760 answer : b"

gain

math_qa__9BZCvyVuk226mRNb

Machine A can finish a job in 6 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 8 hours. How many hours will it take for A, B, and С together to finish the job? Choose the correct choice from the following answers: A) 6 / 5 B) 7 / 4 C) 8 / 3 D) 9 / 2 E) 12 / 5

<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(1/6) + (1/12)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/4) + (1/8)</gadget> <output>3/8 = around 0.375</output> <gadget id="calculator">1 / (3/8)</gadget> <output>8/3 = around 2.666667</output> <result>C</result>

C

Machine A can finish a job in 6 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 8 hours. How many hours will it take for A, B, and С together to finish the job?

inverse(add(add(inverse(6), inverse(12)), inverse(8)))

inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4)

the combined rate is 1 / 6 + 1 / 12 + 1 / 8 = 9 / 24 of the job per hour . the time to complete the job is 24 / 9 = 8 / 3 hours . the answer is c .

physics

math_qa__dEjdIo86xbzsV2Vj

The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? Choose the correct choice from the following answers. A) 75 B) 66 C) 55 D) 44 E) 12

<gadget id="calculator">150 / 2</gadget> <output>75</output> <result>A</result>

A

The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?

divide(150, const_2)

divide(n0,const_2)

let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : a

general

math_qa__SEZwJq7X1GINrGPX

A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? Choose the correct choice from the following options. A) rs . 1148 B) rs . 1160 C) rs . 1190 D) rs . 1202 E) none

<gadget id="calculator">100 - 18</gadget> <output>82</output> <gadget id="calculator">82 * 1_400</gadget> <output>114_800</output> <gadget id="calculator">114_800 / 100</gadget> <output>1_148</output> <result>A</result>

A

A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle?

divide(multiply(subtract(const_100, 18), 1400), const_100)

subtract(const_100,n1)|multiply(n0,#0)|divide(#1,const_100)|

"solution s . p = 82 % of rs . 1400 = rs . ( 82 / 100 × 1400 ) rs . 1148 . answer a"

gain

math_qa__WtlzoN3n3VcYwrVu

At a contest with 3000 participants, 1/2 of the people are aged 8 to 14. Next year, the number of people aged 8 to 14 will increase by 1/6. After this change, what percentage of the total 3000 people will the 8- to 14-year-olds represent? Choose the correct option A) 53.33 % B) 50 % C) 58.33 % D) 55.33 % E) 68 %

<gadget id="calculator">3_000 / 2</gadget> <output>1_500</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 + (1/6)</gadget> <output>7/6 = around 1.166667</output> <gadget id="calculator">1_500 * (7/6)</gadget> <output>1_750</output> <gadget id="calculator">1_750 / 3_000</gadget> <output>7/12 = around 0.583333</output> <gadget id="calculator">(7/12) * 100</gadget> <output>175/3 = around 58.333333</output> <result>C</result>

C

At a contest with 3000 participants, 1/2 of the people are aged 8 to 14. Next year, the number of people aged 8 to 14 will increase by 1/6. After this change, what percentage of the total 3000 people will the 8- to 14-year-olds represent?

multiply(divide(multiply(divide(3000, 2), add(1, divide(1, 6))), 3000), const_100)

divide(n1,n8)|divide(n0,n2)|add(#0,n1)|multiply(#2,#1)|divide(#3,n0)|multiply(#4,const_100)|

"i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 3000 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 6 , we are multiplying it by 1 + 1 / 6 = 7 / 6 , so the answer here must be ( 1 / 2 ) * ( 7 / 6 ) = 7 / 12 = 58.33 % . answer : c"

general

math_qa__gGc60le30anythay

If Henry were to add 7 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full? Choose the correct choice: A) 25 B) 40 C) 64 D) 80 E) 56

<gadget id="calculator">7 / 8</gadget> <output>7/8 = around 0.875</output> <gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(7/8) - (3/4)</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">1 / (1/8)</gadget> <output>8</output> <gadget id="calculator">7 * 8</gadget> <output>56</output> <result>E</result>

E

If Henry were to add 7 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?

multiply(7, divide(const_1, subtract(divide(7, 8), divide(3, 4))))

divide(n3,n4)|divide(n1,n2)|subtract(#0,#1)|divide(const_1,#2)|multiply(n0,#3)|

"7 / 8 x - 3 / 4 x = 7 galls 1 / 8 * x = 7 gallons x = 56 gallons answer e"

general

math_qa__ZDhBoU8DmX88n3dl

The average weight of 16 boys in a class is 50.25 kgs and that of the remaining 8 boys is 45.15 kgs. Find the average weight of all the boys in the class. Choose the correct answer: A) 47.55 kgs B) 48 kgs C) 48.55 kgs D) 49.25 kgs E) none of these

<gadget id="calculator">16 * 50.25</gadget> <output>804</output> <gadget id="calculator">8 * 45.15</gadget> <output>361.2</output> <gadget id="calculator">804 + 361.2</gadget> <output>1_165.2</output> <gadget id="calculator">16 + 8</gadget> <output>24</output> <gadget id="calculator">1_165.2 / 24</gadget> <output>48.55</output> <result>C</result>

C

The average weight of 16 boys in a class is 50.25 kgs and that of the remaining 8 boys is 45.15 kgs. Find the average weight of all the boys in the class.

divide(add(multiply(16, 50.25), multiply(8, 45.15)), add(16, 8))

add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)|

"solution required average = ( 50.25 x 16 + 45.15 x 8 / 16 + 8 ) = ( 804 + 361.20 / 24 ) = 1165.20 / 24 = 48.55 answer c"

general

math_qa__To4RTBDyow6f0Z6y

Solution X is 40% chemical A and 60% chemical B by volume. Solution Y is 50% chemical A and 50% chemical B by volume. If a mixture of X and Y is 47% chemical A, what percent of the mixture is Solution X? Pick one: A) 15 % B) 20 % C) 25 % D) 30 % E) 35 %

<gadget id="calculator">50 - 47</gadget> <output>3</output> <gadget id="calculator">47 - 40</gadget> <output>7</output> <gadget id="calculator">3 / 7</gadget> <output>3/7 = around 0.428571</output> <gadget id="calculator">(3/7) + 1</gadget> <output>10/7 = around 1.428571</output> <gadget id="calculator">(3/7) / (10/7)</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) * 100</gadget> <output>30</output> <result>D</result>

D

Solution X is 40% chemical A and 60% chemical B by volume. Solution Y is 50% chemical A and 50% chemical B by volume. If a mixture of X and Y is 47% chemical A, what percent of the mixture is Solution X?

multiply(divide(divide(subtract(50, 47), subtract(47, 40)), add(divide(subtract(50, 47), subtract(47, 40)), const_1)), const_100)

subtract(n2,n4)|subtract(n4,n0)|divide(#0,#1)|add(#2,const_1)|divide(#2,#3)|multiply(#4,const_100)|

"the volume of the mixture be x + y . 0.4 x + 0.5 y = 0.47 ( x + y ) x = 3 y / 7 x / ( x + y ) = ( 3 y / 7 ) / ( 10 y / 7 ) = 3 / 10 = 30 % . the answer is d ."

gain

math_qa__KXN3uvlAZxf6BdPy

A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 30.00? Choose the correct answer: A) $ 10.00 B) $ 11.20 C) $ 14.40 D) $ 16.80 E) $ 18.00

<gadget id="calculator">100 - 20</gadget> <output>80</output> <gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">100 - 30</gadget> <output>70</output> <gadget id="calculator">70 / 100</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">(7/10) * 30</gadget> <output>21</output> <gadget id="calculator">(4/5) * 21</gadget> <output>84/5 = around 16.8</output> <result>D</result>

D

A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 30.00?

multiply(divide(subtract(const_100, 20), const_100), multiply(divide(subtract(const_100, 30), const_100), 30.00))

subtract(const_100,n2)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(n3,#3)|multiply(#2,#4)|

"for retail price = $ 30 first maximum discounted price = 30 - 30 % of 30 = 30 - 9 = 21 price after additional discount of 20 % = 21 - 20 % of 21 = 21 - 4.2 = 16.8 answer : option d"

gain

math_qa__KtmuWNpyqbwAyFc7

16 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area? Pick one: A) 2 √ 2 B) 4 C) 5 D) 4 √ 2 E) none of these

<gadget id="calculator">16 / 4</gadget> <output>4</output> <result>B</result>

B

16 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?

divide(16, const_4)

divide(n0,const_4)|

"area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 16 = > x / 360 * 2 * pi * r + 2 r = 16 = > 2 a / r + 2 r = 16 = > a = ( r 16 - 2 r ^ 2 ) / 2 = r 8 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 8 - 2 r = 0 r = 4 b"

geometry

math_qa__ek8O8YOWpu7SI5bl

Amar takes as much time in running 21 meters as a car takes in covering 54 meters. What will be the distance covered by Amar during the time the car covers 1.8 km? Select the correct option. A) 700 m B) 500 m C) 670 m D) 700 m E) 640 m

<gadget id="calculator">1.8 * 1_000</gadget> <output>1_800</output> <gadget id="calculator">21 * 1_800</gadget> <output>37_800</output> <gadget id="calculator">37_800 / 54</gadget> <output>700</output> <result>D</result>

D

Amar takes as much time in running 21 meters as a car takes in covering 54 meters. What will be the distance covered by Amar during the time the car covers 1.8 km?

divide(multiply(21, multiply(1.8, const_1000)), 54)

multiply(n2,const_1000)|multiply(n0,#0)|divide(#1,n1)|

"distance covered by amar = 21 / 54 ( 1.8 km ) = 7 / 18 ( 1800 ) = 700 m answer : d"

physics

math_qa__6bwpu8PquFX7rTQm

An alloy weighing 16 ounces is 50% gold. How many ounces of pure gold must be added to create an alloy that is 80% gold? Pick. A) 24 B) 18 C) 9 D) 27 E) 18

<gadget id="calculator">80 - 50</gadget> <output>30</output> <gadget id="calculator">16 * 30</gadget> <output>480</output> <gadget id="calculator">480 / 12</gadget> <output>40</output> <gadget id="calculator">40 - 16</gadget> <output>24</output> <result>A</result>

A

An alloy weighing 16 ounces is 50% gold. How many ounces of pure gold must be added to create an alloy that is 80% gold?

subtract(divide(multiply(16, subtract(80, 50)), const_12), 16)

subtract(n2,n1)|multiply(n0,#0)|divide(#1,const_12)|subtract(#2,n0)|

"an alloy of 16 oz which is 50 % gold means there is 8 oz of gold . to get to an alloy that is 80 % gold , let ' s use this expression : ( 8 + x ) / ( 16 + x ) = 0.8 with x representing the amount of pure gold that must be added to get to 80 % . the expression we are using represents the new total weight of pure gold over the new total new weight of the alloy and this fraction should represent 80 % or 0.8 . you will see that 24 is the correct answer , as 32 / 40 = 0.8 choose a"

gain

math_qa__WGpL1EIokvmOMJWh

From 4 officers and 8 jawans in how many can 6 be chosen to include exactly one officer? Pick: A) 150 B) 164 C) 259 D) 311 E) 224

<gadget id="calculator">factorial(8)</gadget> <output>40_320</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">factorial(5)</gadget> <output>120</output> <gadget id="calculator">40_320 / 120</gadget> <output>336</output> <gadget id="calculator">factorial(3)</gadget> <output>6</output> <gadget id="calculator">336 / 6</gadget> <output>56</output> <gadget id="calculator">56 * 4</gadget> <output>224</output> <result>E</result>

E

From 4 officers and 8 jawans in how many can 6 be chosen to include exactly one officer?

multiply(divide(divide(factorial(8), factorial(subtract(6, const_1))), factorial(const_3)), 4)

factorial(n1)|factorial(const_3)|subtract(n2,const_1)|factorial(#2)|divide(#0,#3)|divide(#4,#1)|multiply(n0,#5)

required number of ways = 4 c 1 * 8 c 5 = 224 answer is e

general