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math_qa__Idc39QpXirH7XNmU

In a certain city, 70 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 80 percent of the registered voters who are Democrats and 30 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ? Options A) 65 % B) 52 % C) 85 % D) 69 % E) 75 %

<gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">70 * (4/5)</gadget> <output>56</output> <gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">30 * (3/10)</gadget> <output>9</output> <gadget id="calculator">56 + 9</gadget> <output>65</output> <result>A</result>

A

In a certain city, 70 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 80 percent of the registered voters who are Democrats and 30 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

add(multiply(70, divide(80, const_100)), multiply(subtract(const_100, 70), divide(30, const_100)))

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

"say there are total of 100 registered voters in that city . thus 70 are democrats and 30 are republicans . 70 * 0.80 = 56 democrats are expected to vote for candidate a ; 30 * 0.30 = 9 republicans are expected to vote for candidate a . thus total of 56 + 9 = 65 registered voters are expected to vote for candidate a , which is 65 % of the total number of registered voters . answer : a"

gain

math_qa__x0dDiisbujo0Al4U

A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 80 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year? Choose the correct choice from the following: A) − 5 % B) 5 % C) 15 % D) 26 % E) 80 %

<gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">1 + (4/5)</gadget> <output>9/5 = around 1.8</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">1 - (3/10)</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">(9/5) * (7/10)</gadget> <output>63/50 = around 1.26</output> <gadget id="calculator">(63/50) - 1</gadget> <output>13/50 = around 0.26</output> <gadget id="calculator">(13/50) * 100</gadget> <output>26</output> <result>D</result>

D

A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 80 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year?

multiply(subtract(multiply(add(const_1, divide(80, const_100)), subtract(const_1, divide(30, const_100))), const_1), const_100)

divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|subtract(#4,const_1)|multiply(#5,const_100)|

"the actual answer is obtained by multiplying 180 % by 70 % and subtracting 100 % from this total . that is : 180 % × 70 % = 126 % ; 126 % − 100 % = 26 % . answer : d"

gain

math_qa__5E7ETtG2mwHvpm8p

Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank? Choose the most appropriate option. A) 10 B) 12 C) 14 D) 16 E) 18

<gadget id="calculator">1 / 16</gadget> <output>1/16 = around 0.0625</output> <gadget id="calculator">1 / 24</gadget> <output>1/24 = around 0.041667</output> <gadget id="calculator">(1/16) + (1/24)</gadget> <output>5/48 = around 0.104167</output> <gadget id="calculator">1 / (5/48)</gadget> <output>48/5 = around 9.6</output> <gadget id="calculator">(48/5) / 4</gadget> <output>12/5 = around 2.4</output> <gadget id="calculator">(12/5) * 5</gadget> <output>12</output> <result>B</result>

B

Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank?

multiply(divide(inverse(add(divide(const_1, 16), divide(const_1, 24))), 4), 5)

divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2)|divide(#3,n3)|multiply(n2,#4)

part filled a in 1 hr = ( 1 / 16 ) part filled b in 1 hr = ( 1 / 24 ) part filled by ( a + b ) together in 1 hr = ( 1 / 16 ) + ( 1 / 24 ) = 5 / 48 so , the tank will be full in 48 / 5 hrs time taken to fill exact quarter tank = ( 48 / 5 ) * ( 5 / 4 ) = 12 hrs answer : b

physics

math_qa__ZJpF4hi56pg184Ej

A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 504. Find the sum? Choose the correct choice: A) 7000 B) 7029 C) 2778 D) 4200 E) 2791

<gadget id="calculator">18 - 12</gadget> <output>6</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">504 / (3/25)</gadget> <output>4_200</output> <result>D</result>

D

A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 504. Find the sum?

divide(504, divide(multiply(subtract(18, 12), const_2), const_100))

subtract(n0,n1)|multiply(#0,const_2)|divide(#1,const_100)|divide(n2,#2)|

"let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 504 = > 36 x / 100 - 24 x / 100 = 504 = > 12 x / 100 = 840 = > x = 4200 . answer : d"

gain

math_qa__6sRLXAVf6vvMHw0M

The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is Pick one A) 22 B) 30 C) 99 D) 38 E) 27

<gadget id="calculator">21 + 23</gadget> <output>44</output> <gadget id="calculator">44 / 2</gadget> <output>22</output> <gadget id="calculator">1 * 8</gadget> <output>8</output> <gadget id="calculator">22 + 8</gadget> <output>30</output> <result>B</result>

B

The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is

add(divide(add(21, 23), const_2), multiply(const_1, 8))

add(n1,n2)|multiply(n0,const_1)|divide(#0,const_2)|add(#2,#1)|

"total age increased = ( 8 * 2 ) years = 16 years . sum of ages of two new men = ( 21 + 23 + 16 ) years = 60 years average age of two new men = ( 60 / 2 ) years = 30 years . answer : b"

general

math_qa__Oy0d7VJQROCU7Pt5

A boy traveled from the village to the post-office at the rate of 12.5 kmph and walked back at the rate of 2 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village. Choose the correct choice from the following. A) 5 km B) 7 km C) 9 km D) 10 km E) 12 km

<gadget id="calculator">48 / 60</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">5 + (4/5)</gadget> <output>29/5 = around 5.8</output> <gadget id="calculator">12.5 * 2</gadget> <output>25</output> <gadget id="calculator">25 * 2</gadget> <output>50</output> <gadget id="calculator">12.5 + 2</gadget> <output>14.5</output> <gadget id="calculator">50 / 14.5</gadget> <output>3.448276</output> <gadget id="calculator">(29/5) * 3.448276</gadget> <output>20.000001</output> <gadget id="calculator">20.000001 / 2</gadget> <output>10.000001</output> <result>D</result>

D

A boy traveled from the village to the post-office at the rate of 12.5 kmph and walked back at the rate of 2 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.

divide(multiply(add(5, divide(48, const_60)), divide(multiply(multiply(12.5, 2), const_2), add(12.5, 2))), const_2)

add(n0,n1)|divide(n3,const_60)|multiply(n0,n1)|add(n2,#1)|multiply(#2,const_2)|divide(#4,#0)|multiply(#3,#5)|divide(#6,const_2)

explanation : solution : average speed = 2 xy / ( x + y ) km / hr = ( 2 * 12.5 * 2 ) / ( 12.5 + 2 ) km / hr = 50 / 14.5 km / hr . total distance = ( 50 / 14.5 * 29 / 5 ) km . = 20 km . required distance = 20 / 2 = 10 km . answer : d

physics

math_qa__bY2BTKUKSFb1HXBA

If the height of a cone is increased by 190% then its volume is increased by? Choose the correct choice: A) 100 B) 777 C) 998 D) 190 E) 2879

<gadget id="calculator">190 * 1</gadget> <output>190</output> <result>D</result>

D

If the height of a cone is increased by 190% then its volume is increased by?

rectangle_area(190, const_1)

rectangle_area(n0,const_1)|

"100 % answer : d"

geometry

math_qa__XrMxcGqRJ84kWXS3

A green lizard can travel from the green cave to the blue cave in 108 minutes; the blue lizard can travel from the blue cave to the green cave in 25% less time. If the green lizard started to travel 7.5 minutes before the blue lizard, how many minutes after the blue lizard, will the green lizard pass the middle line? Choose one: A) 2 . B) 3.5 . C) 4 . D) 5.5 . E) 6 .

<gadget id="calculator">108 / 2</gadget> <output>54</output> <gadget id="calculator">54 - 7.5</gadget> <output>46.5</output> <gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">108 * (3/4)</gadget> <output>81</output> <gadget id="calculator">81 / 2</gadget> <output>81/2 = around 40.5</output> <gadget id="calculator">46.5 - (81/2)</gadget> <output>6</output> <result>E</result>

E

A green lizard can travel from the green cave to the blue cave in 108 minutes; the blue lizard can travel from the blue cave to the green cave in 25% less time. If the green lizard started to travel 7.5 minutes before the blue lizard, how many minutes after the blue lizard, will the green lizard pass the middle line?

subtract(subtract(divide(108, const_2), 7.5), divide(multiply(108, divide(const_3, const_4)), const_2))

divide(n0,const_2)|divide(const_3,const_4)|multiply(n0,#1)|subtract(#0,n2)|divide(#2,const_2)|subtract(#3,#4)

time take by the green lizard to cover the distance between the caves = 108 mins time take by the green lizard to cover half the distance = 108 / 2 = 54 mins time take by the blue lizard to cover the distance between the caves = 108 x 3 / 4 = 81 mins time take by the blue lizard to cover half the distance = 81 / 2 = 40.5 mins now the green lizard had been travelling for 7.5 mins when the blue lizard started . therefore when the blue lizard starts to move the green lizard will have to cover 54 - 7.5 = 46.5 mins worth of distance at its current speed . difference in time when they both reach the mid point = 46.5 - 40.5 = 6 mins . e is the correct answer .

gain

math_qa__Swv9KbkjqtMQABpz

The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year? Answers. A) 3472 B) 8222 C) 4370 D) 26777 E) 8222

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 + (1/10)</gadget> <output>11/10 = around 1.1</output> <gadget id="calculator">(11/10) * 8_100</gadget> <output>8_910</output> <gadget id="calculator">9_100 - 8_910</gadget> <output>190</output> <gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">1 + (3/20)</gadget> <output>23/20 = around 1.15</output> <gadget id="calculator">(23/20) - (11/10)</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">190 / (1/20)</gadget> <output>3_800</output> <gadget id="calculator">8_100 - 3_800</gadget> <output>4_300</output> <result>C</result>

C

The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year?

subtract(8100, divide(subtract(9100, multiply(add(const_1, divide(10, const_100)), 8100)), subtract(add(const_1, divide(15, const_100)), add(const_1, divide(10, const_100)))))

divide(n2,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(n0,#2)|subtract(#3,#2)|subtract(n3,#4)|divide(#6,#5)|subtract(n0,#7)

let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 − x ) ( 8100 − x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % 15 % or 10 % 10 % . so 8100 + 15100 ⋅ x + 10100 ⋅ ( 8100 − x ) = 91008100 + 15100 ⋅ x + 10100 ⋅ ( 8100 − x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 − x ) = 91008100 + 320 x + 110 ( 8100 − x ) = 9100 120 x = 190120 x = 190 x = 3800 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , respectively . answer : c

general

math_qa__Xfk6cyVfIDsx2klp

An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 3 ? Choose the correct choice A) 1 / 9 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 5 / 6

<gadget id="calculator">99 / 3</gadget> <output>33</output> <gadget id="calculator">33 / 99</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 2</gadget> <output>2/3 = around 0.666667</output> <result>D</result>

D

An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 3 ?

multiply(divide(divide(99, const_3), 99), 2)

divide(n1,const_3)|divide(#0,n1)|multiply(n2,#1)

n ( n + 2 ) to be divisible by 3 either n or n + 2 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 1 , or 3 . thus , the overall probability is 2 / 3 . answer : d .

general

math_qa__MfcOAvVDpHiiccUv

Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? Select the correct option A) 2998 B) 2799 C) 2890 D) 1485 E) 2780

<gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">pi * ((3/2) ** 2) * 14</gadget> <output>63*pi/2 = around 98.960169</output> <gadget id="calculator">(63*pi/2) * 15</gadget> <output>945*pi/2 = around 1_484.402529</output> <result>D</result>

D

Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?

multiply(volume_cylinder(divide(3, const_2), 14), 15)

divide(n1,const_2)|volume_cylinder(#0,n0)|multiply(n2,#1)|

"22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 15 = 1485 answer : d"

physics

math_qa__PPpzSp4MCQRiSmTM

A car started running at a speed of 28 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey. Choose the correct choice from the following answers: A) 37 km B) 76 km C) 25 km D) 15 km E) 30 km

<gadget id="calculator">2 * 10</gadget> <output>20</output> <gadget id="calculator">28 + 20</gadget> <output>48</output> <gadget id="calculator">48 + 28</gadget> <output>76</output> <gadget id="calculator">76 / 2</gadget> <output>38</output> <result>A</result>

A

A car started running at a speed of 28 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.

divide(add(add(28, multiply(2, 10)), 28), 2)

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

"a 37 km the total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in ap whose first term is 28 and last term is 46 = 10 / 2 [ 28 + 46 ] = 370 km ."

physics

math_qa__1uJIzpASVltMnztI

Find the total number of prime factors in the expression (4)^11 x (7)^3 x (11)^2 Choose the correct option: A) 26 B) 22 C) 25 D) 27 E) 29

<gadget id="calculator">2 * 11</gadget> <output>22</output> <gadget id="calculator">22 + 3</gadget> <output>25</output> <gadget id="calculator">25 + 2</gadget> <output>27</output> <result>D</result>

D

Find the total number of prime factors in the expression (4)^11 x (7)^3 x (11)^2

add(add(multiply(2, 11), 3), 2)

multiply(n1,n5)|add(n3,#0)|add(n5,#1)|

"( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 3 x 11 ^ 2 = 2 ^ 22 x 7 ^ 3 x 11 ^ 2 total number of prime factors = ( 22 + 3 + 2 ) = 27 . answer is d ."

general

math_qa__sByZHqk3W9yjP8at

For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 7 of whom are females, by how much does the index for the females exceed the index for the males in the group? Choose the correct choice from the following answers: A) 0.05 B) 0.0625 C) 0.2 D) 0.3 E) 0.6

<gadget id="calculator">20 - 7</gadget> <output>13</output> <gadget id="calculator">13 / 20</gadget> <output>13/20 = around 0.65</output> <gadget id="calculator">7 / 20</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">(13/20) - (7/20)</gadget> <output>3/10 = around 0.3</output> <result>D</result>

D

For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 7 of whom are females, by how much does the index for the females exceed the index for the males in the group?

subtract(divide(subtract(20, 7), 20), divide(7, 20))

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

"index for females = ( 20 - 7 ) / 20 = 13 / 20 = 0.65 index for males = ( 20 - 13 / 20 = 7 / 20 = 0.35 index for females exceeds males by 0.65 - 0.35 = 0.3 answer : d"

general

math_qa__Nmt21DDa19WqEEDP

The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 14%? Choose the correct choice from the following answers: A) 34.375 % B) 48 % C) 50.5 % D) 52 % E) 56 %

<gadget id="calculator">100 - 14</gadget> <output>86</output> <gadget id="calculator">86 / 64</gadget> <output>43/32 = around 1.34375</output> <gadget id="calculator">(43/32) - 1</gadget> <output>11/32 = around 0.34375</output> <gadget id="calculator">(11/32) * 100</gadget> <output>275/8 = around 34.375</output> <result>A</result>

A

The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 14%?

multiply(subtract(divide(subtract(const_100, 14), 64), const_1), const_100)

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

"explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 86 gain % = 22 / 64 * 100 = 34.375 % . answer : option a"

gain

math_qa__svgF3AhJIExyv13y

The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places) Choose the correct choice from the following choices A) 77.14 cm B) 47.14 cm C) 84.92 cm D) 94.94 cm E) 23.57 cm

<gadget id="calculator">2 * (16 + 14)</gadget> <output>60</output> <gadget id="calculator">60 / 4</gadget> <output>15</output> <gadget id="calculator">15 / 2</gadget> <output>15/2 = around 7.5</output> <gadget id="calculator">2 * pi * (15/2)</gadget> <output>15*pi = around 47.12389</output> <gadget id="calculator">(15*pi) / 2</gadget> <output>15*pi/2 = around 23.561945</output> <result>E</result>

E

The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)

divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(16, 14)), const_2)), const_2)

rectangle_perimeter(n0,n1)|square_edge_by_perimeter(#0)|divide(#1,const_2)|circumface(#2)|divide(#3,const_2)

let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : e

geometry

math_qa__MooFSOrVnboMgZk8

in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students e in the class ? Choose the correct choice from the following options A) 10 B) 12 C) 15 D) 20 E) 25

<gadget id="calculator">50_000 / 20_000</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(5/2) * 3</gadget> <output>15/2 = around 7.5</output> <gadget id="calculator">100_000 / 20_000</gadget> <output>5</output> <gadget id="calculator">(15/2) + 5</gadget> <output>25/2 = around 12.5</output> <gadget id="calculator">(5/2) + (25/2)</gadget> <output>15</output> <result>C</result>

C

in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students e in the class ?

add(divide(50000, 20000), add(multiply(divide(50000, 20000), const_3), divide(100000, 20000)))

divide(n0,n2)|divide(n1,n2)|multiply(#1,const_3)|add(#0,#2)|add(#3,#1)

the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )

general

math_qa__nt6DO4Hzes3ZTw2J

A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour? Choose one: A) 71.11 B) 71.12 C) 71.1 D) 71.17 E) 71.13

<gadget id="calculator">160 / 64</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">160 / 80</gadget> <output>2</output> <gadget id="calculator">(5/2) + 2</gadget> <output>9/2 = around 4.5</output> <gadget id="calculator">1 / (9/2)</gadget> <output>2/9 = around 0.222222</output> <gadget id="calculator">320 * (2/9)</gadget> <output>640/9 = around 71.111111</output> <result>A</result>

A

A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?

multiply(320, divide(const_1, add(divide(160, 64), divide(160, 80))))

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

"car travels first 160 km at 64 km / hr time taken to travel first 160 km = distancespeed = 16064 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 16080 total distance traveled = 160 + 160 = 2 × 160 total time taken = 16064 + 16080 average speed = total distance traveledtotal time taken = 2 × 16016064 + 16080 = 2164 + 180 = 2 × 64 × 8080 + 64 = 2 × 64 × 80144 = 2 × 8 × 8018 = 6409 = 71.11 km / hr answer : a"

general

math_qa__CK56cGSI3RSMQTaG

A prize of $800 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award? Choices: A) $ 200 B) $ 220 C) $ 280 D) $ 300 E) $ 340

<gadget id="calculator">800 * 2</gadget> <output>1_600</output> <gadget id="calculator">1_600 / 5</gadget> <output>320</output> <gadget id="calculator">800 - 320</gadget> <output>480</output> <gadget id="calculator">20 * 3</gadget> <output>60</output> <gadget id="calculator">60 / 5</gadget> <output>12</output> <gadget id="calculator">20 - 12</gadget> <output>8</output> <gadget id="calculator">8 - 1</gadget> <output>7</output> <gadget id="calculator">7 * 20</gadget> <output>140</output> <gadget id="calculator">480 - 140</gadget> <output>340</output> <result>E</result>

E

A prize of $800 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?

subtract(subtract(800, divide(multiply(800, 2), 5)), multiply(subtract(subtract(20, divide(multiply(20, 3), 5)), const_1), 20))

multiply(n0,n3)|multiply(n1,n5)|divide(#0,n4)|divide(#1,n4)|subtract(n0,#2)|subtract(n1,#3)|subtract(#5,const_1)|multiply(n1,#6)|subtract(#4,#7)|

"total value of the prize = $ 800 number of people = 20 2 / 5 of 800 ( = $ 320 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 800 - 320 = $ 480 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 480 - 140 = $ 340 , hence e is the correct answer ."

general

math_qa__K8ve4y2lA9X30QCb

Mary works in a restaurant a maximum of 50 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week? Select A) 300 B) 420 C) 460 D) 320 E) 400

<gadget id="calculator">50 * 8</gadget> <output>400</output> <gadget id="calculator">50 - 20</gadget> <output>30</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">8 * (1/4)</gadget> <output>2</output> <gadget id="calculator">30 * 2</gadget> <output>60</output> <gadget id="calculator">400 + 60</gadget> <output>460</output> <result>C</result>

C

Mary works in a restaurant a maximum of 50 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?

add(multiply(50, 8), multiply(subtract(50, 20), multiply(8, divide(25, const_100))))

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

"mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 30 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 30 ) = $ 300 . the total amount is $ 160 + $ 300 = $ 460 answer c 460 ."

gain

math_qa__EjnAebLkHeQ1LTUW

An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 4 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank. Pick one: A) 8600 litres B) 3200 litres C) 12800 litres D) 11200 litres E) 13200 litres

<gadget id="calculator">4 * 60</gadget> <output>240</output> <gadget id="calculator">5 + 3</gadget> <output>8</output> <gadget id="calculator">240 * 8</gadget> <output>1_920</output> <gadget id="calculator">1_920 / 3</gadget> <output>640</output> <gadget id="calculator">640 * 5</gadget> <output>3_200</output> <result>B</result>

B

An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 4 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank.

multiply(divide(multiply(multiply(4, const_60), add(5, 3)), 3), 5)

add(n0,n2)|multiply(n1,const_60)|multiply(#0,#1)|divide(#2,n2)|multiply(n0,#3)

let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 4 * 60 = 240 liters / hour ; net outflow rate when both pipes operate would be x - 240 liters / hour . capacity of the tank = x * 5 hours = ( x - 240 ) * ( 5 + 3 ) hours 5 x = ( x - 240 ) * 8 - - > x = 640 - - > capacity = 5 x = 3200 liters . answer : b .

physics

math_qa__ocYtUp272BCblFqS

You buy a piece of land with an area of √625, how long is one side of the land plot? Choose the correct choice from the following answers A) 28 B) 29 C) 30 D) 31 E) 25

<gadget id="calculator">625 ** (1/2)</gadget> <output>25</output> <result>E</result>

E

You buy a piece of land with an area of √625, how long is one side of the land plot?

sqrt(625)

sqrt(n0)|

"try filling the numbers into the answer y x y = find the closest to 625 . answer e"

geometry

math_qa__eBqF57LaWsK8y0CH

In a division sum, the remainder is 4 and the divisor is 2 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is: Answers. A) 72 B) 90 C) 100 D) 110 E) 120

<gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">12 + 2</gadget> <output>14</output> <gadget id="calculator">14 / 2</gadget> <output>7</output> <gadget id="calculator">14 * 7</gadget> <output>98</output> <gadget id="calculator">98 + 4</gadget> <output>102</output> <result>C</result>

C

In a division sum, the remainder is 4 and the divisor is 2 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:

add(multiply(add(multiply(4, const_3), 2), divide(add(multiply(4, const_3), 2), 2)), 4)

multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)|

"diver = ( 4 * 3 ) + 2 = 14 2 * quotient = 14 quotient = 7 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 7 ) + 2 = 100 c"

general

math_qa__EjdYtGdILt6LQVt1

If the sum of two numbers is 42 and their product is 437, then find the absolute difference between the numbers. Choose the most appropriate option. A) 2 B) 4 C) 3 D) 1 E) 0

<gadget id="calculator">42 ** 2</gadget> <output>1_764</output> <gadget id="calculator">4 * 437</gadget> <output>1_748</output> <gadget id="calculator">1_764 - 1_748</gadget> <output>16</output> <gadget id="calculator">16 ** (1/2)</gadget> <output>4</output> <result>B</result>

B

If the sum of two numbers is 42 and their product is 437, then find the absolute difference between the numbers.

sqrt(subtract(power(42, const_2), multiply(const_4, 437)))

multiply(n1,const_4)|power(n0,const_2)|subtract(#1,#0)|sqrt(#2)

let the numbers be x and y . then , x + y = 42 and xy = 437 x - y = sqrt [ ( x + y ) 2 - 4 xy ] = sqrt [ ( 42 ) 2 - 4 x 437 ] = sqrt [ 1764 – 1748 ] = sqrt [ 16 ] = 4 . required difference = 4 . answer is b .

general

math_qa__27HzLVeLxBViJVqp

for dinner , cara ate 240 grams of bread which was 8 times as much bread as she ate for lunch , and 6 times as much bread as she ate for breakfast . how much bread did cara eat in total ? Pick one: A) 300 B) 310 C) 320 D) 330 E) 340

<gadget id="calculator">240 / 8</gadget> <output>30</output> <gadget id="calculator">240 / 6</gadget> <output>40</output> <gadget id="calculator">30 + 40</gadget> <output>70</output> <gadget id="calculator">240 + 70</gadget> <output>310</output> <result>B</result>

B

for dinner , cara ate 240 grams of bread which was 8 times as much bread as she ate for lunch , and 6 times as much bread as she ate for breakfast . how much bread did cara eat in total ?

add(240, add(divide(240, 8), divide(240, 6)))

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

for breakfast , cara ate 240 / 6 = 40 grams . for lunch , cara ate 240 / 8 = 30 grams . for dinner , cara ate 240 grams . the total is 40 + 30 + 240 = 310 grams . the answer is b .

general

math_qa__A10iLtDmdMh9Iff7

A rectangular Box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road? Choose the correct choice from the following options: A) 3 m B) 4 m C) 5 m D) 6 m E) 2 m

<gadget id="calculator">100 ** 2</gadget> <output>10_000</output> <gadget id="calculator">60 * 40</gadget> <output>2_400</output> <gadget id="calculator">2_400 - 2_109</gadget> <output>291</output> <gadget id="calculator">291 * 4</gadget> <output>1_164</output> <gadget id="calculator">10_000 - 1_164</gadget> <output>8_836</output> <gadget id="calculator">8_836 ** (1/2)</gadget> <output>94</output> <gadget id="calculator">100 - 94</gadget> <output>6</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <result>A</result>

A

A rectangular Box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road?

divide(subtract(const_100, sqrt(subtract(power(const_100, const_2), multiply(subtract(multiply(60, 40), 2109), const_4)))), const_2)

multiply(n0,n1)|power(const_100,const_2)|subtract(#0,n2)|multiply(#2,const_4)|subtract(#1,#3)|sqrt(#4)|subtract(const_100,#5)|divide(#6,const_2)

total area of cross roads = 60 x + 40 x − x 2 but total area of the cross roads = 291 m 2 hence , 60 x + 40 x − x 2 = 291 ⇒ 100 x − x 2 = 291 ⇒ x 2 − 100 x + 291 = 0 ⇒ ( x − 97 ) ( x − 3 ) = 0 ⇒ x = 3 answer : a

geometry

math_qa__MOaLfo46lyBG5fw5

The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 180° of the circle, what percentage of MegaTek employees are in manufacturing? Pick: A) 20 % B) 25 % C) 30 % D) 35 % E) 50 %

<gadget id="calculator">3_600 / 10</gadget> <output>360</output> <gadget id="calculator">180 / 360</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * 100</gadget> <output>50</output> <result>E</result>

E

The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 180° of the circle, what percentage of MegaTek employees are in manufacturing?

multiply(divide(180, divide(const_3600, const_10)), const_100)

divide(const_3600,const_10)|divide(n0,#0)|multiply(#1,const_100)|

"answer : e 180 ° divided by 360 ° equals 0.5 , therefore the sector is equal to 50 % of the total"

physics

math_qa__QRWO8tpb1AcvyMqb

The speed at which a man can row a boat in still water is 25 kmph. If he rows downstream, where the speed of current is 11 kmph, what time will he take to cover 80 metres? Select: A) 18 seconds B) 27 seconds C) 26 seconds D) 12 seconds E) 8 seconds

<gadget id="calculator">25 + 11</gadget> <output>36</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">36 * (5/18)</gadget> <output>10</output> <gadget id="calculator">80 / 10</gadget> <output>8</output> <result>E</result>

E

The speed at which a man can row a boat in still water is 25 kmph. If he rows downstream, where the speed of current is 11 kmph, what time will he take to cover 80 metres?

divide(80, multiply(add(25, 11), const_0_2778))

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

"speed of the boat downstream = 25 + 11 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 80 m = 80 / 10 = 8 seconds . answer : e"

physics

math_qa__4U09bTBZKGKjegjM

For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%. Choose the most appropriate option: A) 10 B) 5 C) 2 D) 3 E) 1

<gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">10 * (1/2)</gadget> <output>5</output> <gadget id="calculator">5 - 3</gadget> <output>2</output> <result>C</result>

C

For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.

subtract(multiply(10, divide(50, const_100)), 3)

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

rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a ∩ b ) = p ( a ) p ( b ) the probability that the quarterback throws a completed pass at least once in 2 throws is 1 - ( 7 / 10 ) ^ 2 = 1 - 49 / 100 = 51 / 100 > 50 % answer : c

general

math_qa__AGaOHq7HwD0wUUBW

A and B can do a work in 8 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed? Choices: A) 9.6 days B) 7.6 days C) 4 days D) 8.6 days E) 6.6 days

<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 / (5/24)</gadget> <output>24/5 = around 4.8</output> <gadget id="calculator">(24/5) * 2</gadget> <output>48/5 = around 9.6</output> <result>A</result>

A

A and B can do a work in 8 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?

multiply(inverse(add(inverse(8), inverse(12))), const_2)

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

work done by a and b in the first two hours , working alternately = first hour a + second hour b = 1 / 8 + 1 / 12 = 5 / 24 . total time required to complete the work = 2 * 24 / 5 = 9.6 days . answer : a

physics

math_qa__fGZExuAMa5P8RTWz

In a weight-lifting competition, the total weight of Joe's two lifts was 1800 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift? Answers: A) 225 B) 275 C) 325 D) 350 E) 700

<gadget id="calculator">1_800 + 300</gadget> <output>2_100</output> <gadget id="calculator">2_100 / 3</gadget> <output>700</output> <result>E</result>

E

In a weight-lifting competition, the total weight of Joe's two lifts was 1800 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?

divide(add(1800, 300), const_3)

add(n0,n1)|divide(#0,const_3)

this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1800 pounds . we sum the two variables to obtain : f + s = 1800 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 1800 3 f = 2100 f = 700 answer is e .

general

math_qa__6eFaWPoNRjOUCHaQ

In a division, divident is 729, divisior is 38 and quotient is 19. Find the remainder. Choose the correct choice from the following: A) 4 B) 3 C) 2 D) 5 E) 7

<gadget id="calculator">729 % 38</gadget> <output>7</output> <result>E</result>

E

In a division, divident is 729, divisior is 38 and quotient is 19. Find the remainder.

reminder(729, 38)

reminder(n0,n1)|

"explanation : 729 = 38 x 19 + r 729 = 722 + r r = 729 - 722 = 7 answer : option e"

general

math_qa__yZNI6ZsRb9pRWLVN

Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 330 grams of compound X? Choose the correct choice from the following options A) 54 B) 162 C) 250 D) 275 E) 322

<gadget id="calculator">330 * 10</gadget> <output>3_300</output> <gadget id="calculator">2 + 10</gadget> <output>12</output> <gadget id="calculator">3_300 / 12</gadget> <output>275</output> <result>D</result>

D

Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 330 grams of compound X?

divide(multiply(330, 10), add(2, 10))

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

total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 330 gms of x have 330 * 10 / 12 = 275 gms of b and 330 - 275 = 55 gms of a . cross check : - a / b = 55 / 275 = 2 / 10 ( as given ) ans d

other

math_qa__UHsodzk1XOkxYeAv

The average salary of all the workers in a workshop is Rs. 9000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? Choose one: A) 23 B) 21 C) 52 D) 56 E) 14

<gadget id="calculator">12_000 - 9_000</gadget> <output>3_000</output> <gadget id="calculator">7 * 3_000</gadget> <output>21_000</output> <gadget id="calculator">9_000 - 6_000</gadget> <output>3_000</output> <gadget id="calculator">21_000 / 3_000</gadget> <output>7</output> <gadget id="calculator">7 + 7</gadget> <output>14</output> <result>E</result>

E

The average salary of all the workers in a workshop is Rs. 9000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?

add(7, divide(multiply(7, subtract(12000, 9000)), subtract(9000, 6000)))

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

"let the total number of workers be x . then , 9000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3000 x = 42000 = x = 14 . answer : e"

general

math_qa__RJqQL3tJcg0g9xzo

The charge for a single room at Hotel P is 70 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G? Choose the correct choice from the following answers: A) 100 % B) 120 % C) 150 % D) 200 % E) 300 %

<gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">30 / 90</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 100</gadget> <output>100/3 = around 33.333333</output> <gadget id="calculator">100 - (100/3)</gadget> <output>200/3 = around 66.666667</output> <gadget id="calculator">(200/3) / (100/3)</gadget> <output>2</output> <gadget id="calculator">2 * 100</gadget> <output>200</output> <result>D</result>

D

The charge for a single room at Hotel P is 70 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G?

multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 70), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 70), subtract(const_100, 10)), const_100)), const_100)

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

"p = 0.3 r = 0.9 g r = 0.9 g / 0.3 = 3 g thus r is 200 % greater than g . the answer is d ."

gain

math_qa__L5hOZNd33nsY6jC1

Average of 10 matches is 34, How many runs one should should score to increase his average by 4 runs. Choose one: A) 70 B) 76 C) 78 D) 80 E) 88

<gadget id="calculator">34 + 4</gadget> <output>38</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">38 * 11</gadget> <output>418</output> <gadget id="calculator">10 * 34</gadget> <output>340</output> <gadget id="calculator">418 - 340</gadget> <output>78</output> <result>C</result>

C

Average of 10 matches is 34, How many runs one should should score to increase his average by 4 runs.

subtract(multiply(add(34, 4), add(10, const_1)), multiply(10, 34))

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

explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 34 ) = 418 - 340 = 78 answer : option c

general

math_qa__eUxkdiwu33PWduxs

What least number should be added to 1021, so that the sum is completely divisible by 25? Choose the correct choice from the following A) 4 B) 3 C) 2 D) 0 E) 5

<gadget id="calculator">1_021 % 25</gadget> <output>21</output> <gadget id="calculator">25 - 21</gadget> <output>4</output> <result>A</result>

A

What least number should be added to 1021, so that the sum is completely divisible by 25?

subtract(25, reminder(1021, 25))

reminder(n0,n1)|subtract(n1,#0)|

"1021 ã · 25 = 40 with remainder = 21 21 + 4 = 25 . hence 4 should be added to 1021 so that the sum will be divisible by 25 answer : option a"

general

math_qa__xRYCii1KGlNWJ4ZZ

A reduction of 10% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? Choose the correct choice from the following answers: A) s . 42 B) s . 46 C) s . 40 D) s . 41 E) s . 16

<gadget id="calculator">800 * 10</gadget> <output>8_000</output> <gadget id="calculator">8_000 / 100</gadget> <output>80</output> <gadget id="calculator">80 / 5</gadget> <output>16</output> <result>E</result>

E

A reduction of 10% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?

divide(divide(multiply(800, 10), const_100), 5)

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

"800 * ( 10 / 100 ) = 80 - - - - 5 ? - - - - 1 = > rs . 16 answer : e"

gain

math_qa__D6xlcCzG8xRIWvqF

The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 17000, then find the annual income of A? Choose the correct answer A) rs . 571200 B) rs . 180000 C) rs . 201600 D) rs . 504000 E) none of these

<gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">1 + (3/25)</gadget> <output>28/25 = around 1.12</output> <gadget id="calculator">17_000 * (28/25)</gadget> <output>19_040</output> <gadget id="calculator">5 / 2</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">19_040 * (5/2)</gadget> <output>47_600</output> <gadget id="calculator">47_600 * 12</gadget> <output>571_200</output> <result>A</result>

A

The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 17000, then find the annual income of A?

multiply(multiply(multiply(17000, add(const_1, divide(12, const_100))), divide(5, 2)), 12)

divide(n0,n1)|divide(n2,const_100)|add(#1,const_1)|multiply(n3,#2)|multiply(#0,#3)|multiply(n2,#4)|

"b ' s monthly income = 17000 * 112 / 100 = rs . 19040 b ' s monthly income = 2 parts - - - - > rs . 19040 a ' s monthly income = 5 parts = 5 / 2 * 19040 = rs . 47600 a ' s annual income = rs . 47600 * 12 = rs . 571200 answer : a"

other

math_qa__xVpianAaJp0mBT0W

Two pipes can fill a tank in 18 minutes and 30 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank? Choices. A) 1 / 15 B) 1 / 16 C) 1 / 11 D) 1 / 10 E) 1 / 12

<gadget id="calculator">1 / 18</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">(1/18) + (1/30)</gadget> <output>4/45 = around 0.088889</output> <gadget id="calculator">1 / 45</gadget> <output>1/45 = around 0.022222</output> <gadget id="calculator">(4/45) - (1/45)</gadget> <output>1/15 = around 0.066667</output> <result>A</result>

A

Two pipes can fill a tank in 18 minutes and 30 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?

subtract(add(divide(const_1, 18), divide(const_1, 30)), divide(const_1, 45))

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

part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 30 - 1 / 45 = 1 / 15 so , the tank becomes full in 15 minutes . answer : a

physics

math_qa__dyDCoSjLPScsEI5a

17 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? Options: A) 154 B) 184 C) 240 D) 272 E) 306

<gadget id="calculator">17 - 1</gadget> <output>16</output> <gadget id="calculator">17 * 16</gadget> <output>272</output> <result>D</result>

D

17 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?

multiply(17, subtract(17, const_1))

subtract(n0,const_1)|multiply(n0,#0)|

"2 * 17 c 2 = 2 * 136 = 272 the answer is d ."

general

math_qa__Pb6iC0iHvF5sXsgs

What will be the reminder when (13^13+13) is divided by 14? Choose the correct choice from the following answers A) 16 B) 14 C) 12 D) 18 E) 21

<gadget id="calculator">13 ** 13</gadget> <output>302_875_106_592_253</output> <gadget id="calculator">302_875_106_592_253 + 13</gadget> <output>302_875_106_592_266</output> <gadget id="calculator">302_875_106_592_266 / 14</gadget> <output>151_437_553_296_133/7 = around 21_633_936_185_161.855469</output> <gadget id="calculator">floor(151_437_553_296_133/7)</gadget> <output>21_633_936_185_161</output> <gadget id="calculator">14 * 21_633_936_185_161</gadget> <output>302_875_106_592_254</output> <gadget id="calculator">302_875_106_592_266 - 302_875_106_592_254</gadget> <output>12</output> <result>C</result>

C

What will be the reminder when (13^13+13) is divided by 14?

subtract(add(power(13, 13), 13), multiply(14, floor(divide(add(power(13, 13), 13), 14))))

power(n0,n0)|add(n0,#0)|divide(#1,n3)|floor(#2)|multiply(n3,#3)|subtract(#1,#4)

( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 13 ^ 13 + 1 ) will be divisible by ( 13 + 1 ) ; ( 13 ^ 13 + 1 ) + 12 when divided by 14 will give 12 as remainder . correct option : c

general

math_qa__sV8e9eqk2MMxdrzs

The remainder when positive integer nn (n>1n>1) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1. What is the least value of nn? Select the correct option: A) 76 B) 101 C) 126 D) 151 E) 176

<gadget id="calculator">25 * 7</gadget> <output>175</output> <result>E</result>

E

The remainder when positive integer nn (n>1n>1) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1. What is the least value of nn?

multiply(25, 7)

multiply(n2,n4)

we ' re asked to find the least number that gives us a remainder of 1 when divided by 25 and gives us a remainder of 1 when divided by 7 . you might notice , rather quickly , that all of the answers gives us a remainder when divided by 25 . . . 76 = 75 + 1 101 = 100 + 1 126 = 125 + 1 151 = 150 + 1 176 = 175 + 1 so the real question is ` ` which of these 5 is the least number that has a remainder of 1 when divided by 7 ? ' ' from here , you can just do the ` ` brute force ' ' math : a : 76 / 7 = 10 r 6 not a match b : 101 / 7 = 14 r 3 not a match c : 126 / 7 = 18 r 0 not a match d : 151 / 7 = 21 r 4 not a match none of these numbers ` ` fits ' ' the description , so the answer must be e . e : 176 / 7 = 25 r 1 ; answer : e

general

math_qa__DZnsvSghlWkwtJM8

a tank is filled in sixteen hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ? Choose one: A) 56 hours B) 28 hours C) 55 hours D) 66 hours E) 47 hours

<gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">6 + 1</gadget> <output>7</output> <gadget id="calculator">7 / 2</gadget> <output>7/2 = around 3.5</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">12 + 4</gadget> <output>16</output> <gadget id="calculator">(7/2) * 16</gadget> <output>56</output> <result>A</result>

A

a tank is filled in sixteen hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ?

multiply(divide(add(add(const_4, const_2), const_1), const_2), add(multiply(3, const_4), const_4))

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

1 / a + 1 / b + 1 / c = 1 / 16 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 16 = > ( 1 + 2 + 4 ) / 2 b = 1 / 16 = > 2 b / 7 = 16 = > b = 56 hours . answer : a

general

math_qa__qtUICEEqVZp6IU5g

Two numbers N and 16 have LCM = 48 and GCF = 18. Find N. Choose the correct choice. A) 24 B) 34 C) 44 D) 54 E) 64

<gadget id="calculator">48 * 18</gadget> <output>864</output> <gadget id="calculator">864 / 16</gadget> <output>54</output> <result>D</result>

D

Two numbers N and 16 have LCM = 48 and GCF = 18. Find N.

divide(multiply(48, 18), 16)

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

"the product of two integers is equal to the product of their lcm and gcf . hence . 16 × n = 48 × 18 n = 48 × 18 / 16 = 54 correct answer d"

physics

math_qa__NCqIhKbQz5FGD607

Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical? Choose the correct option A) 25 % B) 22.2 % C) 20 % D) 12.5 % E) 11.7 %

<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 - (1/3)</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(1/6) * (2/3)</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">1 - (1/6)</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">(1/9) + (5/6)</gadget> <output>17/18 = around 0.944444</output> <gadget id="calculator">(1/9) / (17/18)</gadget> <output>2/17 = around 0.117647</output> <gadget id="calculator">(2/17) * 100</gadget> <output>200/17 = around 11.764706</output> <result>E</result>

E

Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical?

multiply(divide(multiply(divide(1, 6), subtract(1, divide(1, 3))), add(multiply(divide(1, 6), subtract(1, divide(1, 3))), subtract(1, divide(1, 6)))), const_100)

divide(n1,n2)|divide(n3,n4)|subtract(n3,#1)|subtract(n3,#0)|multiply(#0,#2)|add(#4,#3)|divide(#4,#5)|multiply(#6,const_100)|

"welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 3 is 600 * 1 / 3 so it reduced 200 people , so there is 400 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 400 clerical left / 3400 people total you get ( a ) 11.7 % answer : e"

general

math_qa__Iw0O7tav4wQq91sr

Two trains leave a station traveling in the same direction. Train A leaves traveling at a constant speed of 50 mph, while train B leaves traveling at a constant speed of 80 mph. If train B left the station 30 minutes after train A left, in how many minutes will train B overtake train A? Pick one: A) 30 B) 40 C) 50 D) 60 E) 70

<gadget id="calculator">50 * 30</gadget> <output>1_500</output> <gadget id="calculator">1_500 / 60</gadget> <output>25</output> <gadget id="calculator">80 - 50</gadget> <output>30</output> <gadget id="calculator">25 / 30</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">(5/6) * 60</gadget> <output>50</output> <result>C</result>

C

Two trains leave a station traveling in the same direction. Train A leaves traveling at a constant speed of 50 mph, while train B leaves traveling at a constant speed of 80 mph. If train B left the station 30 minutes after train A left, in how many minutes will train B overtake train A?

multiply(divide(divide(multiply(50, 30), const_60), subtract(80, 50)), const_60)

multiply(n0,n2)|subtract(n1,n0)|divide(#0,const_60)|divide(#2,#1)|multiply(#3,const_60)

we can use a form of the equation d = rt [ distance = rate * time ] train a will have traveled for 30 minutes longer when train b overtakes it so time of train a : t + 30 minutes = t + 1 / 2 hours ( switch to hours since the rates are in hours ) time of train b : t rate of train a : 50 mph rate of train b : 80 mph the distance traveled by each will be the same when b overtakes a so set the right side of d = rt equal to each other for the two trains 50 * ( t + 1 / 2 ) = 80 * t 50 t + 25 = 80 t 25 = 30 t 25 / 30 = t 5 / 6 hours = t which is 5 / 6 * 60 = 50 minutes c

physics

math_qa__F0Xy1hMljwOYdeaR

let the least number of 6 digits , which when divided by 4 , 610 and 15 leaves in each case the same remainder of 2 , be n . the sum of the digits in n is : Choose one: A) 3 B) 4 C) 5 D) 6 E) 7

<gadget id="calculator">1 + 2</gadget> <output>3</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <result>C</result>

C

let the least number of 6 digits , which when divided by 4 , 610 and 15 leaves in each case the same remainder of 2 , be n . the sum of the digits in n is :

add(add(add(const_1, 2), const_1), const_1)

add(n4,const_1)|add(#0,const_1)|add(#1,const_1)

solution least number of 6 digital is 100000 . l . c . m . of 4 , 610 and 15 = 60 . on dividing 100000 by 60 , the remainder obtained is 40 . so , least number of 6 digits divisible by 4 , 610 and 15 = 100000 + ( 60 - 40 ) = 100020 . so , n = ( 100020 + 2 ) = 100022 . sum of digits in n = ( 1 + 2 + 2 ) = 5 . answer c

general

math_qa__nu1bXVPZSZ4C8viA

If a = 105 and a^3= 21 * 25 * 35 * b, what is the value of b? Options: A) 35 B) 42 C) 45 D) 49 E) 63

<gadget id="calculator">105 ** 3</gadget> <output>1_157_625</output> <gadget id="calculator">21 * 25</gadget> <output>525</output> <gadget id="calculator">525 * 35</gadget> <output>18_375</output> <gadget id="calculator">1_157_625 / 18_375</gadget> <output>63</output> <result>E</result>

E

If a = 105 and a^3= 21 * 25 * 35 * b, what is the value of b?

divide(power(105, 3), multiply(multiply(21, 25), 35))

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

"first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 35 = 7 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 7 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 * 5 ^ 3 * 7 ^ 2 b = 3 ^ 2 * 7 = 9 * 7 = 63 correct answer e ."

general

math_qa__vRAaT0OmYOIs7Wya

What is the maximum number of pieces of birthday cake of size 2” by 2” that can be cut from a cake 20” by 20”? Choose the correct choice from the following options A) 5 B) 100 C) 16 D) 20 E) 25

<gadget id="calculator">20 * 20</gadget> <output>400</output> <gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">400 / 4</gadget> <output>100</output> <result>B</result>

B

What is the maximum number of pieces of birthday cake of size 2” by 2” that can be cut from a cake 20” by 20”?

divide(multiply(20, 20), multiply(2, 2))

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

the prompt is essentially asking for the maximum number of 2 x 2 squares that can be cut from a larger 20 by 20 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 10 ' pieces ' each , we have ( 10 ) ( 10 ) = 100 total smaller squares ( at maximum ) . b

physics

math_qa__Wj7L8ChkpUQPynkW

At the faculty of Aerospace Engineering, 302 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? Answers. A) 444 B) 432 C) 346 D) 422 E) 448

<gadget id="calculator">112 / 2</gadget> <output>56</output> <gadget id="calculator">302 - 56</gadget> <output>246</output> <gadget id="calculator">232 - 56</gadget> <output>176</output> <gadget id="calculator">246 + 176</gadget> <output>422</output> <result>D</result>

D

At the faculty of Aerospace Engineering, 302 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?

add(subtract(302, divide(112, const_2)), subtract(232, divide(112, const_2)))

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

"302 + 232 - 112 ( since 112 is counted twice ) = 422 d is the answer"

other

math_qa__rNP9q92SgkYRWEPu

In a group of 100 people, 55 have visited Iceland and 43 have visited Norway. If 61 people have visited both Iceland and Norway, how many people have visited neither country? Pick one: A) 60 B) 61 C) 62 D) 63 E) 64

<gadget id="calculator">55 + 43</gadget> <output>98</output> <gadget id="calculator">98 - 61</gadget> <output>37</output> <gadget id="calculator">100 - 37</gadget> <output>63</output> <result>D</result>

D

In a group of 100 people, 55 have visited Iceland and 43 have visited Norway. If 61 people have visited both Iceland and Norway, how many people have visited neither country?

subtract(100, subtract(add(55, 43), 61))

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

"this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 100 = 55 + 43 - 61 + ( # in neither group ) = 63 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"

other

math_qa__8AKLN1fL9lXzhhxB

A car was driving at 60 Km/h for 20 minutes, and then at 90Km/h for another 40 minutes. What was its average speed? Select the correct option: A) 80 . B) 75 C) 70 D) 65 . E) 54 .

<gadget id="calculator">20 + 40</gadget> <output>60</output> <gadget id="calculator">20 / 60</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 60</gadget> <output>20</output> <gadget id="calculator">40 / 60</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(2/3) * 90</gadget> <output>60</output> <gadget id="calculator">20 + 60</gadget> <output>80</output> <gadget id="calculator">60 / 60</gadget> <output>1</output> <gadget id="calculator">80 / 1</gadget> <output>80</output> <result>A</result>

A

A car was driving at 60 Km/h for 20 minutes, and then at 90Km/h for another 40 minutes. What was its average speed?

divide(add(multiply(divide(20, add(20, 40)), 60), multiply(divide(40, add(20, 40)), 90)), divide(add(20, 40), const_60))

add(n1,n3)|divide(n1,#0)|divide(n3,#0)|divide(#0,const_60)|multiply(n0,#1)|multiply(n2,#2)|add(#4,#5)|divide(#6,#3)|

"driving at 60 km / h for 20 minutes , distance covered = 60 * 1 / 3 = 20 km driving at 90 km / h for 40 minutes , distance covered = 90 * 2 / 3 = 60 km average speed = total distance / total time = 80 / 1 = 80 km / h answer : a"

general

math_qa__RsI9NhggjFIL73pp

If (A+B) = 5, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)? Choose one: A) 16 . B) 8 . C) 7 . D) 2 . E) - 1 .

<gadget id="calculator">5 + 3</gadget> <output>8</output> <gadget id="calculator">8 - 9</gadget> <output>-1</output> <result>E</result>

E

If (A+B) = 5, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?

subtract(add(5, 3), 9)

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

given a + b = 5 b + c = 9 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 5 - 9 + 3 = - 1 . option e . . .

general

math_qa__WIXgehdInXkdnl2L

In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 13 percent of revenues. The profits in 2009 were what percent of the profits in 2008? Choose the correct choice: A) 80 % B) 105 % C) 120 % D) 124.2 % E) 104 %

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 - (1/5)</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">13 * (4/5)</gadget> <output>52/5 = around 10.4</output> <gadget id="calculator">(52/5) / 10</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">(26/25) * 100</gadget> <output>104</output> <result>E</result>

E

In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 13 percent of revenues. The profits in 2009 were what percent of the profits in 2008?

multiply(divide(multiply(13, subtract(const_1, divide(20, const_100))), 10), const_100)

divide(n3,const_100)|subtract(const_1,#0)|multiply(n4,#1)|divide(#2,n1)|multiply(#3,const_100)

x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,13 = 13 / 100 x = 80 * 13 / 100 x = 10.4 10.4 / 10 = 1,04 = 104 % , answer e

gain

math_qa__wKd1tRYqFTDaRyhc

150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture? Choose the correct choice from the following answers. A) 1 / 2 B) 1 / 3 C) 1 / 4 D) 1 / 6 E) 1 / 5

<gadget id="calculator">150 * 30</gadget> <output>4_500</output> <gadget id="calculator">4_500 / 100</gadget> <output>45</output> <gadget id="calculator">400 * 12</gadget> <output>4_800</output> <gadget id="calculator">4_800 / 100</gadget> <output>48</output> <gadget id="calculator">45 + 48</gadget> <output>93</output> <gadget id="calculator">150 + 400</gadget> <output>550</output> <gadget id="calculator">93 / 550</gadget> <output>93/550 = around 0.169091</output> <result>D</result>

D

150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture?

divide(add(divide(multiply(150, 30), const_100), divide(multiply(400, 12), const_100)), add(150, 400))

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

"do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration c would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"

general

math_qa__8AhJz8zantRmlMD6

A train is moving at a speed of 100 km/hour. The length of the train is 100 metre. In how much time will it cross a pole? Select the correct option A) 1 second B) 2.5 second C) 4 second D) 3.6 second E) 4.5 second

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">100 * (5/18)</gadget> <output>250/9 = around 27.777778</output> <gadget id="calculator">100 / (250/9)</gadget> <output>18/5 = around 3.6</output> <result>D</result>

D

A train is moving at a speed of 100 km/hour. The length of the train is 100 metre. In how much time will it cross a pole?

divide(100, multiply(100, const_0_2778))

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

in order to cross the pole , the train will need to cover its own length of 100 meter . to cover 100 x 1000 meter , train takes 60 minutes or 60 x 60 = 3600 second . so , to cover 100 meter , train would take 3600 x 100 / 100 x 1000 = 3.6 second . answer : d .

physics

math_qa__sbyzxtXi6AAMZRMD

A ladder 14 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 9 feet from the base of the wall. If the top of the ladder slips down 1 feet, how many feet will the bottom of the ladder slip? Choose the correct choice from the following options: A) 4 B) 10 C) 18 D) 19 E) 25

<gadget id="calculator">14 ** 2</gadget> <output>196</output> <gadget id="calculator">9 ** 2</gadget> <output>81</output> <gadget id="calculator">196 - 81</gadget> <output>115</output> <gadget id="calculator">115 ** (1/2)</gadget> <output>sqrt(115) = around 10.723805</output> <gadget id="calculator">(sqrt(115)) - 1</gadget> <output>-1 + sqrt(115) = around 9.723805</output> <gadget id="calculator">(-1 + sqrt(115)) ** 2</gadget> <output>(-1 + sqrt(115))**2 = around 94.552389</output> <gadget id="calculator">196 - ((-1 + sqrt(115))**2)</gadget> <output>196 - (-1 + sqrt(115))**2 = around 101.447611</output> <gadget id="calculator">(196 - (-1 + sqrt(115))**2) ** (1/2)</gadget> <output>sqrt(196 - (-1 + sqrt(115))**2) = around 10.07212</output> <result>B</result>

B

A ladder 14 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 9 feet from the base of the wall. If the top of the ladder slips down 1 feet, how many feet will the bottom of the ladder slip?

sqrt(subtract(power(14, const_2), power(subtract(sqrt(subtract(power(14, const_2), power(9, const_2))), 1), const_2)))

power(n0,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)|subtract(#3,n2)|power(#4,const_2)|subtract(#0,#5)|sqrt(#6)|

"14 ^ 2 - 9 ^ 2 = 115 it means that the height is equal to 10.72 . since the top of the ladder slips down 1 feet , then the height of the wall = 10.72 - 1 = 9.72 the bottom = sqrt ( 14 ^ 2 - 9.72 ^ 2 ) = sqrt ( 196 - 94.47 ) = 10.07 ~ = 10 ans is b"

gain

math_qa__1EM5vyAFwU6odiH8

A trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.30 per metre of cloth. How much profit will the trder earn on 40 metres of cloth? Choose the most appropriate option: A) rs . 950 B) rs . 1500 C) rs . 1000 D) rs . 1200 E) none of these

<gadget id="calculator">30 * 40</gadget> <output>1_200</output> <result>D</result>

D

A trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.30 per metre of cloth. How much profit will the trder earn on 40 metres of cloth?

multiply(30, 40)

multiply(n0,n2)|

"explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 30 = rs . 175 cp on 40 metres = 175 x 40 = rs . 7000 profit earned on 40 metres cloth = rs . 8200 – rs . 7000 = rs . 1200 . answer : option d"

gain

math_qa__D7VI5AgjSbfYbpCQ

A train 330 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Options: A) 5 B) 6 C) 7 D) 18 E) 9

<gadget id="calculator">60 + 6</gadget> <output>66</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">66 * (5/18)</gadget> <output>55/3 = around 18.333333</output> <gadget id="calculator">330 / (55/3)</gadget> <output>18</output> <result>D</result>

D

A train 330 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?

divide(330, multiply(add(60, 6), const_0_2778))

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

"speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 330 * 3 / 55 = 18 sec . answer : option d"

physics

math_qa__3ZAEL7bn3CgTnOfq

If -3/(a - 3) = 3/(a + 2), then a = ? Choose the correct choice from the following. A) 1 / 2 B) 2 / 3 C) 3 / 4 D) 4 / 5 E) 5 / 6

<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">3 / 6</gadget> <output>1/2 = around 0.5</output> <result>A</result>

A

If -3/(a - 3) = 3/(a + 2), then a = ?

divide(3, multiply(3, 2))

multiply(n0,n3)|divide(n0,#0)

multiply all terms of the given equation by ( a - 3 ) ( a + 2 ) , simplify and solve ( a - 3 ) ( a + 2 ) [ - 3 / ( a - 3 ) ] = ( a - 3 ) ( a + 2 ) [ 3 / ( a + 2 ) ] - 3 ( a + 2 ) = 3 ( a - 3 ) a = 1 / 2 correct answer a

general

math_qa__LkeBf3fefn6gZ2On

Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January? Choose the correct choice from the following answers. A) 391 B) 400 C) 410 D) 423 E) 445

<gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">1 + (3/20)</gadget> <output>23/20 = around 1.15</output> <gadget id="calculator">460 / (23/20)</gadget> <output>400</output> <result>B</result>

B

Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January?

divide(460, add(const_1, divide(15, const_100)))

divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)

given : january * 1.15 = december - - > january * 1.15 = 460 - - > january = 460 / 1.15 = 400 . answer : b .

gain

math_qa__ko7L8eRbrvgk6YBe

if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the second part is ? Choose the correct choice from the following answers. A) 426 B) 526 C) 207 D) 165 E) 297

<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">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/2) + (1/3)</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">(3/4) + (5/6)</gadget> <output>19/12 = around 1.583333</output> <gadget id="calculator">782 / (19/12)</gadget> <output>9_384/19 = around 493.894737</output> <gadget id="calculator">(9_384/19) * (1/3)</gadget> <output>3_128/19 = around 164.631579</output> <result>D</result>

D

if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the second part is ?

multiply(divide(782, add(divide(3, 4), add(divide(1, 2), divide(1, 3)))), divide(1, 3))

divide(n2,n3)|divide(n2,n1)|divide(n1,n7)|add(#0,#1)|add(#3,#2)|divide(n0,#4)|multiply(#5,#1)

given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 4 / 19 = rs . 165 answer : d

general

math_qa__vemSEWnzzkWNrj68

A number is doubled and 5 is added. If the resultant is trebled, it becomes 117. What is that number? Choose the correct answer A) 12 B) 29 C) 27 D) 17 E) 99

<gadget id="calculator">3 * 5</gadget> <output>15</output> <gadget id="calculator">117 - 15</gadget> <output>102</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">102 / 6</gadget> <output>17</output> <result>D</result>

D

A number is doubled and 5 is added. If the resultant is trebled, it becomes 117. What is that number?

divide(subtract(117, multiply(const_3, 5)), multiply(const_3, const_2))

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

"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 117 6 x + 15 = 117 6 x = 102 x = 17 answer : d"

general

math_qa__LAKiZQClwo68lEwA

Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. Choose the correct choice A) 306.05 B) 306.00 C) 306.04 D) 306.05 E) 306.01

<gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">1 + (1/25)</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(26/25) ** (3/2)</gadget> <output>26*sqrt(26)/125 = around 1.060596</output> <gadget id="calculator">5_000 * (26*sqrt(26)/125)</gadget> <output>1040*sqrt(26) = around 5_302.980294</output> <gadget id="calculator">(1040*sqrt(26)) - 5_000</gadget> <output>-5000 + 1040*sqrt(26) = around 302.980294</output> <result>A</result>

A

Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.

subtract(multiply(5000, power(add(1, divide(4, const_100)), divide(const_3, 2))), 5000)

divide(n1,const_100)|divide(const_3,n4)|add(#0,n2)|power(#2,#1)|multiply(n0,#3)|subtract(#4,n0)|

"a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : a"

general

math_qa__70H7Lm736bPkG3es

What is the greatest of 3 consecutive integers whose sum is 24 ? Options. A) 3 B) 76 C) 8 D) 9 E) 10

<gadget id="calculator">24 - 3</gadget> <output>21</output> <gadget id="calculator">21 / 3</gadget> <output>7</output> <gadget id="calculator">7 + 2</gadget> <output>9</output> <result>D</result>

D

What is the greatest of 3 consecutive integers whose sum is 24 ?

add(divide(subtract(24, 3), 3), const_2)

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

explanation : the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 24 ; = > 3 n = 21 ; = > n = 7 the greatest of the three numbers is therefore 7 + 2 = 9 answer : d ) 9

physics

math_qa__Pnbt1NLX1t3zR1Qc

I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price? Pick. A) $ 2000 B) $ 2500 C) $ 2400 D) $ 3120 E) $ 1540

<gadget id="calculator">120 * 10</gadget> <output>1_200</output> <gadget id="calculator">15 - 10</gadget> <output>5</output> <gadget id="calculator">1_200 / 5</gadget> <output>240</output> <gadget id="calculator">240 * 100</gadget> <output>24_000</output> <gadget id="calculator">24_000 / 10</gadget> <output>2_400</output> <result>C</result>

C

I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price?

divide(multiply(divide(multiply(120, 10), subtract(15, 10)), const_100), 10)

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

"115 % of cost - 110 % of cost = $ 120 5 % of cost = $ 120 cost = 120 * 100 / 5 = $ 2400 answer is c"

gain

math_qa__Eghxn7VlnABmlcFT

In a division, divident is 760, divisior is 36 and quotient is 21. Find the remainder. Choose the correct choice from the following choices A) 4 B) 3 C) 2 D) 5 E) 6

<gadget id="calculator">760 % 36</gadget> <output>4</output> <result>A</result>

A

In a division, divident is 760, divisior is 36 and quotient is 21. Find the remainder.

reminder(760, 36)

reminder(n0,n1)|

"explanation : 760 = 36 x 21 + r 760 = 756 + r r = 760 - 756 = 4 answer : option a"

general

math_qa__qhtkpIxW7ykNbN5U

A certain car uses 12 gallons of gasoline in traveling 360 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased? Choose the correct choice from the following: A) 2 B) 4 C) 6 D) 8 E) 10

<gadget id="calculator">360 / 10</gadget> <output>36</output> <gadget id="calculator">360 / 12</gadget> <output>30</output> <gadget id="calculator">36 - 30</gadget> <output>6</output> <result>C</result>

C

A certain car uses 12 gallons of gasoline in traveling 360 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?

subtract(divide(360, 10), divide(360, 12))

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

"360 / 10 = 36 . the difference is 36 - 30 = 6 . answer c"

physics

math_qa__yBTnNf7BXbQsJP8k

In an election between two candidates - Lange and Sobel - 70% of the voters voted for Sobel. Of the election`s voters, 60% were male. If 35% of the female voters voted for Lange, what percentage of the male voters voted for Sobel? Choose one. A) 14 B) 16 C) 26 D) 44 E) 65

<gadget id="calculator">100 - 60</gadget> <output>40</output> <gadget id="calculator">40 * 35</gadget> <output>1_400</output> <gadget id="calculator">1_400 / 100</gadget> <output>14</output> <gadget id="calculator">40 - 14</gadget> <output>26</output> <gadget id="calculator">70 - 26</gadget> <output>44</output> <result>D</result>

D

In an election between two candidates - Lange and Sobel - 70% of the voters voted for Sobel. Of the election`s voters, 60% were male. If 35% of the female voters voted for Lange, what percentage of the male voters voted for Sobel?

subtract(70, subtract(subtract(const_100, 60), divide(multiply(subtract(const_100, 60), 35), const_100)))

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

m f total l 16 14 30 s 44 70 tot 60 40 100 35 % of 40 = 14 - - - - - - female voters that means 16 male voted for l so 60 - 16 = 44 d is correct

gain

math_qa__3zqPbFQTdKfDlsE3

A 100-litre mixture of milk and water contains 49 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x? Select the correct option A) 27.5 litres B) 26.67 litres C) 27.67 litres D) 28.57 litres E) 26 litres

<gadget id="calculator">25 / 49</gadget> <output>25/49 = around 0.510204</output> <gadget id="calculator">(25/49) ** (1/2)</gadget> <output>5/7 = around 0.714286</output> <gadget id="calculator">1 - (5/7)</gadget> <output>2/7 = around 0.285714</output> <gadget id="calculator">100 * (2/7)</gadget> <output>200/7 = around 28.571429</output> <result>D</result>

D

A 100-litre mixture of milk and water contains 49 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

multiply(100, subtract(const_1, sqrt(divide(25, 49))))

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

"working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 49 % ( 1 - x / 100 ) ^ 2 = 25 % * 100 % ( 1 - x / 100 ) ^ 2 = 25 / 49 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 5 / 7 ) ^ 2 100 - x = 500 / 7 x = 28.57 . . . ans d"

general

math_qa__Tc1ng27PKpgkoe9j

The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 46. What is a possible value for the mean of the distribution? Choose the correct option: A) 46 B) 52 C) 48 D) 49 E) 50

<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">46 + 6</gadget> <output>52</output> <gadget id="calculator">52 + 1</gadget> <output>53</output> <result>B</result>

B

The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 46. What is a possible value for the mean of the distribution?

add(add(46, multiply(3, 2)), const_1)

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

"the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 46 : { mean } - 3 * { sd } > 46 ; { mean } - 6 > 46 ; { mean } > 52 . answer : b ."

general

math_qa__CUE9RjuMf4JCxdHA

4 friends a , b , c and d decided to share a lot of apples . each of them had half of the total plus half an apple in order . after each of them took their share 3 time , no apples were left . how many apples were there ? Answers A) 4096 B) 4055 C) 4092 D) 4085 E) 4095

<gadget id="calculator">4 * 1_000</gadget> <output>4_000</output> <gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">4_000 + 100</gadget> <output>4_100</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">4_100 - 5</gadget> <output>4_095</output> <result>E</result>

E

4 friends a , b , c and d decided to share a lot of apples . each of them had half of the total plus half an apple in order . after each of them took their share 3 time , no apples were left . how many apples were there ?

subtract(add(multiply(4, const_1000), multiply(const_10, const_10)), add(const_3, const_2))

add(const_2,const_3)|multiply(n0,const_1000)|multiply(const_10,const_10)|add(#1,#2)|subtract(#3,#0)

whenever the rate of reduction is ' half of the total and half of it ' , the answer is always ( 2 ^ n ) - 1 , where ' n ' is the number of times the process is repeated . here , the process is repeated 12 times . so answer is ( 2 ^ 12 ) - 1 = 4095 answer e

general

math_qa__NhNIcZ3HF0PLnizF

Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 4 hours respectively. The ratio of their speeds is: Choose the correct choice from the following answers: A) 2 : 4 B) 4 : 3 C) 6 : 7 D) 9 : 16 E) none of these

<gadget id="calculator">4 ** (1/2)</gadget> <output>2</output> <gadget id="calculator">16 ** (1/2)</gadget> <output>4</output> <gadget id="calculator">2 / 4</gadget> <output>1/2 = around 0.5</output> <result>A</result>

A

Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 4 hours respectively. The ratio of their speeds is:

divide(sqrt(4), sqrt(16))

sqrt(n1)|sqrt(n0)|divide(#0,#1)|

"let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 4 : â ˆ š 16 = 2 : 4 . answer a"

physics

math_qa__rvPO7C02qr5LPCOX

A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 2 years ago? Pick one: A) 8 B) 12 C) 12 D) 14 E) 16

<gadget id="calculator">6 + 8</gadget> <output>14</output> <gadget id="calculator">14 - 2</gadget> <output>12</output> <result>B</result>

B

A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 2 years ago?

subtract(add(6, 8), 2)

add(n1,n2)|subtract(#0,n4)

let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 2 years ago ? i . e . d - 2 = 14 - 2 = 12 years answer : b

general

math_qa__D44uckTYROjqIQsS

A river 4m deep and 22 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is? Select: A) 4500 B) 2678 C) 2933 D) 2761 E) 2882

<gadget id="calculator">4 * 22</gadget> <output>88</output> <gadget id="calculator">2 * 1_000</gadget> <output>2_000</output> <gadget id="calculator">88 * 2_000</gadget> <output>176_000</output> <gadget id="calculator">1 * 60</gadget> <output>60</output> <gadget id="calculator">176_000 / 60</gadget> <output>8_800/3 = around 2_933.333333</output> <result>C</result>

C

A river 4m deep and 22 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?

divide(multiply(multiply(4, 22), multiply(2, const_1000)), multiply(const_1, const_60))

multiply(n0,n1)|multiply(n2,const_1000)|multiply(const_1,const_60)|multiply(#0,#1)|divide(#3,#2)

( 2000 * 4 * 22 ) / 60 = 2933 m 3 answer : c

physics

math_qa__fUOKZs7D7ymDfsSh

A drink vendor has 40 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required? Select: A) 35 B) 37 C) 42 D) 50 E) 69

<gadget id="calculator">gcd(40, 144)</gadget> <output>8</output> <gadget id="calculator">gcd(8, 368)</gadget> <output>8</output> <gadget id="calculator">368 / 8</gadget> <output>46</output> <gadget id="calculator">40 / 8</gadget> <output>5</output> <gadget id="calculator">144 / 8</gadget> <output>18</output> <gadget id="calculator">5 + 18</gadget> <output>23</output> <gadget id="calculator">46 + 23</gadget> <output>69</output> <result>E</result>

E

A drink vendor has 40 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?

add(divide(368, gcd(gcd(40, 144), 368)), add(divide(40, gcd(gcd(40, 144), 368)), divide(144, gcd(gcd(40, 144), 368))))

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

the number of liters in each can = hcf of 40 , 144 and 368 = 8 liters . number of cans of maaza = 40 / 8 = 5 number of cans of pepsi = 144 / 8 = 18 number of cans of sprite = 368 / 8 = 46 the total number of cans required = 5 + 18 + 46 = 69 cans . answer : e

general

math_qa__SO4u8J4BNSP1USXx

if x is 3 times larger than n , and if 2 n + 3 is 20 % of 25 , what is the value of ? Pick one: A) 1 B) 2 C) 3 D) 6 E) 12

<gadget id="calculator">25 * 20</gadget> <output>500</output> <gadget id="calculator">500 / 100</gadget> <output>5</output> <gadget id="calculator">5 - 3</gadget> <output>2</output> <gadget id="calculator">2 / 2</gadget> <output>1</output> <gadget id="calculator">1 * 3</gadget> <output>3</output> <result>C</result>

C

if x is 3 times larger than n , and if 2 n + 3 is 20 % of 25 , what is the value of ?

multiply(divide(subtract(divide(multiply(25, 20), const_100), 3), 2), 3)

multiply(n3,n4)|divide(#0,const_100)|subtract(#1,n0)|divide(#2,n1)|multiply(n0,#3)

then the wordings of question are misleading . moreover , it ' d also be a bad way to convey x = 4 n , if it really wanted to convey so . from other questions that i have seen , proper wordings could be : if x is three times as large as n or simply , if x is three times n . c

general

math_qa__6CJ67aRUjmc1l8d8

A one-foot stick is marked in 1/3 and 1/5 portion. How many total markings will there be, including the end points? Choose the most appropriate option: A) 10 B) 7 C) 6 D) 5 E) 8

<gadget id="calculator">3 + 5</gadget> <output>8</output> <result>E</result>

E

A one-foot stick is marked in 1/3 and 1/5 portion. How many total markings will there be, including the end points?

add(3, 5)

add(n1,n3)|

"lcm of 15 = 15 1 / 3 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 ( total = 4 ) 1 / 5 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 . . . . . . 15 ( total = 6 ) overlapping markings are 0 . . . . . . . . 15 ( total = 2 ) total markings = 4 + 6 - 2 = 8 answer = e"

general

math_qa__Si4xfICaHs8I95oc

In Arun's opinion, his weight is greater than 64 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 67 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ? Choose the correct choice from the following answers: A) 86.5 kg B) 66.5 kg C) 46.5 kg D) 65.5 kg E) 16.5 kg

<gadget id="calculator">64 + 1</gadget> <output>65</output> <gadget id="calculator">67 + 65</gadget> <output>132</output> <gadget id="calculator">132 / 2</gadget> <output>66</output> <result>D</result>

D

In Arun's opinion, his weight is greater than 64 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 67 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?

divide(add(67, add(64, const_1)), const_2)

add(n0,const_1)|add(n4,#0)|divide(#1,const_2)|

"let arun ' s weight be x kg . according to arun , 64 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 67 . the values satisfying all the above conditions are 65 and 66 . required average = ( 65 + 66 ) / 2 = 65.5 kg answer : d"

general

math_qa__j7Exl1PN7tebjXe7

Two trains are moving in opposite directions with speed of 110 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds Choose the correct choice from the following answers: A) 26 B) 48 C) 47 D) 36 E) 25

<gadget id="calculator">1.1 + 0.9</gadget> <output>2</output> <gadget id="calculator">110 + 90</gadget> <output>200</output> <gadget id="calculator">2 / 200</gadget> <output>1/100 = around 0.01</output> <gadget id="calculator">(1/100) * 3_600</gadget> <output>36</output> <result>D</result>

D

Two trains are moving in opposite directions with speed of 110 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds

multiply(divide(add(1.10, 0.9), add(110, 90)), const_3600)

add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)|

"explanation : relative speed = 110 + 90 = 200 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 200 hr = 1 / 100 hr = 3600 / 100 = 36 seconds answer : option d"

physics

math_qa__PV745jhOHqd9QhyV

In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,10). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0? Choose the most appropriate option. A) 1 / 5 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 2 / 5

<gadget id="calculator">0 + 10</gadget> <output>10</output> <gadget id="calculator">4 / 10</gadget> <output>2/5 = around 0.4</output> <result>E</result>

E

In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,10). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?

divide(const_4, add(0, const_10))

add(n0,const_10)|divide(const_4,#0)

the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e .

geometry

math_qa__XgR31rFfyOhVv4WM

Into a room you store 38 black bottles and 4 green bottles, and you turn off the light. If you ask to someone look for 2 bottles without turn on the light, what is the probability of both the selected bottles will be green? Choose the correct choice from the following choices. A) 1 / 574 B) 2 / 574 C) 1 / 287 D) 2 / 287 E) 3 / 287

<gadget id="calculator">4 - 1</gadget> <output>3</output> <gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">38 + 4</gadget> <output>42</output> <gadget id="calculator">42 - 1</gadget> <output>41</output> <gadget id="calculator">42 * 41</gadget> <output>1_722</output> <gadget id="calculator">12 / 1_722</gadget> <output>2/287 = around 0.006969</output> <result>D</result>

D

Into a room you store 38 black bottles and 4 green bottles, and you turn off the light. If you ask to someone look for 2 bottles without turn on the light, what is the probability of both the selected bottles will be green?

divide(multiply(4, subtract(4, const_1)), multiply(add(38, 4), subtract(add(38, 4), const_1)))

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

there are 4 green bottles in a group of 38 + 4 that is 42 . thus the probability of picking 2 green bottles is : ( 4 / 42 ) ( 3 / 41 ) = 2 / 287 . the correct answer is d .

other

math_qa__Bspw9WiedOmdMaMM

A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.27000. A's share is? Answers A) 9000 B) 2778 C) 6000 D) 2889 E) 6612

<gadget id="calculator">1 * 12</gadget> <output>12</output> <gadget id="calculator">12 - 6</gadget> <output>6</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">12 + 12</gadget> <output>24</output> <gadget id="calculator">12 - 8</gadget> <output>4</output> <gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">24 + 12</gadget> <output>36</output> <gadget id="calculator">27_000 / 36</gadget> <output>750</output> <gadget id="calculator">12 * 750</gadget> <output>9_000</output> <result>A</result>

A

A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.27000. A's share is?

multiply(multiply(const_1, const_12), divide(27000, add(add(multiply(const_1, const_12), multiply(subtract(const_12, 6), const_2)), multiply(subtract(const_12, 8), const_3))))

multiply(const_1,const_12)|subtract(const_12,n0)|subtract(const_12,n1)|multiply(#1,const_2)|multiply(#2,const_3)|add(#0,#3)|add(#5,#4)|divide(n2,#6)|multiply(#7,#0)

x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 27000 = 9000 answer : a

gain

math_qa__YTAXYd60m7sgAUyc

Pat, kate and mark charged a total of 198 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate. Choose the correct choice from the following: A) 18 B) 36 C) 72 D) 110 E) 108

<gadget id="calculator">1 + 2</gadget> <output>3</output> <gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">3 + 6</gadget> <output>9</output> <gadget id="calculator">198 / 9</gadget> <output>22</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">22 * 5</gadget> <output>110</output> <result>D</result>

D

Pat, kate and mark charged a total of 198 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.

multiply(divide(198, add(add(1, const_2), multiply(const_2, 3))), subtract(multiply(const_2, 3), 1))

add(n1,const_2)|multiply(n2,const_2)|add(#0,#1)|subtract(#1,n1)|divide(n0,#2)|multiply(#4,#3)|

"let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 198 - total hours charged for , x = 22 . mat charged 6 x - x or 5 x for more hours than kate , or for 110 hours . d is correct"

general

math_qa__2V33u4oPSilGPqPE

Kul is 22 years old and Saras is 33 years. Find the ratio of Saras's age to Kul's age. Choose the correct choice from the following options: A) 3 / 1 B) 3 / 2 C) 5 / 2 D) 5 / 3 E) none of these

<gadget id="calculator">33 / 22</gadget> <output>3/2 = around 1.5</output> <result>B</result>

B

Kul is 22 years old and Saras is 33 years. Find the ratio of Saras's age to Kul's age.

divide(33, 22)

divide(n1,n0)

explanation : kul is 22 years old . saras is 33 years old . saras ' s age : kul ' s age = 33 : 22 = 3 : 2 answer : b

other

math_qa__DrNjQwnB6lVSdOYS

What is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage? Choose the correct choice from the following options: A) 93.9 B) 96.3 C) 93.2 D) 96.7 E) 96.21

<gadget id="calculator">100 - 7</gadget> <output>93</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">93 + (1/5)</gadget> <output>466/5 = around 93.2</output> <result>C</result>

C

What is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage?

add(subtract(100, 7), divide(1, 5))

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

"explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 7 + 1 / 5 93.2 thus the cp is rs 93.2 . answer : c"

gain

math_qa__3RwweZupFi6t2ejM

Right triangle PQR is the base of the prism in the figure above. If PQ=PR=√14 and the height of the prism is 8, what is the volume of the prism? Choose the correct choice. A) 12 B) 45 C) 87 D) 56 E) 23

<gadget id="calculator">14 ** (1/2)</gadget> <output>sqrt(14) = around 3.741657</output> <gadget id="calculator">((sqrt(14)) * (sqrt(14))) / 2</gadget> <output>7</output> <gadget id="calculator">7 * 8</gadget> <output>56</output> <result>D</result>

D

Right triangle PQR is the base of the prism in the figure above. If PQ=PR=√14 and the height of the prism is 8, what is the volume of the prism?

multiply(triangle_area(sqrt(14), sqrt(14)), 8)

sqrt(n0)|triangle_area(#0,#0)|multiply(n1,#1)|

"volume of prism = area of base * height = 1 / 2 * ( square root of 14 ) * ( square root of 14 ) * 8 = 56 answer : d"

geometry

math_qa__F8MqNTu26YOeH0Ja

How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which at least one digit is repeated ? Answers A) 39760 B) 49760 C) 59760 D) 69760 E) 70000

<gadget id="calculator">10 ** 5</gadget> <output>100_000</output> <gadget id="calculator">10 * 9</gadget> <output>90</output> <gadget id="calculator">5 + 3</gadget> <output>8</output> <gadget id="calculator">90 * 8</gadget> <output>720</output> <gadget id="calculator">5 + 2</gadget> <output>7</output> <gadget id="calculator">720 * 7</gadget> <output>5_040</output> <gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">5_040 * 6</gadget> <output>30_240</output> <gadget id="calculator">100_000 - 30_240</gadget> <output>69_760</output> <result>D</result>

D

How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which at least one digit is repeated ?

subtract(power(const_10, 5), multiply(multiply(multiply(multiply(const_10, 9), add(5, const_3)), add(5, const_2)), add(5, const_1)))

add(n0,const_1)|add(n0,const_2)|add(n0,const_3)|multiply(n2,const_10)|power(const_10,n0)|multiply(#2,#3)|multiply(#1,#5)|multiply(#0,#6)|subtract(#4,#7)

zip codes with 5 digits ( all five digits can be repeated ) : 10 ^ 5 = 100,000 zip codes with no digit being repeated : 10 * 9 * 8 * 7 * 6 = 30,240 zip codes with at least one digit being repeated : 100,000 - 30,240 = 69,760 = 69760 ans : d

general

math_qa__EerUxz9UuyA0NyCW

If I walk at 3 km/h, I miss the bus by 12 minutes. If I walk at 6 km/h, I reach 10 minutes before the arrival of the bus. How far I walk to reach the bus stand ? Choose the correct choice from the following answers: A) 2.19 km B) 2.22 km C) 2.00 km D) 1.19 km E) 1.99 km

<gadget id="calculator">3 * 6</gadget> <output>18</output> <gadget id="calculator">6 - 3</gadget> <output>3</output> <gadget id="calculator">18 / 3</gadget> <output>6</output> <gadget id="calculator">12 + 10</gadget> <output>22</output> <gadget id="calculator">22 / 60</gadget> <output>11/30 = around 0.366667</output> <gadget id="calculator">6 * (11/30)</gadget> <output>11/5 = around 2.2</output> <result>A</result>

A

If I walk at 3 km/h, I miss the bus by 12 minutes. If I walk at 6 km/h, I reach 10 minutes before the arrival of the bus. How far I walk to reach the bus stand ?

multiply(divide(multiply(3, 6), subtract(6, 3)), divide(add(12, 10), const_60))

add(n1,n3)|multiply(n0,n2)|subtract(n2,n0)|divide(#1,#2)|divide(#0,const_60)|multiply(#3,#4)|

"d = product of speed difference of time / difference of speed d = 3 x 6 / 60 [ 12 â ˆ ’ ( â ˆ ’ 10 ) / 6 - 3 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 2.19 km answer a"

physics

math_qa__QeWp7AMTVdZc4QyZ

g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(e) is divisible by 4^11, what is the smallest possible value for e? Choose one. A) 22 B) 24 C) 28 D) 32 E) 44

<gadget id="calculator">2 * 12</gadget> <output>24</output> <result>B</result>

B

g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(e) is divisible by 4^11, what is the smallest possible value for e?

multiply(2, 12)

multiply(n2,n7)|

"g ( e ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"

general

math_qa__pxj5oDWmHFK8699p

The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 220 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? Pick: A) 44 B) 64 C) 70 D) 80 E) 84

<gadget id="calculator">220 / 5</gadget> <output>44</output> <gadget id="calculator">44 * 12</gadget> <output>528</output> <gadget id="calculator">528 / 2</gadget> <output>264</output> <gadget id="calculator">264 - 220</gadget> <output>44</output> <result>A</result>

A

The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 220 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?

subtract(divide(multiply(divide(220, 5), 12), 2), 220)

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

"let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 220 / ( 220 + x ) = 5 / 6 x = 44 the answer is a ."

other

math_qa__SrJZgXdgk9Rss7HM

Recipe requires 15mins to cook. you have 7 mins hourglass and a 11 mins hourglass with you. how will you measure 15 mins using them? Choose the correct choice from the following answers A) 15 mins B) 12 mins C) 13 mins D) 17 mins E) 20 mins

<gadget id="calculator">11 - 7</gadget> <output>4</output> <gadget id="calculator">11 + 4</gadget> <output>15</output> <result>A</result>

A

Recipe requires 15mins to cook. you have 7 mins hourglass and a 11 mins hourglass with you. how will you measure 15 mins using them?

add(11, subtract(11, 7))

subtract(n2,n1)|add(n2,#0)

correct answer : a put up both hour glasses . time starts when 7 min hourglass turns empty . and 11 min hourglass will run for 4 min . now flip 11 min hour glass upside down as soon as it runs empty . it will be empty in another 11 mins . and time is up . so 4 + 11 = 15 mins

physics

math_qa__557rNPqPMqiQiGd3

What will be the result of 7^8 - 6/2 + 9^3 +3+12 ? Answers. A) 95 B) 64 C) 1012 D) 9 E) 0

<gadget id="calculator">7 * 8</gadget> <output>56</output> <gadget id="calculator">56 - 6</gadget> <output>50</output> <gadget id="calculator">50 / 2</gadget> <output>25</output> <gadget id="calculator">25 + 9</gadget> <output>34</output> <gadget id="calculator">34 * 3</gadget> <output>102</output> <gadget id="calculator">102 - 7</gadget> <output>95</output> <result>A</result>

A

What will be the result of 7^8 - 6/2 + 9^3 +3+12 ?

subtract(multiply(add(divide(subtract(multiply(7, 8), 6), 2), 9), 3), 7)

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

the multiplication ( e . g . 7 ^ 8 ) and division ( e . g . 6 / 2 ) is done first and then the sum ( e . g . 3 + 12 ) and subtraction ( e . g . 56 - 3 ) , and the answer is 95 , option a .

general

math_qa__cMscI400NGJHK7Z5

Erik's mother gave him $86 to go to the store. Erik bought 3 loaves of bread and 3 cartons of orange juice. Each loaf of bread cost $3 and each carton of orange juice cost $6. How much money does Erik have left? Options: A) $ 24 B) $ 27 C) $ 59 D) $ 75 E) $ 35

<gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">3 * 6</gadget> <output>18</output> <gadget id="calculator">9 + 18</gadget> <output>27</output> <gadget id="calculator">86 - 27</gadget> <output>59</output> <result>C</result>

C

Erik's mother gave him $86 to go to the store. Erik bought 3 loaves of bread and 3 cartons of orange juice. Each loaf of bread cost $3 and each carton of orange juice cost $6. How much money does Erik have left?

subtract(86, add(multiply(3, 3), multiply(3, 6)))

multiply(n1,n1)|multiply(n1,n4)|add(#0,#1)|subtract(n0,#2)

step 1 : find the cost of the loaves of bread . 3 × $ 3 = $ 9 step 2 : find the cost of the orange juice . 3 × $ 6 = $ 18 step 3 : find the total cost of the groceries . $ 9 + $ 18 = $ 27 step 4 : find the amount of money left . $ 86 – $ 27 = $ 59 erik has $ 59 left . answer is c .

general

math_qa__KrfVVLty9lC4O0ln

The value of a machine depreciates at 22% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made? Choose the correct answer A) $ 255260 B) $ 435260 C) $ 125260 D) $ 115260 E) $ 155260

<gadget id="calculator">22 / 100</gadget> <output>11/50 = around 0.22</output> <gadget id="calculator">1 - (11/50)</gadget> <output>39/50 = around 0.78</output> <gadget id="calculator">(39/50) * (39/50)</gadget> <output>1_521/2_500 = around 0.6084</output> <gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">100 ** (1/2)</gadget> <output>10</output> <gadget id="calculator">10_000 * 10</gadget> <output>100_000</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 * 100</gadget> <output>500</output> <gadget id="calculator">500 * 100</gadget> <output>50_000</output> <gadget id="calculator">100_000 + 50_000</gadget> <output>150_000</output> <gadget id="calculator">(1_521/2_500) * 150_000</gadget> <output>91_260</output> <gadget id="calculator">22 + 2</gadget> <output>24</output> <gadget id="calculator">24 * 100</gadget> <output>2_400</output> <gadget id="calculator">2_400 * 10</gadget> <output>24_000</output> <gadget id="calculator">91_260 + 24_000</gadget> <output>115_260</output> <result>D</result>

D

The value of a machine depreciates at 22% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?

add(multiply(multiply(subtract(1, divide(22, const_100)), subtract(1, divide(22, const_100))), add(multiply(multiply(const_100, const_100), sqrt(const_100)), multiply(multiply(divide(sqrt(const_100), const_2), const_100), const_100))), multiply(multiply(add(22, const_2), const_100), sqrt(const_100)))

add(n0,const_2)|divide(n0,const_100)|multiply(const_100,const_100)|sqrt(const_100)|divide(#3,const_2)|multiply(#2,#3)|multiply(#0,const_100)|subtract(n1,#1)|multiply(#4,const_100)|multiply(#7,#7)|multiply(#6,#3)|multiply(#8,const_100)|add(#5,#11)|multiply(#12,#9)|add(#13,#10)|

"the value of the machine after two years = 0.78 * 0.78 * 1 , 50,000 = $ 91,260 sp such that a profit of $ 24,000 is made = 91,260 + 24,000 = $ 1 , 15,260 d"

gain

math_qa__04lL8IxD0AjMBzpp

1 ltr of water is added with 3 ltr of a solution containing 33%of alcohol in the water. The %of alcohol in the new mixture is? Pick one: A) 22 % B) 23 % C) 24.5 % D) 24.75 % E) 30 %

<gadget id="calculator">33 / 100</gadget> <output>33/100 = around 0.33</output> <gadget id="calculator">(33/100) * 3</gadget> <output>99/100 = around 0.99</output> <gadget id="calculator">1 + 3</gadget> <output>4</output> <gadget id="calculator">(99/100) / 4</gadget> <output>99/400 = around 0.2475</output> <gadget id="calculator">100 * (99/400)</gadget> <output>99/4 = around 24.75</output> <result>D</result>

D

1 ltr of water is added with 3 ltr of a solution containing 33%of alcohol in the water. The %of alcohol in the new mixture is?

multiply(const_100, divide(multiply(divide(33, const_100), 3), add(1, 3)))

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

"we have a 3 litre solution containing 33 % of alcohol in the water . = > quantity of alcohol in the solution = 3 ã — 33 / 100 now 1 litre of water is added to the solution . = > total quantity of the new solution = 3 + 1 = 4 percentage of alcohol in the new solution = 3 ã — 33 / 100 4 ã — 100 = 3 ã — 331004 ã — 100 = 3 ã — 8.25 / 100 = 24.75 % d"

general

math_qa__cCRYbAt030KjhCzb

12 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? Choose the correct choice from the following answers: A) 5 B) 12 C) 18 D) 24 E) 28

<gadget id="calculator">12 * 8</gadget> <output>96</output> <gadget id="calculator">1 / 96</gadget> <output>1/96 = around 0.010417</output> <gadget id="calculator">(1/96) * 12</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">12 - 9</gadget> <output>3</output> <gadget id="calculator">(7/8) / 3</gadget> <output>7/24 = around 0.291667</output> <gadget id="calculator">(7/24) / (1/96)</gadget> <output>28</output> <result>E</result>

E

12 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?

divide(divide(subtract(const_1, multiply(divide(const_1, multiply(12, 8)), 12)), subtract(12, 9)), divide(const_1, multiply(12, 8)))

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

"1 . we need to find out the time taken by 3 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 12 * 8 = 96 days 4 . but on day 1 twelve workers had already worked finishing 1 / 8 of the job . so 3 workers have to finish only 7 / 8 of the job . 5 . total time taken by 3 workers can be got from formula used at ( 2 ) . i . e . , 3 * total time taken = 96 . total time taken by 3 workers to finish the complete job is 96 / 3 = 32 days . 6 . time taken by 6 workers to finish 7 / 8 of the job is 7 / 8 * 32 = 28 days . the answer is choice e"

physics

math_qa__yCsV75hBr3B6mel9

A’s speed is 20/15 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat? Choose one: A) 1 / 17 B) 3 / 17 C) 1 / 10 D) 5 / 20 E) 3 / 10

<gadget id="calculator">20 - 15</gadget> <output>5</output> <gadget id="calculator">5 / 20</gadget> <output>1/4 = around 0.25</output> <result>D</result>

D

A’s speed is 20/15 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?

divide(subtract(20, 15), 20)

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

"we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 15 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 5 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 5 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 15 meters ) to reach the finish line . so b should get a head start of 5 / 20 th of the race . answer ( d )"

general

math_qa__ih41DsH0UMWkNH7f

The sum of the even numbers between 1 and n is 81*82, where n is an odd number, then n=? Choose the correct choice. A) 163 B) 171 C) 177 D) 185 E) 193

<gadget id="calculator">81 * 2</gadget> <output>162</output> <gadget id="calculator">162 + 1</gadget> <output>163</output> <result>A</result>

A

The sum of the even numbers between 1 and n is 81*82, where n is an odd number, then n=?

add(multiply(81, const_2), 1)

multiply(n1,const_2)|add(#0,n0)|

"let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 81 * 82 then a = 81 and n = 163 . the answer is a ."

general