Question: donovan and michael are racing around a circular 400 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 36 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?

<gadget id="calculator">400 / 36</gadget>
<output>100/9 = around 11.111111</output>

<gadget id="calculator">400 / 45</gadget>
<output>80/9 = around 8.888889</output>

<gadget id="calculator">(100/9) - (80/9)</gadget>
<output>20/9 = around 2.222222</output>

<gadget id="calculator">400 / (20/9)</gadget>
<output>180</output>

<gadget id="calculator">180 / 36</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 8
B. 7
C. 6
D. 5
E. 9

divide(divide(400, subtract(divide(400, 36), divide(400, 45))), 36)

Explanation: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 400 / 45 = > 80 / 9 2 . speed / rate of michael = distance / time = > 400 / 36 = > 100 / 9 relative speed between them = 100 / 9 - 80 / 9 = > 20 / 9 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 400 , relative rate = 20 / 9 total time taken by micheal to surpass donovan = distance / rate = > 400 * 9 / 20 = > 3600 / 10 = > 180 no . of laps taken by michael = total time / michael ' s rate = > 180 / 36 = > 5 hence correct answer is 5 laps . d"


Question: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 9 people to do 9 times of that particular work ?

<gadget id="calculator">9 / 9</gadget>
<output>1</output>

<gadget id="calculator">3 * 1</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 1
B. 2
C. 3
D. 9
E. 12

Explanation: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 9 people can do 9 / 3 of the work in one day . 9 people can do 9 times the work in 3 days . the answer is c ."


Question: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.5 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :

<gadget id="calculator">15.8 - 15.4</gadget>
<output>0.4</output>

<gadget id="calculator">16.5 - 15.8</gadget>
<output>0.7</output>

<gadget id="calculator">0.4 / 0.7</gadget>
<output>0.571429</output>
<result>0.571429</result>

Choices:
A. 2 : 5
B. 2 : 3
C. 2 : 4
D. 2 : 1
E. 4 : 7

Explanation: "let the ratio be k : 1 . then , k * 16.5 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.5 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.7 = 4 / 7 required ratio = 4 / 7 : 1 = 4 : 7 . answer : e"


Question: 4 wolves , wolverine , man - hunter , blue - wolf , and jasmine , caught rabbits for their evening meal . if man - hunter caught 3 more rabbits than blue - wolf did , jasmine caught 3 less than wolverine did , and wolverine caught 1 more than man - hunter did , how many more fewer rabbits did blue - wolf catch than jasmine ?

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">3 + 3</gadget>
<output>6</output>

<gadget id="calculator">5 - 6</gadget>
<output>-1</output>
<result>-1</result>

Choices:
A. - 3
B. - 2
C. - 5
D. - 12
E. - 1

Explanation: in this word problem , the first key is to turn the story into equations : man - hunter caught 3 more than blue - wolf did : m = 3 + b jasmine caught 3 less than wolverine did : j = w - 3 wolverine caught 3 more than man - hunter did : w = 1 + m then , in classic gmat style , the problem does n ' t ask you to solve for a single variable , but instead to solve for the difference between b and j ( how many more rabbits did blue - wolf catch than jasmine did ? ) . this means that your goal is to get the equations in terms of b and j so that you can solve for the expression b - j . taking the first equation and solving for b , you have b = m - 3 . taking the second equation and solving for j you have j = w - 3 , and then with the third equation you can replace w with 1 + m so that both b and j are in terms of m : j = ( 1 + m ) - 3 . so if b = m - 3 and j = m - 2 , then : b - j = ( m - 3 ) - ( m - 2 ) b - j = m - 3 - m + 2 ( remove the parentheses by distributing the multiplication ) b - j = - 1 , so the answer is e .


Question: a bullet train 160 m long is running with a speed of 70 kmph . in what time will it pass a man who is running at 8 kmph in the direction opposite to that in which the bullet train is going ?

<gadget id="calculator">70 + 8</gadget>
<output>78</output>

<gadget id="calculator">78 * 1_000</gadget>
<output>78_000</output>

<gadget id="calculator">78_000 / 3_600</gadget>
<output>65/3 = around 21.666667</output>

<gadget id="calculator">160 / (65/3)</gadget>
<output>96/13 = around 7.384615</output>
<result>96/13 = around 7.384615</result>

Choices:
A. 23 sec
B. 15 sec
C. 7.38 sec
D. 6.92 sec
E. 16 sec

divide(160, divide(multiply(add(70, 8), const_1000), const_3600))

Explanation: "c 7.38 sec speed of the bullet train relative to man = ( 70 + 8 ) kmph = 78 * 5 / 18 m / sec = 65 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 160 m at ( 65 / 3 ) m / sec = ( 160 * 3 / 65 ) sec = 7.38 sec"


Question: a man can do a job in 5 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?

<gadget id="calculator">1 / 25</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/5) + (1/20)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/25) + (1/4)</gadget>
<output>29/100 = around 0.29</output>

<gadget id="calculator">1 / (29/100)</gadget>
<output>100/29 = around 3.448276</output>
<result>100/29 = around 3.448276</result>

Choices:
A. 6.3
B. 6.9
C. 3.5
D. 6.1
E. 6.2

divide(const_1, add(divide(const_1, 25), add(divide(const_1, 5), divide(const_1, 20))))

Explanation: "1 day work of the three persons = ( 1 / 5 + 1 / 20 + 1 / 25 ) = 29 / 100 so , all three together will complete the work in 100 / 29 = 3.5 days . answer : c"


Question: in a kilometer race , a beats b by 52 meters or 18 seconds . what time does a take to complete the race ?

<gadget id="calculator">1 * 1_000</gadget>
<output>1_000</output>

<gadget id="calculator">52 / 18</gadget>
<output>26/9 = around 2.888889</output>

<gadget id="calculator">1_000 / (26/9)</gadget>
<output>4_500/13 = around 346.153846</output>

<gadget id="calculator">(4_500/13) - 18</gadget>
<output>4_266/13 = around 328.153846</output>
<result>4_266/13 = around 328.153846</result>

Choices:
A. 277 sec
B. 190 sec
C. 328 sec
D. 367 sec
E. 376 sec

subtract(divide(multiply(const_1, const_1000), divide(52, 18)), 18)

Explanation: "time taken by b run 1000 meters = ( 1000 * 18 ) / 52 = 346 sec . time taken by a = 346 - 18 = 328 sec . answer : c"


Question: a towel , when bleached , lost 30 % of its length and 25 % of its breadth . what is the percentage decrease in area ?

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>

<gadget id="calculator">100 - 30</gadget>
<output>70</output>

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">70 * 75</gadget>
<output>5_250</output>

<gadget id="calculator">10_000 - 5_250</gadget>
<output>4_750</output>

<gadget id="calculator">4_750 / 100</gadget>
<output>95/2 = around 47.5</output>
<result>95/2 = around 47.5</result>

Choices:
A. 24 %
B. 30 %
C. 44 %
D. 54 %
E. 47.5 %

divide(subtract(multiply(const_100, const_100), multiply(subtract(const_100, 30), subtract(const_100, 25))), const_100)

Explanation: "percentage change in area = ( − 30 − 25 + ( 30 × 25 ) / 100 ) % = − 47.5 % i . e . , area is decreased by 47.5 % answer : e"


Question: a train 270 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :

<gadget id="calculator">270 / 1_000</gadget>
<output>27/100 = around 0.27</output>

<gadget id="calculator">25 + 2</gadget>
<output>27</output>

<gadget id="calculator">(27/100) / 27</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">3_600 * (1/100)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 30 sec
B. 32 sec
C. 36 sec
D. 38 sec
E. 40 sec

multiply(const_3600, divide(divide(270, const_1000), add(25, 2)))

Explanation: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 270 × 2 / 15 ) sec = 36 sec answer : c"


Question: speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4864 km and comes back to the starting point . the total time taken by him is :

<gadget id="calculator">14 + 1.2</gadget>
<output>15.2</output>

<gadget id="calculator">4_864 / 15.2</gadget>
<output>320</output>

<gadget id="calculator">14 - 1.2</gadget>
<output>12.8</output>

<gadget id="calculator">4_864 / 12.8</gadget>
<output>380</output>

<gadget id="calculator">320 + 380</gadget>
<output>700</output>
<result>700</result>

Choices:
A. 700
B. 200
C. 540
D. 120
E. 635

Explanation: "explanation : speed downstream = ( 14 + 1.2 ) = 15.2 kmph speed upstream = ( 14 - 1.2 ) = 12.8 kmph total time taken = 4864 / 15.2 + 4864 / 12.8 = 320 + 380 = 700 hours . answer : a"


Question: you enter a weight loss challenge game and manage to lose 13 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?

<gadget id="calculator">13 / 100</gadget>
<output>13/100 = around 0.13</output>

<gadget id="calculator">1 - (13/100)</gadget>
<output>87/100 = around 0.87</output>

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">1 + (1/50)</gadget>
<output>51/50 = around 1.02</output>

<gadget id="calculator">(87/100) * (51/50)</gadget>
<output>4_437/5_000 = around 0.8874</output>

<gadget id="calculator">1 - (4_437/5_000)</gadget>
<output>563/5_000 = around 0.1126</output>

<gadget id="calculator">(563/5_000) * 100</gadget>
<output>563/50 = around 11.26</output>
<result>563/50 = around 11.26</result>

Choices:
A. 13 %
B. 9.22 %
C. 11.26 %
D. 14 %
E. 12 %

multiply(subtract(const_1, multiply(subtract(const_1, divide(13, const_100)), add(const_1, divide(2, const_100)))), const_100)

Explanation: ( 100 % - 13 % ) * ( 100 % + 2 % ) = 0.87 * 1.02 = 11.26 % the weigh in records your weight loss at 11.26 % ! the answer is c


Question: i bought two books ; for rs . 500 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?

<gadget id="calculator">100 + 19</gadget>
<output>119</output>

<gadget id="calculator">500 * 119</gadget>
<output>59_500</output>

<gadget id="calculator">100 - 15</gadget>
<output>85</output>

<gadget id="calculator">85 + 119</gadget>
<output>204</output>

<gadget id="calculator">59_500 / 204</gadget>
<output>875/3 = around 291.666667</output>
<result>875/3 = around 291.666667</result>

Choices:
A. 337
B. 280
C. 299.67
D. 266.67
E. 291.67

divide(multiply(500, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19)))

Explanation: "x * ( 85 / 100 ) = ( 500 - x ) 119 / 100 x = 291.67 answer : e"


Question: in a group of ducks and cows , the total number of legs are 40 more than twice the number of heads . find the total number of cows .

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 12
B. 14
C. 16
D. 18
E. 20

Explanation: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 40 more than twice the number of heads = > 2 ( d + 2 c ) = 40 + 2 ( c + d ) = > d + 2 c = 20 + c + d = > 2 c = 20 + c = > c = 20 i . e . , total number of cows = 20 answer is e ."


Question: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?

<gadget id="calculator">102 + 138</gadget>
<output>240</output>

<gadget id="calculator">240 / 2</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 90
B. 100
C. 120
D. 160
E. 200

Explanation: "solution : let x be the number he chose , then 2 * x * 138 = 102 2 x = 240 x = 120 correct answer c"


Question: the product of two successive numbers is 4160 . which is the smaller of the two numbers ?

<gadget id="calculator">4_160 ** (1/2)</gadget>
<output>8*sqrt(65) = around 64.498062</output>
<result>8*sqrt(65) = around 64.498062</result>

Choices:
A. 78
B. 64
C. 88
D. 67
E. 37

Explanation: "b 4160 from the given alternatives , 64 × 65 = 4160 ∴ smaller number = 64"


Question: soymilk are sold in packages of two or 3 only . if hannah bought 17 soymilk exactly , what could be the number of large packs hannah bought ?

<gadget id="calculator">2 * 4</gadget>
<output>8</output>

<gadget id="calculator">17 - 8</gadget>
<output>9</output>

<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 1
B. 4
C. 3
D. 5
E. 8

divide(subtract(17, multiply(const_2, const_4)), 3)

Explanation: let number of packs of three = t let number of packs of two = w 3 t + 2 w = 17 now , we need to test for values of w . since sum 17 is odd and 2 w will always be even , therefore w ca n ' t be even . now , we can test for values w = 1 , 3 and 5 2 * 4 + 3 * 3 = 8 + 9 = 17 answer c


Question: what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21.50 ?

<gadget id="calculator">25 - 21.5</gadget>
<output>3.5</output>

<gadget id="calculator">21.5 - 16</gadget>
<output>5.5</output>

<gadget id="calculator">3.5 / 5.5</gadget>
<output>0.636364</output>
<result>0.636364</result>

Choices:
A. 10 : 7
B. 9 : 8
C. 7 : 11
D. 13 : 11
E. 14 : 8

Explanation: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3.50 : 5.50 = 7 : 11"


Question: a 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?

<gadget id="calculator">300 / 18</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) * 33</gadget>
<output>550</output>

<gadget id="calculator">550 - 300</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 250
B. 266
C. 230
D. 288
E. 271

subtract(multiply(divide(300, 18), 33), 300)

Explanation: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 33 = 50 / 3 3 ( x + 300 ) = 1650 è x = 250 m . answer : a"


Question: bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">60 * 3</gadget>
<output>180</output>

<gadget id="calculator">1 / 180</gadget>
<output>1/180 = around 0.005556</output>

<gadget id="calculator">(1/60) + (1/180)</gadget>
<output>1/45 = around 0.022222</output>

<gadget id="calculator">1 / (1/45)</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 30
B. 45
C. 50
D. 25
E. 60

divide(const_1, add(divide(const_1, 60), divide(const_1, multiply(60, const_3))))

Explanation: "let capacity of p be x liters then capacity of q = x / 3 liters capacity of the drum = 60 x required number of turns = 60 x / ( x + x / 3 ) = 60 x * 3 / 4 x = 45 answer is b"


Question: if 4 / ( 1 + 3 / x ) = 1 , then x =

<gadget id="calculator">4 - 1</gadget>
<output>3</output>

<gadget id="calculator">3 / 3</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 3
B. 1
C. 1 / 3
D. - 1 / 3
E. - 3

Explanation: "the expression 4 / ( 1 + 3 / x ) = 1 should have been equal to something . if 4 / ( 1 + 3 / x ) = 1 = > 4 x / ( x + 3 ) = 1 = > 4 x = x + 3 = > 3 x = 3 = > x = 1 correct option : b"


Question: a 16 % stock yielding 10 % is quoted at :

<gadget id="calculator">100 / 10</gadget>
<output>10</output>

<gadget id="calculator">10 * 16</gadget>
<output>160</output>
<result>160</result>

Choices:
A. 83.33
B. 110
C. 112
D. 120
E. 160

Explanation: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 16 , money invested = rs . ( 100 / 10 x 16 ) = rs . 160 . â ˆ ´ market value of rs . 100 stock = rs . 160 answer e"


Question: there are , in a certain league , 20 teams , and each team face another team for a total of 10 times . how many games are played in the season ?

<gadget id="calculator">20 - 1</gadget>
<output>19</output>

<gadget id="calculator">19 * 10</gadget>
<output>190</output>

<gadget id="calculator">20 / 2</gadget>
<output>10</output>

<gadget id="calculator">190 * 10</gadget>
<output>1_900</output>
<result>1_900</result>

Choices:
A. 1900
B. 3600
C. 2400
D. 180
E. 5400

multiply(multiply(subtract(20, const_1), 10), divide(20, const_2))

Explanation: "1 st team : 190 2 nd team : 180 3 rd team : 170 similarly the last team will play 0 therefore ( 190 + 180 + 170 . . . . 10 ) 10 ( 19 + 18 + 17 + 16 . . . . 1 ) 10 ( n ( n + 1 ) / 2 ) = 10 ( 19 * 20 / 2 ) = 1900 answer : a"


Question: if integer k is equal to the sum of all even multiples of 15 between 390 and 615 , what is the greatest prime factor of k ?

<gadget id="calculator">615 / 15</gadget>
<output>41</output>

<gadget id="calculator">floor(41)</gadget>
<output>41</output>

<gadget id="calculator">41 * 15</gadget>
<output>615</output>

<gadget id="calculator">390 / 15</gadget>
<output>26</output>

<gadget id="calculator">floor(26)</gadget>
<output>26</output>

<gadget id="calculator">26 * 15</gadget>
<output>390</output>

<gadget id="calculator">615 - 390</gadget>
<output>225</output>

<gadget id="calculator">225 / 15</gadget>
<output>15</output>

<gadget id="calculator">15 + 1</gadget>
<output>16</output>

<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 5
B. 7
C. 8
D. 13
E. 17

divide(add(divide(subtract(multiply(floor(divide(615, 15)), 15), multiply(floor(divide(390, 15)), 15)), 15), const_1), const_2)

Explanation: "if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600 . using arithmetic progression to find n : 600 = 390 + ( n - 1 ) 30 210 + 30 = 30 n 240 = 3 n = > n = 8 the sum would be : 8 * mean mean = [ 600 + 390 ] / 2 = 495 8 * 495 c"


Question: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 54 , what is the total amount ?

<gadget id="calculator">100 / 45</gadget>
<output>20/9 = around 2.222222</output>

<gadget id="calculator">(20/9) * 54</gadget>
<output>120</output>

<gadget id="calculator">30 / 45</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 54</gadget>
<output>36</output>

<gadget id="calculator">120 + 36</gadget>
<output>156</output>

<gadget id="calculator">156 + 54</gadget>
<output>210</output>
<result>210</result>

Choices:
A. 166
B. 105
C. 178
D. 177
E. 210

add(add(multiply(divide(const_100, 45), 54), multiply(divide(30, 45), 54)), 54)

Explanation: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 54 35 - - - ? = > 210 answer : e"


Question: the expenditure of a businessman increase consistently by 10 % per year . if his present expenditure is rs . 20000 then what will his expenditure be after 2 years ?

<gadget id="calculator">100 + 10</gadget>
<output>110</output>

<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>

<gadget id="calculator">20_000 * (121/100)</gadget>
<output>24_200</output>
<result>24_200</result>

Choices:
A. 24500
B. 24400
C. 24300
D. 24200
E. 24100

multiply(20000, power(divide(add(const_100, 10), const_100), 2))

Explanation: explanation : expenditure = 20000 x 1.1 x 1.1 = 24200 answer : option d


Question: farm tax is levied on the 25 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :

<gadget id="calculator">480 / 3_840</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 100</gadget>
<output>1_250</output>

<gadget id="calculator">1_250 / 25</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 15 %
B. 25 %
C. 50 %
D. 0.2083 %
E. none

divide(multiply(multiply(divide(480, 3840), const_100), const_100), 25)

Explanation: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 25 ) = 50 % the correct answer is ( c ) ."


Question: a textile manufacturing firm employees 100 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 100 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :

<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 * 100</gadget>
<output>500_000</output>

<gadget id="calculator">75_000 * 2</gadget>
<output>150_000</output>

<gadget id="calculator">150_000 + 75_000</gadget>
<output>225_000</output>

<gadget id="calculator">500_000 - 225_000</gadget>
<output>275_000</output>

<gadget id="calculator">100 - 1</gadget>
<output>99</output>

<gadget id="calculator">99 / 100</gadget>
<output>99/100 = around 0.99</output>

<gadget id="calculator">(99/100) * 500_000</gadget>
<output>495_000</output>

<gadget id="calculator">150_000 * (99/100)</gadget>
<output>148_500</output>

<gadget id="calculator">495_000 - 148_500</gadget>
<output>346_500</output>

<gadget id="calculator">346_500 - 75_000</gadget>
<output>271_500</output>

<gadget id="calculator">275_000 - 271_500</gadget>
<output>3_500</output>
<result>3_500</result>

Choices:
A. 13000
B. 7000
C. 10000
D. 3500
E. none of these

subtract(subtract(multiply(multiply(5, const_1000), const_100), add(multiply(75000, const_2), 75000)), subtract(subtract(multiply(divide(subtract(100, 1), 100), multiply(multiply(5, const_1000), const_100)), multiply(multiply(75000, const_2), divide(subtract(100, 1), 100))), 75000))

Explanation: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 99 / 100 ) â ˆ ’ 150000 ã — ( 99 / 100 ) â ˆ ’ 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 71,500 = > rs . 3,500 . answer : d"


Question: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 18 minutes , how much time will she spend doing yoga ? ( rounded to minutes )

<gadget id="calculator">2 + 3</gadget>
<output>5</output>

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">18 * (3/5)</gadget>
<output>54/5 = around 10.8</output>

<gadget id="calculator">(3/5) * (3/5)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(54/5) / (9/25)</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30 min .
B. 41 min .
C. 17 min .
D. 23 min .
E. 25 min .

divide(multiply(18, divide(3, add(2, 3))), multiply(divide(3, add(2, 3)), divide(3, add(2, 3))))

Explanation: "the ratio is 2 : 3 = gym : ride , so ( 18 ) ( 3 / 2 ) = 27 minutes at the gym , and 27 + 18 = 45 minutes exercise , so ( 2 / 3 ) ( 45 ) = 30 minutes yoga . answer : a"


Question: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 1 . what is the value of 13 y – x ?

<gadget id="calculator">2 * 4</gadget>
<output>8</output>

<gadget id="calculator">8 - 1</gadget>
<output>7</output>

<gadget id="calculator">8 * 3</gadget>
<output>24</output>

<gadget id="calculator">2 * 11</gadget>
<output>22</output>

<gadget id="calculator">24 - 22</gadget>
<output>2</output>

<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">13 * (7/2)</gadget>
<output>91/2 = around 45.5</output>

<gadget id="calculator">11 * (7/2)</gadget>
<output>77/2 = around 38.5</output>

<gadget id="calculator">(77/2) + 4</gadget>
<output>85/2 = around 42.5</output>

<gadget id="calculator">(91/2) - (85/2)</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 2
B. 3
C. 4
D. 5
E. 6

subtract(multiply(13, divide(subtract(multiply(2, 4), 1), subtract(multiply(8, 3), multiply(2, 11)))), add(multiply(11, divide(subtract(multiply(2, 4), 1), subtract(multiply(8, 3), multiply(2, 11)))), 4))

Explanation: ( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 3 = x 13 y - x = 3 the answer is b .


Question: what is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad ?

<gadget id="calculator">15.17 * 100</gadget>
<output>1_517</output>

<gadget id="calculator">9.02 * 100</gadget>
<output>902</output>

<gadget id="calculator">1_517 * 902</gadget>
<output>1_368_334</output>

<gadget id="calculator">4 * 10</gadget>
<output>40</output>

<gadget id="calculator">40 + 1</gadget>
<output>41</output>

<gadget id="calculator">41 ** 2</gadget>
<output>1_681</output>

<gadget id="calculator">1_368_334 / 1_681</gadget>
<output>814</output>
<result>814</result>

Choices:
A. 814
B. 266
C. 287
D. 999
E. 661

divide(rectangle_area(multiply(15.17, const_100), multiply(9.02, const_100)), square_area(add(multiply(const_4, const_10), const_1)))

Explanation: explanation : length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = required number of tiles = = 814 answer : a ) 814


Question: if a drawing has an outer circle of diameter 30 and an inner circle of diameter 24 , then what fraction of outer circle ' s surface is not covered by the inner circle ?

<gadget id="calculator">30 / 2</gadget>
<output>15</output>

<gadget id="calculator">15 ** 2</gadget>
<output>225</output>

<gadget id="calculator">pi * 225</gadget>
<output>225*pi = around 706.858347</output>

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

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>

<gadget id="calculator">pi * 144</gadget>
<output>144*pi = around 452.389342</output>

<gadget id="calculator">(225*pi) - (144*pi)</gadget>
<output>81*pi = around 254.469005</output>

<gadget id="calculator">(81*pi) / (225*pi)</gadget>
<output>9/25 = around 0.36</output>
<result>9/25 = around 0.36</result>

Choices:
A. 3 / 6
B. 8 / 24
C. 14 / 16
D. 9 / 25
E. 2 / 3

divide(subtract(multiply(const_pi, power(divide(30, const_2), const_2)), multiply(const_pi, power(divide(24, const_2), const_2))), multiply(const_pi, power(divide(30, const_2), const_2)))

Explanation: the questions asks us to find the surface which is not covered by the inner circle i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the inner circle = pi * r ^ 2 , where r = 12 = > pi * 144 area of the outer circle = pi * 225 surface not covered by the inner circle = pi * 225 - pi * 144 = pi * 81 fraction of outer circle ' s surface is not covered by the inner circle = pi * 81 / total area of the outer circle = > pi * 81 / pi * 225 = 9 / 25 answer is d


Question: x can finish a work in 24 days . y can finish the same work in 16 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">10 * (1/16)</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">(3/8) / (1/24)</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 3
B. 5
C. 6
D. 8
E. 9

divide(subtract(const_1, multiply(10, divide(const_1, 16))), divide(const_1, 24))

Explanation: "work done by x in 1 day = 1 / 24 work done by y in 1 day = 1 / 16 work done by y in 10 days = 10 / 16 = 5 / 8 remaining work = 1 – 5 / 8 = 3 / 8 number of days in which x can finish the remaining work = ( 3 / 8 ) / ( 1 / 24 ) = 9 e"


Question: some of 45 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(2/5) - (9/20)</gadget>
<output>-1/20 = around -0.05</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) - (9/20)</gadget>
<output>-1/5 = around -0.2</output>

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

Choices:
A. 2 / 5
B. 1 / 4
C. 1 / 5
D. 1 / 7
E. 2 / 3

divide(subtract(divide(40, const_100), divide(45, const_100)), subtract(divide(25, const_100), divide(45, const_100)))

Explanation: "let total paint = 1 let amount replaced = x 45 ( 1 - x ) + 25 x = 40 x = 1 / 4 answer : b"


Question: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 59 ?

<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>

<gadget id="calculator">4 * 17</gadget>
<output>68</output>

<gadget id="calculator">68 * 59</gadget>
<output>4_012</output>
<result>4_012</result>

Choices:
A. 3944
B. 920
C. 7290
D. 6928
E. 4012

Explanation: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 59 = rs . 4012 . answer : option e"


Question: at jerri ’ s pet shop , 60 cups of bird seed are used every 5 days to feed 20 parakeets . how many cups of bird seed would be required to feed 10 parakeets for 5 days ?

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 45.6
B. 20
C. 9
D. 30
E. 65

Explanation: let ' s go step - by - step . 60 cups are used over a 5 day period , which means 12 cups a day . this feeds 20 parakeets , which means each parakeet needs . 60 of a cup every day . for 10 parakeets , we need 10 * . 60 cups = 6 cups a day . over 5 days , we need 30 cups . choice d .


Question: a jar of 180 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?

<gadget id="calculator">180 * 2</gadget>
<output>360</output>

<gadget id="calculator">360 * 4</gadget>
<output>1_440</output>

<gadget id="calculator">2 ** 2</gadget>
<output>4</output>

<gadget id="calculator">1_440 + 4</gadget>
<output>1_444</output>

<gadget id="calculator">1_444 ** (1/2)</gadget>
<output>38</output>

<gadget id="calculator">38 - 2</gadget>
<output>36</output>

<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 16
B. 18
C. 20
D. 22
E. 24

divide(subtract(sqrt(add(multiply(multiply(180, 2), const_4), power(2, 2))), 2), 2)

Explanation: "180 = 18 * 10 = 20 * 9 there are 18 people in the group today . the answer is b ."


Question: a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is :

<gadget id="calculator">12.4 - 0.4</gadget>
<output>12</output>

<gadget id="calculator">5 * 12</gadget>
<output>60</output>

<gadget id="calculator">60 - 26</gadget>
<output>34</output>

<gadget id="calculator">34 / 0.4</gadget>
<output>85</output>
<result>85</result>

Choices:
A. 18
B. 17
C. 76
D. 85
E. 86

divide(subtract(multiply(5, subtract(12.4, 0.4)), 26), 0.4)

Explanation: "let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d"


Question: the average of first 5 multiples of 5 is

<gadget id="calculator">5 * 2</gadget>
<output>10</output>

<gadget id="calculator">5 + 10</gadget>
<output>15</output>

<gadget id="calculator">5 * 3</gadget>
<output>15</output>

<gadget id="calculator">15 + 15</gadget>
<output>30</output>

<gadget id="calculator">5 * 4</gadget>
<output>20</output>

<gadget id="calculator">30 + 20</gadget>
<output>50</output>

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">50 + 25</gadget>
<output>75</output>

<gadget id="calculator">75 / 5</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 3
B. 6
C. 9
D. 12
E. 15

divide(add(add(add(add(5, multiply(5, const_2)), multiply(5, const_3)), multiply(5, const_4)), multiply(5, 5)), 5)

Explanation: solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e


Question: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 50 percent of the drive from the center , what percent of the round - trip has the technician completed ?

<gadget id="calculator">100 / 2</gadget>
<output>50</output>

<gadget id="calculator">50 * 50</gadget>
<output>2_500</output>

<gadget id="calculator">2_500 / 100</gadget>
<output>25</output>

<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 70
B. 65
C. 60
D. 75
E. 80

add(divide(const_100, const_2), divide(multiply(50, divide(const_100, const_2)), const_100))

Explanation: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 50 % of 50 % i . e 25 % . so he completed 50 + 25 = 75 % of total trip . d"


Question: the difference of two numbers is 1415 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?

<gadget id="calculator">1_415 + 15</gadget>
<output>1_430</output>

<gadget id="calculator">6 - 1</gadget>
<output>5</output>

<gadget id="calculator">1_430 / 5</gadget>
<output>286</output>
<result>286</result>

Choices:
A. 270
B. 280
C. 290
D. 300
E. 310

divide(add(1415, 15), subtract(6, const_1))

Explanation: let the smaller number be x . then larger number = ( x + 1415 ) . x + 1415 = 6 x + 15 5 x = 1400 x = 280 smaller number = 280 . b )


Question: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">75 * (1/4)</gadget>
<output>75/4 = around 18.75</output>

<gadget id="calculator">75 - (75/4)</gadget>
<output>225/4 = around 56.25</output>

<gadget id="calculator">100 - (225/4)</gadget>
<output>175/4 = around 43.75</output>

<gadget id="calculator">(175/4) / (225/4)</gadget>
<output>7/9 = around 0.777778</output>

<gadget id="calculator">100 * (7/9)</gadget>
<output>700/9 = around 77.777778</output>
<result>700/9 = around 77.777778</result>

Choices:
A. 32.5
B. 77.78
C. 48
D. 65
E. 67.5

multiply(const_100, divide(subtract(const_100, subtract(subtract(const_100, 25), multiply(subtract(const_100, 25), divide(25, const_100)))), subtract(subtract(const_100, 25), multiply(subtract(const_100, 25), divide(25, const_100)))))

Explanation: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 56.25 4 ) now 56.25 has to be added byx % in order to equal the original price . 56.25 + ( x % ) 56.25 = 100 . solving this eq for x , we get x = 77.78 ans is b ."


Question: of the 180 people at a party , 70 were women , and 30 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?

<gadget id="calculator">180 - 50</gadget>
<output>130</output>

<gadget id="calculator">130 - 30</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 40
B. 50
C. 60
D. 70
E. 100

Explanation: "total people at party = 180 women = 70 so men 180 - 70 = 110 no . of pple who tried appetizer = 180 - 50 ( given info ) = 130 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 130 - 30 = 100 correct option e"


Question: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 25 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?

<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 12.5 minutes .
B. 25 minutes
C. 35 minutes .
D. 35 minutes
E. 75 minutes

Explanation: "if the distance between the two houses is d . then speed of danny = ( d / 25 ) speed of steve = ( d / 50 ) [ steve takes 50 minutes to reach danny ' s house . double the time taken by danny ) obviously speed of danny is twice that of steve . now in order to cover distance ( d / 2 ) [ they meet in middle ] , steve will take : ( d / 2 ) / ( d / 50 ) = 25 minutes . distance is same and danny ' s speed is twice of steve . thus he will take 12.5 minutes to cover this same distance . steve take 25 - 12.5 = 12.5 minutes longer . a is the answer ."


Question: we run a business that rents out canoes and kayaks . a canoe rental costs $ 15 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 405 in revenue . how many more canoes than kayaks were rented out ?

<gadget id="calculator">3 - 2</gadget>
<output>1</output>

<gadget id="calculator">3 * 15</gadget>
<output>45</output>

<gadget id="calculator">2 * 18</gadget>
<output>36</output>

<gadget id="calculator">45 + 36</gadget>
<output>81</output>

<gadget id="calculator">405 / 81</gadget>
<output>5</output>

<gadget id="calculator">1 * 5</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 5
B. 6
C. 7
D. 8
E. 9

multiply(subtract(3, 2), divide(405, add(multiply(3, 15), multiply(2, 18))))

Explanation: "let x be the number of canoes . then 2 x / 3 is the number of kayaks . 15 x + ( 2 x / 3 ) * 18 = 405 15 x + 12 x = 405 27 x = 405 x = 15 ( canoes ) 2 x / 3 = 10 ( kayaks ) there were 15 - 10 = 5 more canoes rented out . the answer is a ."


Question: in a company the manager wants to give some gifts to all of the workers . in each block there are about 100 workers are there . the total amount for giving the gifts for all the workers is $ 4000 . the worth of the gift is $ 4 . how many blocks are there in the company ?

<gadget id="calculator">4_000 / 4</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 / 100</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 12
B. 10
C. 15
D. 17
E. 20

Explanation: each employee will get a gift worth of = $ 4 total employees = 4000 / 4 = 1000 total blocks = 1000 / 100 = 10 correct option is b


Question: in what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

<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">60 / 10</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 2
B. 7
C. 8
D. 6
E. 9

Explanation: "t = 60 / 36 * 18 / 5 = 6 sec answer : d"


Question: a man buys 54 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?

<gadget id="calculator">100 - 1</gadget>
<output>99</output>

<gadget id="calculator">54 * 99</gadget>
<output>5_346</output>

<gadget id="calculator">46 * 100</gadget>
<output>4_600</output>

<gadget id="calculator">5_346 - 4_600</gadget>
<output>746</output>

<gadget id="calculator">746 / 4_600</gadget>
<output>373/2_300 = around 0.162174</output>

<gadget id="calculator">100 * (373/2_300)</gadget>
<output>373/23 = around 16.217391</output>
<result>373/23 = around 16.217391</result>

Choices:
A. 7.6 %
B. 7.7 %
C. 16.21 %
D. 13.6 %
E. 7.8 %

multiply(const_100, divide(subtract(multiply(54, subtract(const_100, 1)), multiply(46, const_100)), multiply(46, const_100)))

Explanation: "explanation : let marked price be re . 1 each c . p . of 54 pens = rs . 46 s . p . of 54 pens = 99 % of rs . 54 = rs . 53.46 profit % = ( profit / c . p . ) x 100 profit % = ( 7.46 / 46 ) x 100 = 16.21 % answer : c"


Question: find the area of a cuboid of length 15 cm , breadth 10 cm . and height 16 cm .

<gadget id="calculator">15 * 10</gadget>
<output>150</output>

<gadget id="calculator">150 * 16</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. 2400 cm cube
B. 2410 cm cube
C. 2420 cm cube
D. 2430 cm cube
E. 2480 cm cube

Explanation: "area of a cuboid = lxbxh = 15 cm x 10 cm x 16 cm = 2400 cm cube answer : a"


Question: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 6 days . in how many days b alone can do the work ?

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">5 * (1/15)</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 / (1/9)</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 5 days
B. 7 days
C. 12 days
D. 9 days
E. 10 days

inverse(multiply(inverse(6), subtract(const_1, multiply(5, inverse(15)))))

Explanation: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 6 x = 9 days answer : option d"


Question: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 15 and 41 inclusive .

<gadget id="calculator">41 + 1</gadget>
<output>42</output>

<gadget id="calculator">42 / 2</gadget>
<output>21</output>

<gadget id="calculator">21 ** 2</gadget>
<output>441</output>

<gadget id="calculator">15 - 2</gadget>
<output>13</output>

<gadget id="calculator">13 + 1</gadget>
<output>14</output>

<gadget id="calculator">14 / 2</gadget>
<output>7</output>

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

<gadget id="calculator">441 - 49</gadget>
<output>392</output>
<result>392</result>

Choices:
A. 351
B. 392
C. 410
D. 424
E. 450

subtract(power(divide(add(41, const_1), 2), 2), power(divide(add(subtract(15, 2), const_1), 2), 2))

Explanation: "we ' re dealing with a sequence of consecutive odd integers : 15 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 15 + 41 = 56 2 ) now look at the ' next smallest ' and the ' next biggest ' : 17 + 39 = 56 now we have proof that there is no middle term . we have 7 bunches of 56 . 7 ( 56 ) = 392 b"


Question: the cost price of a radio is rs . 1800 and it was sold for rs . 1430 , find the loss % ?

<gadget id="calculator">1_800 - 1_430</gadget>
<output>370</output>

<gadget id="calculator">370 / 1_800</gadget>
<output>37/180 = around 0.205556</output>

<gadget id="calculator">(37/180) * 100</gadget>
<output>185/9 = around 20.555556</output>
<result>185/9 = around 20.555556</result>

Choices:
A. 18 %
B. 20.5 %
C. 30 %
D. 45 %
E. 12 %

multiply(divide(subtract(1800, 1430), 1800), const_100)

Explanation: "1800 - - - - 370 100 - - - - ? = > 20.5 % answer : b"


Question: what is the dividend . divisor 17 , the quotient is 8 and the remainder is 5

<gadget id="calculator">17 * 8</gadget>
<output>136</output>

<gadget id="calculator">136 + 5</gadget>
<output>141</output>
<result>141</result>

Choices:
A. 145
B. 141
C. 150
D. 153
E. 158

Explanation: "d = d * q + r d = 17 * 8 + 5 d = 136 + 5 d = 141 answer : b"


Question: a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 15 seconds ?

<gadget id="calculator">60 * 1</gadget>
<output>60</output>

<gadget id="calculator">60 / 3</gadget>
<output>20</output>

<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>

Choices:
A. 1 / 4
B. 1 / 3
C. 1 / 2
D. 2 / 3
E. 3 / 4

subtract(const_1, divide(15, divide(multiply(const_60, const_1), 3)))

Explanation: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 15 seconds ) = 1 - p ( man in dark for max of 15 seconds ) = 1 - 15 / 20 = 1 - 3 / 4 = 1 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 5 / 20 seconds = 1 / 4 . answer is a"


Question: john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 3 , 4 , or 5 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?

<gadget id="calculator">3 * 5</gadget>
<output>15</output>

<gadget id="calculator">3 / 15</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>

Choices:
A. 1 / 2
B. 1 / 3
C. 1 / 5
D. 2 / 15
E. 4 / 15

Explanation: john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 2 / 5 = 2 / 15 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 1 / 5 = 1 / 15 p ( john runs farther ) = 2 / 15 + 1 / 15 = 3 / 15 = 1 / 5 the answer is c .


Question: two bullet train s 140 m and 210 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :

<gadget id="calculator">140 + 210</gadget>
<output>350</output>

<gadget id="calculator">60 + 40</gadget>
<output>100</output>

<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">350 / (250/9)</gadget>
<output>63/5 = around 12.6</output>
<result>63/5 = around 12.6</result>

Choices:
A. 15.8 sec .
B. 12.6 sec .
C. 11.8 sec .
D. 10.8 sec .
E. 08.8 sec .

Explanation: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 210 ) m = 350 m . required time = 350 x 9 / 250 = 54 / 5 = 12.6 sec . answer b"


Question: 4 friends are pooling their money for pizza . emma has 8 dollars . daya has 25 % more money than emma , jeff has 2 / 5 of the money daya has , and brenda has 4 more dollars than jeff . how much money does brenda have ?

<gadget id="calculator">25 + 100</gadget>
<output>125</output>

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 8</gadget>
<output>10</output>

<gadget id="calculator">10 * 2</gadget>
<output>20</output>

<gadget id="calculator">20 / 5</gadget>
<output>4</output>

<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 14
B. 6
C. 7
D. 8
E. 10

add(divide(multiply(multiply(divide(add(25, const_100), const_100), 8), 2), 5), 4)

Explanation: d 8 emma has 8 dollars . daya has 25 % more dollars than emma . daya = 8 + 8 x 25 % = 8 + 8 x . 25 = 8 + 2 = 10 jeff has 2 / 5 of what daya has . = 10 x 2 / 5 = 4 brenda has 4 more dollars than jeff . = 4 + 4 = 8 brenda has 8 dollars . the correct answer is d .


Question: in one alloy there is 12 % chromium while in another alloy it is 8 % . 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .

<gadget id="calculator">12 * 35</gadget>
<output>420</output>

<gadget id="calculator">420 / 100</gadget>
<output>21/5 = around 4.2</output>

<gadget id="calculator">8 * 40</gadget>
<output>320</output>

<gadget id="calculator">320 / 100</gadget>
<output>16/5 = around 3.2</output>

<gadget id="calculator">(21/5) + (16/5)</gadget>
<output>37/5 = around 7.4</output>

<gadget id="calculator">35 + 40</gadget>
<output>75</output>

<gadget id="calculator">(37/5) / 75</gadget>
<output>37/375 = around 0.098667</output>

<gadget id="calculator">(37/375) * 100</gadget>
<output>148/15 = around 9.866667</output>
<result>148/15 = around 9.866667</result>

Choices:
A. 8.8 %
B. 9.75 %
C. 9.2 %
D. 8.6 %
E. 8.4 %

multiply(divide(add(divide(multiply(12, 35), const_100), divide(multiply(8, 40), const_100)), add(35, 40)), const_100)

Explanation: "the amount of chromium in the new 35 + 45 = 80 kg alloy is 0.12 * 35 + 0.08 * 45 = 7.8 kg , so the percentage is 7.8 / 80 * 100 = 9.75 % . answer : b ."


Question: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 26 miles , how many miles was mike ' s ride ?

<gadget id="calculator">2.5 + 5</gadget>
<output>7.5</output>

<gadget id="calculator">0.25 * 26</gadget>
<output>6.5</output>

<gadget id="calculator">7.5 + 6.5</gadget>
<output>14</output>

<gadget id="calculator">14 - 2.5</gadget>
<output>11.5</output>

<gadget id="calculator">11.5 / 0.25</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 20
B. 30
C. 36
D. 46
E. 54

Explanation: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 26 ) = $ 14 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 14 0.25 * x = 11.5 x = 46 miles the answer is d ."


Question: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.91 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?

<gadget id="calculator">22 / 100</gadget>
<output>11/50 = around 0.22</output>

<gadget id="calculator">18 * 2</gadget>
<output>36</output>

<gadget id="calculator">(11/50) * 36</gadget>
<output>198/25 = around 7.92</output>

<gadget id="calculator">8.91 - (198/25)</gadget>
<output>0.99</output>

<gadget id="calculator">15 * 3</gadget>
<output>45</output>

<gadget id="calculator">45 - 36</gadget>
<output>9</output>

<gadget id="calculator">0.99 / 9</gadget>
<output>0.11</output>

<gadget id="calculator">(11/50) - 0.11</gadget>
<output>0.11</output>

<gadget id="calculator">0.11 * 100</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 9 %
B. 10 %
C. 11 %
D. 12 %
E. 15 %

multiply(subtract(divide(22, const_100), divide(subtract(8.91, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100)

Explanation: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.91 9.9 - 45 x + 36 x = 8.91 9 x = 0.99 x = 0.11 the answer is c ."


Question: find the simple interest on $ 10000 at 4 % per annum for 12 months ?

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">10_000 * (1/25)</gadget>
<output>400</output>
<result>400</result>

Choices:
A. $ 400
B. $ 500
C. $ 650
D. $ 710
E. $ 1000

Explanation: "p = $ 10000 r = 4 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 4 * 1 / 100 = $ 400 answer is a"


Question: a contractor undertakes to built a walls in 50 days . he employs 40 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?

<gadget id="calculator">100 - 40</gadget>
<output>60</output>

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">40 * (3/5)</gadget>
<output>24</output>

<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">24 / (2/5)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 60
B. 30
C. 35
D. 20
E. none of these

divide(multiply(40, divide(subtract(const_100, 40), const_100)), divide(const_4, const_10))

Explanation: "40 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 40 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 40 × 25 × 0.6 / 25 × 0.4 = 60 men answera"


Question: the average weight of 6 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?

<gadget id="calculator">6 * 4.5</gadget>
<output>27</output>

<gadget id="calculator">27 + 75</gadget>
<output>102</output>
<result>102</result>

Choices:
A. 160 kg
B. 175 kg
C. 180 kg
D. 102 kg
E. 190 kg

Explanation: "total weight increased = ( 6 x 4.5 ) kg = 27 kg . weight of new person = ( 75 + 27 ) kg = 102 kg option d"


Question: sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1500 , what is the gain percent ?

<gadget id="calculator">300 + 900</gadget>
<output>1_200</output>

<gadget id="calculator">1_500 - 1_200</gadget>
<output>300</output>

<gadget id="calculator">300 / 1_200</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 10 %
B. 15 %
C. 20 %
D. 25 %
E. 30 %

Explanation: "selling price / total cost = 1500 / 1200 = 1.25 the gain percent is 25 % . the answer is d ."


Question: a , b , c , d , e are the 5 electronic shops in the naza market , which have 20 , 30 , 60 , 80 and 50 t . v . sets with them respectively , then the average number of t . v . sets in each shop is

<gadget id="calculator">60 + 80</gadget>
<output>140</output>

<gadget id="calculator">20 + 30</gadget>
<output>50</output>

<gadget id="calculator">50 + 50</gadget>
<output>100</output>

<gadget id="calculator">140 + 100</gadget>
<output>240</output>

<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 24
B. 48
C. 50
D. 60
E. none

Explanation: answer average number of t . v . sets = ( 20 + 30 + 60 + 80 + 50 ) / 5 = 48 correct option : b


Question: a no . when divided by 281 gives a remainder 160 , what remainder will be obtainedby dividingthe same no . 21 ?

<gadget id="calculator">281 + 160</gadget>
<output>441</output>

<gadget id="calculator">441 / 21</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 21
B. 22
C. 23
D. 24
E. 25

Explanation: "281 + 160 = 441 / 21 = 21 ( remainder ) a"


Question: in the rectangular coordinate system , points ( 16 , 0 ) and ( – 16 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?

<gadget id="calculator">16 ** 2</gadget>
<output>256</output>

<gadget id="calculator">256 ** (1/2)</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 2
B. 4
C. 8
D. 16
E. none of the above

Explanation: "d it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 16 d"


Question: the speed of a railway engine is 74 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :

<gadget id="calculator">74 - 24</gadget>
<output>50</output>

<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>

<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">74 / (50/3)</gadget>
<output>111/25 = around 4.44</output>

<gadget id="calculator">(111/25) ** 2</gadget>
<output>12_321/625 = around 19.7136</output>
<result>12_321/625 = around 19.7136</result>

Choices:
A. 49
B. 18
C. 16
D. 17
E. 19

power(divide(74, divide(subtract(74, 24), sqrt(9))), const_2)

Explanation: "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 74 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 74 - k * sqrt ( 9 ) = 74 - 3 k k = 16.67 now , we need to know : what value of n makes s go to zero ? 0 = 74 - 16.67 * sqrt ( n ) 16.67 * sqrt ( n ) = 74 sqrt ( n ) = 4.44 n = 4.44 ^ 2 > 19 with 20 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 19 is the maximum number of cars the engine can pull and still move . e"


Question: the sum of even numbers between 1 and 31 is

<gadget id="calculator">31 + 1</gadget>
<output>32</output>

<gadget id="calculator">31 / 2</gadget>
<output>31/2 = around 15.5</output>

<gadget id="calculator">floor(31/2)</gadget>
<output>15</output>

<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">32 * (15/2)</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 16
B. 128
C. 240
D. 512
E. none

multiply(add(31, 1), divide(floor(divide(31, const_2)), const_2))

Explanation: "solution required numbers are 2 , 4 , 6 , . . 30 . this is an a . p containing 15 terms . required sum = n / 2 ( first term + last term ) ‹ = › 15 / 2 ( 2 + 30 ) ‹ = › 240 . answer c"


Question: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 50 , what is the value of c â ˆ ’ a ?

<gadget id="calculator">50 * 2</gadget>
<output>100</output>

<gadget id="calculator">45 * 2</gadget>
<output>90</output>

<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 25
B. 10
C. 90
D. 14
E. it can not be determined from the information given

subtract(multiply(50, const_2), multiply(45, const_2))

Explanation: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 100 - - 2 subtracting 1 from 2 we have c - a = 10 ; answer : b"


Question: a certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday ( inc . the first day it was planted ) . if this plant grew by 30 % b / w the 4 th day and 10 th day after it was planted , how many feet per day does the plant grow

<gadget id="calculator">100 + 30</gadget>
<output>130</output>

<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">(13/10) * 11</gadget>
<output>143/10 = around 14.3</output>

<gadget id="calculator">(143/10) - 11</gadget>
<output>33/10 = around 3.3</output>

<gadget id="calculator">(13/10) * 4</gadget>
<output>26/5 = around 5.2</output>

<gadget id="calculator">10 - (26/5)</gadget>
<output>24/5 = around 4.8</output>

<gadget id="calculator">(33/10) / (24/5)</gadget>
<output>11/16 = around 0.6875</output>
<result>11/16 = around 0.6875</result>

Choices:
A. 2
B. 4.5
C. 0.69
D. 5.5
E. 3

divide(subtract(multiply(divide(add(const_100, 30), const_100), 11), 11), subtract(10, multiply(divide(add(const_100, 30), const_100), 4)))

Explanation: if the plant is 11 feet tall when it is planted , it will be 11 + k feet tall at the end of the day ( where k is the constant length it grows by every day ) . similarly , at the end of the 4 th day the plant must be 11 + 4 k feet tall and at the end of the 10 th day it must be 11 + 10 k feet tall . therefore 6 k = 0.3 ( 11 + 4 k ) = > k = 0.69 therefore the plant grows by 0.69 feet every day . option ( c )


Question: john and steve are speed walkers in a race . john is 14 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?

<gadget id="calculator">14 + 2</gadget>
<output>16</output>

<gadget id="calculator">3.7 * 16</gadget>
<output>59.2</output>

<gadget id="calculator">4.2 - 3.7</gadget>
<output>0.5</output>

<gadget id="calculator">59.2 / 0.5</gadget>
<output>118.4</output>

<gadget id="calculator">118.4 + 16</gadget>
<output>134.4</output>

<gadget id="calculator">134.4 / 4.2</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 32 seconds
E. 51 seconds

Explanation: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 14 + 2 - - - > 0.5 t = 16 - - - > t = 32 seconds . d is the correct answer ."


Question: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing theaverage by 4 year . find what was theoriginal strength of class ?

<gadget id="calculator">40 - 4</gadget>
<output>36</output>

<gadget id="calculator">12 * 36</gadget>
<output>432</output>

<gadget id="calculator">12 * 32</gadget>
<output>384</output>

<gadget id="calculator">432 - 384</gadget>
<output>48</output>

<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 11
B. 12
C. 17
D. 19
E. 21

divide(subtract(multiply(12, subtract(40, 4)), multiply(12, 32)), 4)

Explanation: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"


Question: running at the same constant rate , 5 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?

<gadget id="calculator">270 / 5</gadget>
<output>54</output>

<gadget id="calculator">54 * 4</gadget>
<output>216</output>

<gadget id="calculator">216 * 10</gadget>
<output>2_160</output>
<result>2_160</result>

Choices:
A. 648
B. 1,800
C. 2,160
D. 10,800
E. 64,800

multiply(multiply(divide(270, 5), 4), 10)

Explanation: "5 machines produce 270 bottles per minute ; 1 machine produces 270 / 5 = 54 bottles per minute ; 10 machines produce 54 * 10 = 540 bottles per minute ; in 4 minutes 10 machines produce 540 * 4 = 2,160 bottles . answer : c ."


Question: the radius of the wheel of a bus is 100 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is

<gadget id="calculator">1_000 * 66</gadget>
<output>66_000</output>

<gadget id="calculator">100 * 66_000</gadget>
<output>6_600_000</output>

<gadget id="calculator">60 * 1</gadget>
<output>60</output>

<gadget id="calculator">6_600_000 / 60</gadget>
<output>110_000</output>

<gadget id="calculator">2 * 100</gadget>
<output>200</output>

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">2 + 12</gadget>
<output>14</output>

<gadget id="calculator">4 * 2</gadget>
<output>8</output>

<gadget id="calculator">2 + 8</gadget>
<output>10</output>

<gadget id="calculator">10 ** 2</gadget>
<output>100</output>

<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>

<gadget id="calculator">3 + (7/50)</gadget>
<output>157/50 = around 3.14</output>

<gadget id="calculator">200 * (157/50)</gadget>
<output>628</output>

<gadget id="calculator">110_000 / 628</gadget>
<output>27_500/157 = around 175.159236</output>
<result>27_500/157 = around 175.159236</result>

Choices:
A. 175
B. 250
C. 300
D. 330
E. none of these

divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 100), add(const_3, divide(add(const_2, multiply(const_3, const_4)), power(add(const_2, multiply(const_4, const_2)), const_2)))))

Explanation: "radius of the wheel of bus = 100 cm . then , circumference of wheel = 2 ï € r = 200 ï € = 628.57 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 628.57 = 175 answer a"


Question: if n is an integer and 101 n ^ 2 is less than or equal to 6400 , what is the greatest possible value of n ?

<gadget id="calculator">6_400 / 101</gadget>
<output>6_400/101 = around 63.366337</output>

<gadget id="calculator">(6_400/101) ** (1/2)</gadget>
<output>80*sqrt(101)/101 = around 7.960298</output>

<gadget id="calculator">floor(80*sqrt(101)/101)</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 8
C. 9
D. 10
E. 11

Explanation: 101 * n ^ 2 < = 6400 n ^ 2 < = 6400 / 101 which will be less than 81 since 6400 / 100 = 64 which is the square of 9 next closest value of n where n ^ 2 < = 64 is 7 ans a


Question: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 390 m long ?

<gadget id="calculator">390 / 1_000</gadget>
<output>39/100 = around 0.39</output>

<gadget id="calculator">360 / 1_000</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(39/100) + (9/25)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) / 45</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">(1/60) * 3_600</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 38 sec
B. 35 sec
C. 44 sec
D. 40 sec
E. 60 sec

multiply(divide(add(divide(390, const_1000), divide(360, const_1000)), 45), const_3600)

Explanation: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 390 = 750 meter time taken to cross the platform = 750 / ( 25 / 2 ) = 750 × 2 / 25 = 60 seconds answer : option e"


Question: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is a ' s share ?

<gadget id="calculator">5 + 2</gadget>
<output>7</output>

<gadget id="calculator">7 + 4</gadget>
<output>11</output>

<gadget id="calculator">11 + 3</gadget>
<output>14</output>

<gadget id="calculator">4 / 14</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">3 / 14</gadget>
<output>3/14 = around 0.214286</output>

<gadget id="calculator">(2/7) - (3/14)</gadget>
<output>1/14 = around 0.071429</output>

<gadget id="calculator">500 / (1/14)</gadget>
<output>7_000</output>

<gadget id="calculator">5 / 14</gadget>
<output>5/14 = around 0.357143</output>

<gadget id="calculator">7_000 * (5/14)</gadget>
<output>2_500</output>
<result>2_500</result>

Choices:
A. rs . 2500
B. rs . 1000
C. rs . 1500
D. rs . 2000
E. none

multiply(divide(500, subtract(divide(4, add(add(add(5, 2), 4), 3)), divide(3, add(add(add(5, 2), 4), 3)))), divide(5, add(add(add(5, 2), 4), 3)))

Explanation: sol . let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 500 ⇔ x = 500 . ∴ a ' s share = rs . 5 x = rs . ( 5 x 500 ) = rs . 2500 . answer a


Question: a certain high school has 500 students . of these students , 50 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?

<gadget id="calculator">50 + 20</gadget>
<output>70</output>

<gadget id="calculator">70 - 10</gadget>
<output>60</output>

<gadget id="calculator">500 - 60</gadget>
<output>440</output>
<result>440</result>

Choices:
A. 430
B. 440
C. 450
D. 460
E. 470

subtract(500, subtract(add(50, 20), 10))

Explanation: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 50 y = 20 z = 10 so , we have 50 students taking music , 20 taking art and 10 taking both music and art . 40 student taking just music 10 student taking just art 10 student taking both music and art total = 60 students we ' re asked for the total number of students who are taking neither course . that is 500 - 60 = 440 . b"


Question: praveen starts business with rs . 3920 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">1 - (5/12)</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">3_920 / (7/12)</gadget>
<output>6_720</output>

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">6_720 / (2/3)</gadget>
<output>10_080</output>
<result>10_080</result>

Choices:
A. s . 10080
B. s . 8000
C. s . 8500
D. s . 9000
E. s . 6000

divide(divide(3920, subtract(const_1, divide(5, const_12))), divide(2, 3))

Explanation: "let hari ’ s capital be rs . x . then , 3920 * 12 / 7 x = 2 / 3 = > 14 x = 141120 = > x = 10080 . answer : a"


Question: a woman can do a piece of work in 40 days . man is 25 % more efficient than woman . in how many days a man can do the same piece of work ?

<gadget id="calculator">100 + 25</gadget>
<output>125</output>

<gadget id="calculator">40 / 125</gadget>
<output>8/25 = around 0.32</output>

<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 32 days
B. 36 days
C. 38 days
D. 40 days
E. 53 days

multiply(divide(40, add(const_100, 25)), const_100)

Explanation: the ratio of the efficiencies of a woman and man = 100 : 125 = 4 : 5 the ratio of the days taken by woman and man to finish the work = 5 : 4 woman takes 32 days to finish the work . = > 5 parts = 40 the number of days taken by man to finish the work = 4 parts = 40 / 5 x 4 = 32 days a


Question: the ratio between the present ages of a and b is 3.5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?

<gadget id="calculator">3.5 + 3.5</gadget>
<output>7</output>

<gadget id="calculator">3.5 - 3</gadget>
<output>0.5</output>

<gadget id="calculator">7 / 0.5</gadget>
<output>14</output>

<gadget id="calculator">3.5 * 14</gadget>
<output>49</output>

<gadget id="calculator">49 + 3.5</gadget>
<output>52.5</output>

<gadget id="calculator">3 * 14</gadget>
<output>42</output>

<gadget id="calculator">42 - 3.5</gadget>
<output>38.5</output>

<gadget id="calculator">52.5 / 38.5</gadget>
<output>1.363636</output>
<result>1.363636</result>

Choices:
A. 14 : 4
B. 13 : 0
C. 15 : 11
D. 13 : 12
E. 13 : 17

divide(add(multiply(3.5, divide(add(3.5, 3.5), subtract(3.5, 3))), 3.5), subtract(multiply(3, divide(add(3.5, 3.5), subtract(3.5, 3))), 3.5))

Explanation: "let the present ages of a and b be 3.5 x and 3 x years respectively . then , ( 3.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 0.5 x = 8 = > x = 16 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 60 : 44 = 15 : 11 . answer : c"


Question: ram , who is half as efficient as krish , will take 21 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?

<gadget id="calculator">1 / 21</gadget>
<output>1/21 = around 0.047619</output>

<gadget id="calculator">21 / 2</gadget>
<output>21/2 = around 10.5</output>

<gadget id="calculator">1 / (21/2)</gadget>
<output>2/21 = around 0.095238</output>

<gadget id="calculator">(1/21) + (2/21)</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">1 / (1/7)</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 16 days
B. 12 days
C. 8 days
D. 7 days
E. 18 days

inverse(add(divide(const_1, 21), divide(const_1, divide(21, const_2))))

Explanation: "number of days taken by ram to complete task = 21 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 24 days is 21 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 21 w / 3 w = 7 days answer d"


Question: calculate the l . c . m of 7 / 10 , 8 / 9 , 3 / 8 , 5 / 12 is :

<gadget id="calculator">7 * 8</gadget>
<output>56</output>

<gadget id="calculator">3 * 5</gadget>
<output>15</output>

<gadget id="calculator">56 * 15</gadget>
<output>840</output>
<result>840</result>

Choices:
A. 840
B. 70
C. 740
D. 140
E. 940

multiply(multiply(7, 8), multiply(3, 5))

Explanation: required l . c . m = l . c . m . of 7 , 8 , 3 , 5 / h . c . f . of 10 , 9 , 8 , 12 = 840 / 1 = 840 answer is a


Question: a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?

<gadget id="calculator">18 / 2</gadget>
<output>9</output>

<gadget id="calculator">9 / 24</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>

Choices:
A. 5 / 12
B. 3 / 5
C. 1 / 2
D. 3 / 8
E. 5 / 6

Explanation: so we are looking for the area of the cloth over the area of the table area of the cloth = ( pi ) ( r ) ^ 2 which is about ( 3 ) ( 9 ) ( 9 ) area of the table = ( 24 ) ( 24 ) so the quick way to estimate is looking at the fraction like this : ( 3 / 24 ) ( 81 / 24 ) i hope this is easy to follow , so with some simplification i get ( 1 / 8 ) ( 3 ) = ( 3 / 8 ) answer is d


Question: a man swims downstream 36 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?

<gadget id="calculator">18 / 3</gadget>
<output>6</output>

<gadget id="calculator">36 / 3</gadget>
<output>12</output>

<gadget id="calculator">6 + 12</gadget>
<output>18</output>

<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 7
B. 8
C. 9
D. 2
E. 4

divide(add(divide(18, 3), divide(36, 3)), const_2)

Explanation: "36 - - - 3 ds = 12 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 12 + 6 ) / 2 = 9 answer : c"


Question: the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is ?

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">109.25 - (1/4)</gadget>
<output>109</output>
<result>109</result>

Choices:
A. 366
B. 106
C. 102
D. 109
E. 122

Explanation: "cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : d"


Question: the price of maruti car rises by 30 percent while the sales of the car come down by 20 % . what is the percentage change in the total revenue ?

<gadget id="calculator">30 + 100</gadget>
<output>130</output>

<gadget id="calculator">20 * 130</gadget>
<output>2_600</output>

<gadget id="calculator">2_600 / 100</gadget>
<output>26</output>

<gadget id="calculator">130 - 26</gadget>
<output>104</output>

<gadget id="calculator">104 - 100</gadget>
<output>4</output>
<result>4</result>

Choices:
A. - 4 %
B. - 2 %
C. + 4 %
D. + 2 %
E. none of these

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

Explanation: solution : let initial price of maruti car be rs . 100 . as price increases 30 % , price of car will become , ( 100 + 30 % of 100 ) = rs . 130 . due to increase in price , sales is down by 20 % . it means , it is going make 20 % less revenue as expected after increment of price . so , new revenue = ( 130 - 20 % of 130 ) = rs . 104 . the initial revenue was rs . 100 which becomes rs . 104 at the end . it means there is 4 % increment in the total revenue . mind calculation method : 100 = = 30 % ↑ ( price effect ) = = > 130 = = 20 % ↓ ( sales effects ) = = > 104 . hence , 4 % rises . answer : option c


Question: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 21 ( q + 1 ) , what is the least possible value of p + q ?

<gadget id="calculator">21 + 17</gadget>
<output>38</output>

<gadget id="calculator">38 - 2</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 36
B. 42
C. 44
D. 46
E. none

Explanation: "17 ( p + 1 ) = 21 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 21 / 17 - - > the least positive value of p + 1 is 21 , so the least value of p is 20 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 20 + 16 = 36 . answer : a ."


Question: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?

<gadget id="calculator">100 - 60</gadget>
<output>40</output>

<gadget id="calculator">100 + 25</gadget>
<output>125</output>

<gadget id="calculator">40 / 125</gadget>
<output>8/25 = around 0.32</output>

<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(8/25) * (5/4)</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

Choices:
A. 1 / 3
B. 2 / 5
C. 3 / 4
D. 3 / 2
E. 2 / 3

multiply(divide(subtract(const_100, 60), add(const_100, 25)), divide(5, 4))

Explanation: "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 5 / 4 ) * 4 = 2 / 5 the answer is b ."


Question: three rugs have a combined area of 212 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?

<gadget id="calculator">212 - 140</gadget>
<output>72</output>

<gadget id="calculator">72 - 24</gadget>
<output>48</output>

<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 18 square meters
B. 20 square meters
C. 24 square meters
D. 28 square meters
E. 30 square meters

divide(subtract(subtract(212, 140), 24), const_2)

Explanation: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 212 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 24 . answer : c ."


Question: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction q of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?

<gadget id="calculator">1 + 2</gadget>
<output>3</output>

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">2 / 9</gadget>
<output>2/9 = around 0.222222</output>

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(2/9) * (3/4)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(2/9) - (1/6)</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">(2/3) - (1/18)</gadget>
<output>11/18 = around 0.611111</output>

<gadget id="calculator">9 - 2</gadget>
<output>7</output>

<gadget id="calculator">7 / 9</gadget>
<output>7/9 = around 0.777778</output>

<gadget id="calculator">(11/18) / (7/9)</gadget>
<output>11/14 = around 0.785714</output>
<result>11/14 = around 0.785714</result>

Choices:
A. 11 / 14
B. 13 / 18
C. 4 / 7
D. 3 / 7
E. 3 / 14

divide(subtract(divide(2, add(1, 2)), subtract(divide(2, 9), multiply(divide(2, 9), divide(3, 4)))), divide(subtract(9, 2), 9))

Explanation: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus q = 11 / 14 of the remaining votes must be against . answer : a ."


Question: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 12 even numbers . his mother immediately worked out the answer . how much had he scored in math ?

<gadget id="calculator">12 + 1</gadget>
<output>13</output>

<gadget id="calculator">13 * 12</gadget>
<output>156</output>
<result>156</result>

Choices:
A. 156
B. 146
C. 158
D. 187
E. 160

Explanation: "a 156 sum = ( n x n ) + n hence , 12 x 12 = 144 + 12 = 156"


Question: during a certain season , a team won 70 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?

<gadget id="calculator">70 - 70</gadget>
<output>0</output>

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(7/10) - (1/2)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">0 / (1/5)</gadget>
<output>0</output>

<gadget id="calculator">100 + 0</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 180
B. 170
C. 156
D. 150
E. 100

add(100, divide(subtract(70, 70), subtract(divide(70, 100), divide(50, 100))))

Explanation: "we are first given that a team won 70 percent of its first 100 games . this means the team won 0.7 x 100 = 70 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 70 + 0.5 t – 50 = 0.7 t 20 = 0.2 t 200 = 2 t 100 = t answer is e ."


Question: if x 2 + kx - 3 , is divisible by ( x - 1 ) , what is the value of k

<gadget id="calculator">1 ** 2</gadget>
<output>1</output>

<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<result>2</result>

Choices:
A. - 1
B. 1
C. 2
D. - 1
E. 0

Explanation: explanation : if x 2 + kx - 3 is divisible by ( x - 1 ) then x = 1 ( 1 ) 2 + 1 ( k ) - 3 = 0 1 + k - 3 = 0 k = 2 answer : option c


Question: if ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 then what is the least value of x + y + z ? if x , y , z are all integer no .

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

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

<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 8
C. 9
D. 10
E. 11

subtract(divide(multiply(10, 5), 5), const_3)

Explanation: ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 put x = 0 y = - 5 z = 12 then ( 0 - 10 ) ( - 5 - 5 ) ( 12 - 2 ) = 1000 ( - 10 ) ( - 10 ) ( 10 ) = 1000 1000 = 1000 answer : a


Question: a can run 4 times as fast as b and gives b a start of 60 m . how long should the race course be so that a and b might reach in the same time ?

<gadget id="calculator">60 / 4</gadget>
<output>15</output>

<gadget id="calculator">4 - 1</gadget>
<output>3</output>

<gadget id="calculator">15 / 3</gadget>
<output>5</output>

<gadget id="calculator">4 * 5</gadget>
<output>20</output>

<gadget id="calculator">20 + 60</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 70 m
B. 60 m
C. 80 m
D. 65 m
E. 75 m

add(multiply(4, divide(divide(60, 4), subtract(4, const_1))), 60)

Explanation: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 60 m he gains 60 * ( 4 / 3 ) i . e 80 m answer : c"


Question: a train 175 m long , running with a speed of 63 km / hr will pass a tree in ?

<gadget id="calculator">63 * 1_000</gadget>
<output>63_000</output>

<gadget id="calculator">175 / 63_000</gadget>
<output>1/360 = around 0.002778</output>

<gadget id="calculator">(1/360) * 3_600</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 22 sec
B. 16 sec
C. 17 sec
D. 88 sec
E. 10 sec

multiply(divide(175, multiply(63, const_1000)), const_3600)

Explanation: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 175 * 2 / 35 = 10 sec answer : e"


Question: an 80 - liter solution of cool - drink is made from 10 % jasmine water . if 8 liters of jasmine and 12 liters of water were added to the solution , what percent of the solution is jasmine ?

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">80 * (1/10)</gadget>
<output>8</output>

<gadget id="calculator">8 + 8</gadget>
<output>16</output>

<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">(4/25) * 100</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 12 %
B. 14 %
C. 16 %
D. 18 %
E. 20 %

multiply(divide(add(multiply(80, divide(10, const_100)), 8), const_100), const_100)

Explanation: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 80 ) + 8 ) / 100 = 16 / 100 = 16 % the answer is c ."


Question: the length of rectangle is thrice its breadth and its perimeter is 120 m , find the area of the rectangle ?

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">1 * 2</gadget>
<output>2</output>

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

<gadget id="calculator">120 / 8</gadget>
<output>15</output>

<gadget id="calculator">15 * 3</gadget>
<output>45</output>

<gadget id="calculator">45 * 15</gadget>
<output>675</output>
<result>675</result>

Choices:
A. 432 sq m
B. 356 sq m
C. 452 sq m
D. 428 sq m
E. 675 sq m

multiply(multiply(divide(120, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(120, add(multiply(const_3, const_2), multiply(const_1, const_2))))

Explanation: "2 ( 3 x + x ) = 120 l = 45 b = 15 lb = 45 * 15 = 675 answer : e"


Question: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?

<gadget id="calculator">164.5 - 120</gadget>
<output>44.5</output>

<gadget id="calculator">120 + 44.5</gadget>
<output>164.5</output>

<gadget id="calculator">44.5 * 3</gadget>
<output>133.5</output>

<gadget id="calculator">164.5 - 133.5</gadget>
<output>31</output>
<result>31</result>

Choices:
A. $ 21
B. $ 27
C. $ 31
D. $ 41
E. it can not be determined

Explanation: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 44.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 31 . in any case , there is no necessity to know each item ' s price , just the sum . answer : c"


Question: 65 % of x = 20 % of 682.50 . find the value of x ?

<gadget id="calculator">682.5 / 100</gadget>
<output>6.825</output>

<gadget id="calculator">6.825 * 20</gadget>
<output>136.5</output>

<gadget id="calculator">136.5 * 100</gadget>
<output>13_650</output>

<gadget id="calculator">13_650 / 65</gadget>
<output>210</output>
<result>210</result>

Choices:
A. 100
B. 210
C. 150
D. 180
E. 199

divide(multiply(multiply(divide(682.50, const_100), 20), const_100), 65)

Explanation: "65 % of x = 20 % of 682.50 then , 65 / 100 * x = 20 / 100 * 6825 / 10 x = 210 answer is b"


Question: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 120 kilometers ?

<gadget id="calculator">120 / 40</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 4.5
B. 5.5
C. 6.5
D. 3
E. 8.5

Explanation: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 120 kilometers ? 120 ÷ 40 = 3 × 1 gallon = 3 gallons correct answer d"


Question: a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?

<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">(7/2) * 3</gadget>
<output>21/2 = around 10.5</output>

<gadget id="calculator">lcm(7, 21/2)</gadget>
<output>21</output>

<gadget id="calculator">21 + 4</gadget>
<output>25</output>

<gadget id="calculator">25 + 21</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 34
B. 38
C. 42
D. 46
E. 50

add(add(lcm(7, multiply(divide(7, 2), 3)), 4), lcm(7, multiply(divide(7, 2), 3)))

Explanation: "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 4 = 25 . the minimum number of horses and ponies is 46 . the answer is d ."


Question: on the first day of her vacation , louisa traveled 160 miles . on the second day , traveling at the same average speed , she traveled 280 miles . if the 160 - mile trip took 3 hours less than the 280 - mile trip , what was the average speed , in miles per hour ?

<gadget id="calculator">280 - 160</gadget>
<output>120</output>

<gadget id="calculator">120 / 3</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40
B. 45
C. 46
D. 48
E. 50

Explanation: ( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 160 / t = 280 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 160 / 4 = 40 answer : a


Question: evaluate : | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?

<gadget id="calculator">3 - 12</gadget>
<output>-9</output>

<gadget id="calculator">8 * (-9)</gadget>
<output>-72</output>

<gadget id="calculator">5 - (-72)</gadget>
<output>77</output>

<gadget id="calculator">5 - 11</gadget>
<output>-6</output>

<gadget id="calculator">-(-6)</gadget>
<output>6</output>

<gadget id="calculator">77 - 6</gadget>
<output>71</output>
<result>71</result>

Choices:
A. 40
B. 50
C. 60
D. 71
E. 80

subtract(subtract(5, multiply(8, subtract(3, 12))), negate(subtract(5, 11)))

Explanation: "according to order of operations , inner brackets first . hence | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 5 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 5 + 72 | - | 5 - 11 | = | 77 | - | - 6 | = 77 - 6 = 71 correct answer d ) 71"


Question: a 10 % stock yielding 8 % is quoted at ?

<gadget id="calculator">100 / 8</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 10</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 125
B. 170
C. 175
D. 180
E. 185

Explanation: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 10 , money invested = 100 × 10 / 8 = rs . 125 ie , market value of the stock = rs . 125 answer is a ."


Question: if a trader sold two cars each at rs . 325475 and gains 12 % on the first and loses 12 % on the second , then his profit or loss percent on the whole is ?

<gadget id="calculator">12 * 12</gadget>
<output>144</output>

<gadget id="calculator">144 / 100</gadget>
<output>36/25 = around 1.44</output>
<result>36/25 = around 1.44</result>

Choices:
A. 1.44 %
B. 1.43 %
C. 1.34 %
D. 4.44 %
E. 1.74 %

Explanation: sp of each car is rs . 325475 , he gains 12 % on first car and losses 12 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 12 ) ( 12 ) / 100 % = 1.44 % answer : a


Question: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 96 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?

<gadget id="calculator">96 + 88</gadget>
<output>184</output>

<gadget id="calculator">184 / 2</gadget>
<output>92</output>
<result>92</result>

Choices:
A. 198 mph
B. 110 mph
C. 92 mph
D. 100 mph
E. 99 mph

Explanation: "( 96 mph + 88 mph ) / 2 = 92 mph correct answer is : c"


Question: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 20 cm ?

<gadget id="calculator">(20 + 18) * 20 / 2</gadget>
<output>380</output>
<result>380</result>

Choices:
A. 827 cm 2
B. 380 cm 2
C. 285 cm 2
D. 178 cm 2
E. 176 cm 2

Explanation: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 20 ) = 380 cm 2 answer : b"


Question: if x < y < z and y - x > 11 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?

<gadget id="calculator">11 + 2</gadget>
<output>13</output>

<gadget id="calculator">13 + 2</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. 15

Explanation: "we have : 1 ) x < y < z 2 ) y - x > 11 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 11 , the least value for y - x must be 13 , the least value for x must be 2 , and , thus , the least possible value for y must be 15 ( y - 2 = 13 , y = 15 ) 2 < 15 < z , since z is odd , the least possible value for z is 17 z - x = 17 - 2 = 15 answer e"


Question: find k if 24 / k = 4 .

<gadget id="calculator">24 / 4</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 7
C. 8
D. 4
E. 3

Explanation: "since 24 / k = 4 and 24 / 6 = 4 , then k = 6 correct answer a"


Question: a merchandise feedback online portal accords ‘ ratings ’ to a product by recording the percentage of customers who have reported their views as either ‘ satisfied ’ or ‘ unsatisfied ’ only . the portal rounds off the exact percentage value calculated to the closest integral value . if the percentage of unsatisfied customers as recorded by the portal is 57 % , what is the least possible number of people that could have reported their views as ‘ satisfied ’ ?

<gadget id="calculator">4 + 3</gadget>
<output>7</output>

<gadget id="calculator">7 - 4</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 2
B. 3
C. 12
D. 43
E. 57

Explanation: 57 % unsatisfied . so ~ 43 % satisfied but 100 % should be an integer only and since the above percentages are approximations 100 % should be as close as possible to an integer . now substitute value [ 1 ] if 43 % is 2 what is 100 % - > 200 / 43 is not giving a number which is closest to an integer . [ 2 ] if 43 % is 3 what is 100 % - > 300 / 43 [ 43 * 7 = 301 ] . . . therefore closest possible to an integer . [ it also satisfies the least possible and hence we need not check for other choices which are greater than 3 ] therefore ans is b .