Question: tough and tricky questions : work / rate problems . a group of 4 junior lawyers require 7 hours to complete a legal research assignment . how many hours would it take a group of 3 legal assistants to complete the same research assignment assuming that a legal assistant works at two - thirds the rate of a junior lawyer ? source : chili hot gmat

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

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

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

Choices:
A. 14
B. 10
C. 9
D. 6
E. 5

multiply(multiply(divide(const_2, const_3), 3), 7)

Explanation: # of people times the # of hours : 4 * 7 = 28 - - > 4 lawyers do 28 worksin 7 hours . 3 * 14 / 3 = 14 - - > 3 assistants do 14 worksin 4 hours so , since the amount of work the assistants do is half the work the lawyers do , the time will be double , soans a


Question: mahesh can do a piece of work in 30 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">20 * (1/30)</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) / 30</gadget>
<output>1/90 = around 0.011111</output>

<gadget id="calculator">1 / (1/90)</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 90
B. 25
C. 37
D. 41
E. 30

divide(const_1, divide(subtract(const_1, multiply(20, divide(const_1, 30))), 30))

Explanation: "work done by mahesh in 30 days = 20 * 1 / 30 = 2 / 3 remaining work = 1 - 2 / 3 = 1 / 3 1 / 3 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 3 = 90 days answer is a"


Question: if x and y are numbers such that ( x + 6 ) ( y - 6 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 0
B. 16
C. 25
D. 36
E. 49

Explanation: from ( x + 6 ) ( y - 6 ) = 0 it follows that either x = - 6 or y = 6 . thus either x ^ 2 = 36 or y ^ 2 = 36 . now , if x ^ 2 = 36 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 36 + 0 = 36 . similarly if y ^ 2 = 36 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 36 = 36 . answer : d .


Question: the difference of a larger number and a smaller number is 6 . the sum of the larger number and twice the smaller is 15 . what is the larger number ?

<gadget id="calculator">2 * 6</gadget>
<output>12</output>

<gadget id="calculator">15 + 12</gadget>
<output>27</output>

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

<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<result>9</result>

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

divide(add(15, multiply(const_2, 6)), add(const_1, const_2))

Explanation: let x be the larger number and y be the smaller number . x - y = 6 x + 2 ( y ) = 15 solve by substitution : y = x - 6 x + 2 ( x - 6 ) = 15 x + 2 x - 12 = 15 3 x = 27 x = 9 the larger number is 9 , so answer c is correct .


Question: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?

<gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>

<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>

<gadget id="calculator">20 * 30</gadget>
<output>600</output>

<gadget id="calculator">20 * 18</gadget>
<output>360</output>

<gadget id="calculator">600 - 360</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 240 meters
B. 360 meters
C. 420 meters
D. 600 meters
E. can not be determined

subtract(multiply(divide(multiply(72, const_1000), const_3600), 30), multiply(divide(multiply(72, const_1000), const_3600), 18))

Explanation: "explanation : length of the platform = speed of train * extra time taken to cross the platform . length of platform = 72 kmph * 12 seconds convert 72 kmph into m / sec 1 kmph = 518518 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 72 kmph = 518 ∗ 72518 ∗ 72 = 20 m / sec therefore , length of the platform = 20 m / s * 12 sec = 240 meters . correct answer : a"


Question: a vessel of capacity 2 litre has 16 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?

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

<gadget id="calculator">(4/25) * 2</gadget>
<output>8/25 = around 0.32</output>

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

<gadget id="calculator">(2/5) * 6</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">(8/25) + (12/5)</gadget>
<output>68/25 = around 2.72</output>

<gadget id="calculator">(68/25) / 10</gadget>
<output>34/125 = around 0.272</output>

<gadget id="calculator">(34/125) * 100</gadget>
<output>136/5 = around 27.2</output>
<result>136/5 = around 27.2</result>

Choices:
A. 31 % .
B. 71 % .
C. 49 % .
D. 27.2 % .
E. 51 % .

multiply(divide(add(multiply(divide(16, const_100), 2), multiply(divide(40, const_100), 6)), 10), const_100)

Explanation: "16 % of 2 litres = 0.32 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.72 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.2 % answer : d"


Question: the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their surface area ?

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

Choices:
A. 1 : 0
B. 1 : 4
C. 1 : 6
D. 1 : 2
E. 1 : 1

Explanation: 1 : 4 answer : b


Question: there are 3 prizes to be distributed among 10 students . if no students gets more than one prize , then this can be done in ?

<gadget id="calculator">10 * 3</gadget>
<output>30</output>

<gadget id="calculator">10 - 1</gadget>
<output>9</output>

<gadget id="calculator">9 * 10</gadget>
<output>90</output>

<gadget id="calculator">30 + 90</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 10
B. 45
C. 95
D. 120
E. none of these

add(multiply(10, 3), multiply(subtract(10, const_1), 10))

Explanation: explanation : 3 prize among 10 students can be distributed in 10 c 3 ways = 120 ways . answer : d


Question: a student got 72 % in math and 82 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?

<gadget id="calculator">3 * 75</gadget>
<output>225</output>

<gadget id="calculator">72 + 82</gadget>
<output>154</output>

<gadget id="calculator">225 - 154</gadget>
<output>71</output>
<result>71</result>

Choices:
A. 69 %
B. 71 %
C. 73 %
D. 75 %
E. 77 %

subtract(multiply(const_3, 75), add(72, 82))

Explanation: "72 + 82 + x = 3 * 75 x = 71 the answer is b ."


Question: a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital ?

<gadget id="calculator">3_500 * 12</gadget>
<output>42_000</output>

<gadget id="calculator">42_000 * 3</gadget>
<output>126_000</output>

<gadget id="calculator">12 - 5</gadget>
<output>7</output>

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

<gadget id="calculator">126_000 / 14</gadget>
<output>9_000</output>
<result>9_000</result>

Choices:
A. rs . 9228
B. rs . 9129
C. rs . 9120
D. rs . 9000
E. rs . 1922

divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 5), 2))

Explanation: let b ' s capital be rs . x . { 3500 \ 12 } / { 7 x } = { 2 } / { 3 } = > x = 9000 . answer : d


Question: a car dealership has 40 cars on the lot , 15 % of which are silver . if the dealership receives a new shipment of 80 cars , 45 % of which are not silver , what percentage of total number of cars are silver ?

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">40 * (3/20)</gadget>
<output>6</output>

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

<gadget id="calculator">80 * (9/20)</gadget>
<output>36</output>

<gadget id="calculator">6 + 36</gadget>
<output>42</output>

<gadget id="calculator">40 + 80</gadget>
<output>120</output>

<gadget id="calculator">42 / 120</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 30 %
B. 35 %
C. 40 %
D. 45 %
E. 50 %

multiply(divide(add(multiply(40, divide(15, const_100)), multiply(80, divide(45, const_100))), add(40, 80)), const_100)

Explanation: "the number of silver cars is 0.15 * 40 + 0.45 * 80 = 42 the percentage of cars which are silver is 42 / 120 = 35 % the answer is b ."


Question: a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 20 % . what is his average speed for both the trips ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">60 * (6/5)</gadget>
<output>72</output>

<gadget id="calculator">72 + 60</gadget>
<output>132</output>

<gadget id="calculator">132 / 2</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 33
B. 77
C. 48
D. 66
E. 21

divide(add(multiply(60, add(const_1, divide(20, const_100))), 60), const_2)

Explanation: "speed on return trip = 120 % of 60 = 72 km / hr . average speed of trip = 60 + 72 / 2 = 132 / 2 = 66 km / hr answer : d"


Question: a and b can together finish a work in 10 days . they worked together for 5 days and then b left . after another 5 days , a finished the remaining work . in how many days a alone can finish the job ?

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

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

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

Choices:
A. 10
B. 15
C. 20
D. 5
E. 30

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

Explanation: "a + b 5 days work = 5 * 1 / 10 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by a in 5 days whole work will be done by a in 5 * 2 = 10 days answer is a"


Question: a rectangular field has a length 10 meters more than it is width . if the area of the field is 200 , what is the length ( in meters ) of the rectangular field ?

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

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">200 / 10</gadget>
<output>20</output>

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

<gadget id="calculator">(1/3) + 10</gadget>
<output>31/3 = around 10.333333</output>

<gadget id="calculator">(1/4) + (31/3)</gadget>
<output>127/12 = around 10.583333</output>

<gadget id="calculator">10 + (127/12)</gadget>
<output>247/12 = around 20.583333</output>
<result>247/12 = around 20.583333</result>

Choices:
A. 20
B. 22
C. 24
D. 26
E. 28

add(10, add(const_0_25, add(const_0_33, divide(divide(200, 10), const_2))))

Explanation: "area = l * w = ( l ) * ( l - 10 ) = 200 trial and error : 19 * 9 = 171 ( too low ) 20 * 10 = 200 the length is 20 meters . the answer is a ."


Question: a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .

<gadget id="calculator">7 + 8</gadget>
<output>15</output>

<gadget id="calculator">8 / 15</gadget>
<output>8/15 = around 0.533333</output>

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

<gadget id="calculator">15 - 1</gadget>
<output>14</output>

<gadget id="calculator">7 / 14</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(8/15) * (1/2)</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">7 / 15</gadget>
<output>7/15 = around 0.466667</output>

<gadget id="calculator">7 - 1</gadget>
<output>6</output>

<gadget id="calculator">6 / 14</gadget>
<output>3/7 = around 0.428571</output>

<gadget id="calculator">(7/15) * (3/7)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(4/15) + (1/5)</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>

Choices:
A. 7 / 18
B. 7 / 19
C. 7 / 11
D. 7 / 12
E. 7 / 15

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

Explanation: "drawing two balls of same color from seven green balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ways . 7 / 15 answer : e"


Question: if 4 men working 10 hours a day earn rs . 1600 per week , then 9 men working 6 hours a day will earn how much per week ?

<gadget id="calculator">9 * 6</gadget>
<output>54</output>

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

<gadget id="calculator">54 / 40</gadget>
<output>27/20 = around 1.35</output>

<gadget id="calculator">(27/20) * 1_600</gadget>
<output>2_160</output>
<result>2_160</result>

Choices:
A. rs 840
B. rs 1320
C. rs 1620
D. rs 2160
E. none of these

multiply(divide(multiply(9, 6), multiply(4, 10)), 1600)

Explanation: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1600 : x hence 4 * 10 * x = 9 * 6 * 1600 or x = 9 * 6 * 1600 / 4 * 10 = 2160 answer : d"


Question: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 9 more than the correct answer . find the number .

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">9 * (4/5)</gadget>
<output>36/5 = around 7.2</output>

<gadget id="calculator">(36/5) * (4/5)</gadget>
<output>144/25 = around 5.76</output>

<gadget id="calculator">(4/5) * (4/5)</gadget>
<output>16/25 = around 0.64</output>

<gadget id="calculator">1 - (16/25)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(144/25) / (9/25)</gadget>
<output>16</output>

<gadget id="calculator">16 / (4/5)</gadget>
<output>20</output>
<result>20</result>

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

divide(divide(multiply(multiply(9, divide(4, 5)), divide(4, 5)), subtract(const_1, multiply(divide(4, 5), divide(4, 5)))), divide(4, 5))

Explanation: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 9 25 x = 16 x + 180 9 x = 180 x = 20 the answer is c ."


Question: raman mixed 24 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?

<gadget id="calculator">24 * 150</gadget>
<output>3_600</output>

<gadget id="calculator">36 * 125</gadget>
<output>4_500</output>

<gadget id="calculator">3_600 + 4_500</gadget>
<output>8_100</output>

<gadget id="calculator">36 + 24</gadget>
<output>60</output>

<gadget id="calculator">8_100 / 60</gadget>
<output>135</output>

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

<gadget id="calculator">135 * (2/5)</gadget>
<output>54</output>

<gadget id="calculator">135 + 54</gadget>
<output>189</output>
<result>189</result>

Choices:
A. rs . 135
B. rs . 162
C. rs . 189
D. rs . 198
E. none of these

add(divide(add(multiply(24, 150), multiply(36, 125)), add(36, 24)), multiply(divide(add(multiply(24, 150), multiply(36, 125)), add(36, 24)), divide(40, const_100)))

Explanation: cp per kg of mixture = [ 24 ( 150 ) + 36 ( 125 ) ] / ( 24 + 36 ) = rs . 135 sp = cp [ ( 100 + profit % ) / 100 ] = 135 * [ ( 100 + 40 ) / 100 ] = rs . 189 . answer : c


Question: if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 284 pounds . what is jake ’ s present weight , in pounds ?

<gadget id="calculator">284 - 8</gadget>
<output>276</output>

<gadget id="calculator">276 / 3</gadget>
<output>92</output>

<gadget id="calculator">92 * 2</gadget>
<output>184</output>

<gadget id="calculator">184 + 8</gadget>
<output>192</output>
<result>192</result>

Choices:
A. 176
B. 180
C. 184
D. 188
E. 192

add(multiply(divide(subtract(284, 8), const_3), const_2), 8)

Explanation: "j + k = 284 and so k = 284 - j j - 8 = 2 k j - 8 = 2 ( 284 - j ) 3 j = 576 j = 192 the answer is e ."


Question: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 40 days .

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

<gadget id="calculator">4 * 4</gadget>
<output>16</output>

<gadget id="calculator">40 - 16</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 16 days .
B. 17 days .
C. 18 days .
D. 19 days .
E. 24 days .

subtract(40, multiply(divide(40, 10), 4))

Explanation: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 40 * 6 / 10 = 24 days . answer : e"


Question: a towel , when bleached , lost 30 % of its length and 20 % 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 - 20</gadget>
<output>80</output>

<gadget id="calculator">70 * 80</gadget>
<output>5_600</output>

<gadget id="calculator">10_000 - 5_600</gadget>
<output>4_400</output>

<gadget id="calculator">4_400 / 100</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 24 %
B. 30 %
C. 44 %
D. 54 %
E. 64 %

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

Explanation: percentage change in area = ( − 30 − 20 + ( 30 × 20 ) / 100 ) % = − 44 % i . e . , area is decreased by 44 % answer : c


Question: a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is

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

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

<gadget id="calculator">30 - 2</gadget>
<output>28</output>

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

<gadget id="calculator">28 / 1</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 14 years
B. 28 years
C. 20 years
D. 22 years
E. none

divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))

Explanation: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . then â € ¹ = â € º ( x + 30 ) + 2 = 2 ( x + 2 ) â € ¹ = â € º x + 32 = 2 x + 4 x = 28 . answer b"


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 $ 8.73 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">8.73 - (198/25)</gadget>
<output>0.81</output>

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

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

<gadget id="calculator">0.81 / 9</gadget>
<output>0.09</output>

<gadget id="calculator">(11/50) - 0.09</gadget>
<output>0.13</output>

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

Choices:
A. 9 %
B. 10 %
C. 11 %
D. 12 %
E. 13 %

multiply(subtract(divide(22, const_100), divide(subtract(8.73, 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 ) = 8.73 9.9 - 45 x + 36 x = 8.73 9 x = 1.17 x = 0.13 the answer is e ."


Question: a trader bought a car at 20 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?

<gadget id="calculator">100 - 20</gadget>
<output>80</output>

<gadget id="calculator">100 + 80</gadget>
<output>180</output>

<gadget id="calculator">80 * 180</gadget>
<output>14_400</output>

<gadget id="calculator">14_400 / 100</gadget>
<output>144</output>

<gadget id="calculator">144 / 100</gadget>
<output>36/25 = around 1.44</output>

<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>

<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 18 %
B. 13 %
C. 12 %
D. 32 %
E. 44 %

multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 80)), const_100), const_100), const_1), const_100)

Explanation: "original price = 100 cp = 80 s = 80 * ( 180 / 100 ) = 112 100 - 144 = 44 % answer : e"


Question: 800 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?

<gadget id="calculator">15 * 800</gadget>
<output>12_000</output>

<gadget id="calculator">800 + 200</gadget>
<output>1_000</output>

<gadget id="calculator">12_000 / 1_000</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 11.5
B. 12.5
C. 10.5
D. 11
E. 12

Explanation: "800 * 15 = 1000 * x x = 12 answer : e"


Question: n = 1 ! + 2 ! + 3 ! . . . . . + 10 ! . what is the last digit of n ^ n ?

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

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

Choices:
A. 3
B. 4
C. 5
D. 6
E. 7

Explanation: as you see 5 ! till 10 ! each unit digit is zero . so 1 ! + 2 ! + 3 ! + 4 ! = 33 so unit digit 3 + 0 = 3 n = 3 n ^ n = 3 ^ 3 = 27 so last digit is 7 . answer : e


Question: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 250 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?

<gadget id="calculator">250 * 0.8</gadget>
<output>200</output>

<gadget id="calculator">700 * 1.8</gadget>
<output>1_260</output>

<gadget id="calculator">200 + 1_260</gadget>
<output>1_460</output>

<gadget id="calculator">1_460 / 1_000</gadget>
<output>73/50 = around 1.46</output>
<result>73/50 = around 1.46</result>

Choices:
A. 1.46 %
B. 1.93 %
C. 10 %
D. 15 %
E. 19 %

divide(add(multiply(250, 0.8), multiply(700, 1.8)), const_1000)

Explanation: i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 250 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 250 ) / 100 + ( 1.8 * 700 ) / 100 = 14.6 gms % of liquid x in resultant mixture = ( 14.6 / 1000 ) * 100 = 1.46 % a


Question: set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 3 , while all other numbers remain the same , what is the new average of set s ?

<gadget id="calculator">10 * 6.2</gadget>
<output>62</output>

<gadget id="calculator">62 + 3</gadget>
<output>65</output>

<gadget id="calculator">65 / 10</gadget>
<output>13/2 = around 6.5</output>
<result>13/2 = around 6.5</result>

Choices:
A. 6.5
B. 6.7
C. 6.8
D. 6.85
E. 6.9

Explanation: "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 3 then total increased to 62 + 3 = 65 new avg - 65 / 10 = 6.5 . hence answer is a ."


Question: a group of people participate in some curriculum , 30 of them practice yoga , 25 study cooking , 15 study weaving , 6 of them study cooking only , 8 of them study both the cooking and yoga , 7 of them participate all curriculums . how many people study both cooking and weaving ?

<gadget id="calculator">25 - 8</gadget>
<output>17</output>

<gadget id="calculator">17 - 7</gadget>
<output>10</output>

<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<result>4</result>

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

subtract(subtract(subtract(25, 8), 7), 6)

Explanation: "both cooking and weaving = 25 - ( 6 + 8 + 7 ) = 4 so , the correct answer is d ."


Question: a carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet . if the carpenter were to make a similar sandbox twice as long , twice as wide , and twice as high as the first sandbox , what would be the capacity , in cubic feet , of the second sandbox ?

<gadget id="calculator">2 ** 3</gadget>
<output>8</output>

<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 20
B. 40
C. 60
D. 80
E. 100

Explanation: "a quick note on doubling . when you double a length you have 2 * l 1 . when you double all lengths of a rectangle you have ( 2 * l 1 ) ( 2 * l 2 ) = a . an increase of 2 ^ 2 or 4 . when you double all lengths of a rectangular prism you have ( 2 * l 1 ) ( 2 * l 2 ) ( 2 * l 3 ) = v . an increase of 2 ^ 3 or 8 . this leads to the basic relationship : line : 2 * original size rectangle : 4 * original size rectangular prism : 8 * original size answer is d"


Question: find the remainder of the division ( 3 ^ 50 ) / 7 .

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

Explanation: "find the pattern of the remainders after each power : ( 3 ^ 1 ) / 7 remainder 3 ( 3 ^ 2 ) / 7 remainder 2 ( 3 ^ 3 ) / 7 remainder 6 ( 3 ^ 4 ) / 7 remainder 4 ( 3 ^ 5 ) / 7 remainder 5 ( 3 ^ 6 ) / 7 remainder 1 - - > this is where the cycle ends ( 3 ^ 7 ) / 7 remainder 3 - - > this is where the cycle begins again ( 3 ^ 8 ) / 7 remainder 2 continuing the pattern to ( 3 ^ 50 ) / 7 gives us a remainder of 2 final answer : c ) 2"


Question: what is the area inscribed by the lines y = 2 , x = 2 , y = 10 - x on an xy - coordinate plane ?

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

<gadget id="calculator">8 - 2</gadget>
<output>6</output>

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

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

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

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

Choices:
A. 8
B. 10
C. 12
D. 14
E. 18

multiply(subtract(subtract(10, 2), 2), multiply(multiply(const_2, const_0_25), subtract(subtract(10, 2), 2)))

Explanation: first , let ' s graph the lines y = 2 and x = 2 at this point , we need to find the points where the line y = 10 - x intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = 10 - x to get y = 10 - 2 = 8 perfect , when x = 2 , y = 8 , so one point of intersection is ( 28 ) for the horizontal line , we know that y = 2 , so we ' ll plug y = 2 into the equation y = 10 - x to get 2 = 10 - x . solve to get : x = 8 so , when y = 2 , x = 8 , so one point of intersection is ( 82 ) now add these points to our graph and sketch the line y = 10 - x at this point , we can see that we have the following triangle . the base has length 6 and the height is 6 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 6 ) ( 6 ) = 18 answer : e


Question: if n is a positive integer , what is the remainder when ( 4 ^ ( 4 n + 3 ) ) ( 6 ^ n ) is divided by 10 ?

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

<gadget id="calculator">9 * 6</gadget>
<output>54</output>

<gadget id="calculator">54 % 10</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 1
B. 2
C. 4
D. 6
E. 8

reminder(multiply(multiply(const_3, const_3), 6), 10)

Explanation: "this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 8 . c or j in this problem ."


Question: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 20 percent , and on day 3 , it is discounted an additional 40 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?

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

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

<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(2/5) / (9/10)</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">(4/9) * 100</gadget>
<output>400/9 = around 44.444444</output>

<gadget id="calculator">(400/9) + 2</gadget>
<output>418/9 = around 46.444444</output>
<result>418/9 = around 46.444444</result>

Choices:
A. 28 %
B. 48 %
C. 64.8 %
D. 70 %
E. 72 %

add(multiply(divide(divide(40, const_100), subtract(1, divide(1, 10))), const_100), 2)

Explanation: let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 20 % discount = 720 price in day 3 after 40 % discount = 432 so , price in day 3 as percentage of the sale price on day 1 will be = 432 / 900 * 100 = > 48 % answer will definitely be ( b )


Question: each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 28 have long fur , 17 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?

<gadget id="calculator">28 + 17</gadget>
<output>45</output>

<gadget id="calculator">45 - 8</gadget>
<output>37</output>

<gadget id="calculator">45 - 37</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 26
B. 19
C. 11
D. 8
E. 6

Explanation: "no of dogs = 45 long fur = 28 brown = 17 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 28 + 17 - both both = 8 answer d"


Question: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land twice on heads and twice tails ?

<gadget id="calculator">2 ** 4</gadget>
<output>16</output>

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

Choices:
A. 1 / 8
B. 1 / 4
C. 1 / 16
D. 1 / 32
E. 1 / 2

Explanation: must be twice on heads and twice on tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 answer : c


Question: the effective annual rate of interest corresponding to a nominal rate of 14 % per annum payable half - yearly is ?

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

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

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

<gadget id="calculator">49 / 100</gadget>
<output>49/100 = around 0.49</output>

<gadget id="calculator">14 + (49/100)</gadget>
<output>1_449/100 = around 14.49</output>
<result>1_449/100 = around 14.49</result>

Choices:
A. 16.06 %
B. 16.07 %
C. 16.08 %
D. 14.49 %
E. 16.19 %

add(add(divide(14, const_2), divide(14, const_2)), divide(multiply(divide(14, const_2), divide(14, const_2)), const_100))

Explanation: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 7 / 100 ) 2 ] = rs . 14.49 effective rate = ( 114.49 - 100 ) = 14.49 % answer : d"


Question: mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 50 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?

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

<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>

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

<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(1/2) * (8/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 124 %
B. 120 %
C. 96 %
D. 80 %
E. 64 %

multiply(multiply(subtract(const_1, divide(50, const_100)), add(const_1, divide(60, const_100))), const_100)

Explanation: "juan ' s income = 100 ( assume ) ; tim ' s income = 50 ( 50 percent less than juan ' s income ) ; mary ' s income = 80 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 80 ) is 80 % of juan ' s income ( 100 ) . answer : d ."


Question: the circumferences of the fore and hind - wheels of a carriage are 2 2 / 5 and 3 3 / 7 meters respectively . a chalk mark is put on the point of contact of each wheel with the ground at any given moment . how far will the carriage have travelled so that their chalk marks may be again on the ground at the same time ?

<gadget id="calculator">7 * 3</gadget>
<output>21</output>

<gadget id="calculator">21 + 3</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 18 metres
B. 16 metres
C. 38 metres
D. 42 metres
E. 24 metres

Explanation: a little reflection will show that chalk marks will touch the ground together for the first time after the wheels have passed over a distance which is the lcm of 2 2 / 5 metres and 3 3 / 7 metres . lcm of 12 / 5 metres and 24 / 7 metres = 24 metres . answer is e


Question: a 100 - litre mixture of milk and water contains 30.25 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?

<gadget id="calculator">25 / 30.25</gadget>
<output>0.826446</output>

<gadget id="calculator">0.826446 ** (1/2)</gadget>
<output>0.909091</output>

<gadget id="calculator">1 - 0.909091</gadget>
<output>0.090909</output>

<gadget id="calculator">100 * 0.090909</gadget>
<output>9.0909</output>
<result>9.0909</result>

Choices:
A. 9.1 litres
B. 10 litres
C. 8 litres
D. 12 litres
E. 6 litres

multiply(100, subtract(const_1, sqrt(divide(25, 30.25))))

Explanation: working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 30.25 % ( 1 - x / 100 ) ^ 2 = 25 % * 100 % ( 1 - x / 100 ) ^ 2 = 25 / 30.25 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 5 / 5.5 ) ^ 2 100 - x = 500 / 5.5 x = 9.1 . . . ans a


Question: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 12 ) both lie on the line defined by the equation x = ( y / 4 ) - ( 2 / 5 ) , what is the value of p ?

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

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

Explanation: "x = ( y / 4 ) - ( 2 / 5 ) , and so y = 4 x + 8 / 5 . the slope is 4 . ( n + 12 - n ) / ( m + p - m ) = 3 p = 3 the answer is c ."


Question: 1000 men have provisions for 15 days . if 300 more men join them , for how many days will the provisions last now ?

<gadget id="calculator">15 * 1_000</gadget>
<output>15_000</output>

<gadget id="calculator">1_000 + 300</gadget>
<output>1_300</output>

<gadget id="calculator">15_000 / 1_300</gadget>
<output>150/13 = around 11.538462</output>
<result>150/13 = around 11.538462</result>

Choices:
A. 11.5
B. 12.5
C. 12.6
D. 12.2
E. 12.1

Explanation: "1000 * 15 = 1300 * x x = 11.5 answer : a"


Question: the equation of line a is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line a ?

<gadget id="calculator">100 * 3</gadget>
<output>300</output>

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>

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

<gadget id="calculator">16 + 9</gadget>
<output>25</output>

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>

<gadget id="calculator">300 / 5</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 48
B. 50
C. 60
D. 75
E. 100

divide(multiply(100, 3), sqrt(add(power(4, const_2), power(3, const_2))))

Explanation: this can be solve in two steps and without any complex calculation . given : equation of line a as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 750 ) . this can be considered a right angle triangle with right angle at ( 00 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 00 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c


Question: the average age of applicants for a new job is 31 , with a standard deviation of 6 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?

<gadget id="calculator">6 * 2</gadget>
<output>12</output>

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

Choices:
A. 8
B. 13
C. 15
D. 18
E. 30

Explanation: "within one standard deviation of the average age means 31 + / - 7 25 - - 31 - - 37 number of dif . ages - 25 26 27 28 29 30 31 32 33 34 35 36 37 total = 13 b"


Question: 20 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?

<gadget id="calculator">21 * 8</gadget>
<output>168</output>

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

<gadget id="calculator">168 * 60</gadget>
<output>10_080</output>

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

<gadget id="calculator">42 * 6</gadget>
<output>252</output>

<gadget id="calculator">10_080 / 252</gadget>
<output>40</output>

<gadget id="calculator">floor(40)</gadget>
<output>40</output>

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

Choices:
A. 32
B. 87
C. 40
D. 99
E. 77

add(floor(divide(multiply(multiply(21, 8), multiply(20, 3)), multiply(multiply(21, 2), 6))), const_1)

Explanation: "3 w = 2 m 20 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 20 * 21 * 8 = 14 * x * 6 x = 40 answer : c"


Question: machine a produces 100 parts thrice as fast as machine b does . machine b produces 100 parts in 30 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?

<gadget id="calculator">100 / 30</gadget>
<output>10/3 = around 3.333333</output>

<gadget id="calculator">(10/3) * 3</gadget>
<output>10</output>

<gadget id="calculator">10 * 6</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 20
B. 80
C. 40
D. 60
E. 50

multiply(multiply(divide(100, 30), const_3), 6)

Explanation: machine b produces 100 part in 30 minutes . machine a produces 100 parts thrice as fast as b , so machine a produces 100 parts in 30 / 3 = 10 minutes . now , machine a produces 100 parts in 10 minutes which is 100 / 10 = 10 parts / minute . 10 parts x a total of 6 minutes = 60 d


Question: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?

<gadget id="calculator">226 + 423</gadget>
<output>649</output>
<result>649</result>

Choices:
A. 515
B. 545
C. 618 .
D. 644 .
E. 666

Explanation: "solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 515 , so 100 % is approx . 644 . answer is d : 644"


Question: the average of 5 quantities is 9 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?

<gadget id="calculator">5 * 9</gadget>
<output>45</output>

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

<gadget id="calculator">45 - 12</gadget>
<output>33</output>

<gadget id="calculator">33 / 2</gadget>
<output>33/2 = around 16.5</output>
<result>33/2 = around 16.5</result>

Choices:
A. 16.5
B. 10
C. 8
D. 9.5
E. none of these

divide(subtract(multiply(5, 9), multiply(3, 4)), 2)

Explanation: "answer : a ( 5 x 9 - 3 x 4 ) / 2 = 16.5"


Question: the average height of 30 students in a class was calculated as 177 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm . what was the actual average height of the students in the class ?

<gadget id="calculator">30 * 177</gadget>
<output>5_310</output>

<gadget id="calculator">151 - 106</gadget>
<output>45</output>

<gadget id="calculator">5_310 - 45</gadget>
<output>5_265</output>

<gadget id="calculator">5_265 / 30</gadget>
<output>351/2 = around 175.5</output>
<result>351/2 = around 175.5</result>

Choices:
A. 176.5 cm
B. 175.5 cm
C. 174.5 cm
D. 173.5 cm
E. 172.5 cm

divide(subtract(multiply(30, 177), subtract(151, 106)), 30)

Explanation: "the total height was 45 cm too much . the average height should be reduced by 45 cm / 30 = 1.5 cm the answer is b ."


Question: what is the max number of rectangular boxes , each measuring 5 inches by 2 inches by 7 inches , that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches , if all boxes are aligned in the same direction ?

<gadget id="calculator">15 * 20</gadget>
<output>300</output>

<gadget id="calculator">300 * 35</gadget>
<output>10_500</output>

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

<gadget id="calculator">10 * 7</gadget>
<output>70</output>

<gadget id="calculator">10_500 / 70</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 200
B. 350
C. 100
D. 150
E. 120

divide(multiply(multiply(15, 20), 35), multiply(multiply(5, 2), 7))

Explanation: "the 5 inch side should be aligned to the 15 inch side ( 3 layer ) 2 inch side should be aligned to the 20 inch side . ( 10 layer ) 7 inch side should be aligned to the 35 inch side . ( 5 layer ) maximum number of rectangles = 3 * 10 * 5 = 150 answer is d"


Question: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 288 . find the principal ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>

<gadget id="calculator">(1/5) * 2</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">(36/25) - (7/5)</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">288 / (1/25)</gadget>
<output>7_200</output>
<result>7_200</result>

Choices:
A. 2277
B. 2667
C. 3600
D. 7200
E. 1811

divide(288, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1)))

Explanation: "p = 288 ( 100 / 5 ) ^ 2 = > p = 7200 answer : d"


Question: 63.2 is what percent of 867 ?

<gadget id="calculator">63.2 / 867</gadget>
<output>0.072895</output>

<gadget id="calculator">0.072895 * 100</gadget>
<output>7.2895</output>
<result>7.2895</result>

Choices:
A. 6.9
B. 8.99
C. 7.29
D. 7.98
E. 9.21

Explanation: "we assume that 867 is 100 % assume ' x ' is value we looking for here , 867 = 100 % and x % = 63.2 therefore , 100 / x = 867 / 63.2 100 / x = 13.71 x = 7.29 c"


Question: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 15 days to complete the same work . then q alone can do it in

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

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

<gadget id="calculator">(1/10) + (1/15)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) / 2</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/12) - (1/15)</gadget>
<output>1/60 = around 0.016667</output>

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

Choices:
A. 20
B. 22
C. 25
D. 27
E. 60

divide(const_1, subtract(divide(add(divide(const_1, 10), divide(const_1, 15)), const_2), divide(const_1, 15)))

Explanation: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 15 work done by p , q and r in 1 day = 1 / 10 + 1 / 15 = 1 / 6 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 1 / 6 = > work done by p in 1 day = 1 / 12 = > work done by q and r in 1 day = 1 / 12 hence work done by q in 1 day = 1 / 12 â € “ 1 / 15 = 1 / 60 so q alone can do the work in 60 days answer is e ."


Question: a customer purchased a package of ground beef at a cost of $ 1.80 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 20 percent less than the package of ground beef . what was the cost per pound of the steak ?

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

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

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 1</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/2) + (1/3)</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">1.8 / (5/6)</gadget>
<output>2.16</output>
<result>2.16</result>

Choices:
A. $ 2.05
B. $ 2.15
C. $ 2.25
D. $ 2.35
E. $ 2.45

divide(1.8, add(multiply(const_0_25, const_2), multiply(const_0_33, const_1)))

Explanation: for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.80 . let x be the price per pound for the steak . then 0.8 x = 180 x = 180 / 0.8 = $ 2.25 the answer is c .


Question: at a wedding reception , 125 guests ate chicken and 75 guests ate beef . if exactly 100 guests ate only one of the two types of meat , how many guests ate both types of meat ?

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

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

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

Choices:
A. 5
B. 100
C. 7
D. 4
E. 50

Explanation: say x guests ate both types of meat . ( 125 - x ) + ( 75 - x ) = 100 - - > x = 50 . answer : e .


Question: the average temperature for monday , tuesday and wednsday is 36.3 degrees c . the average temperature for tuesday , wednesday and thursday is 36.7 degrees c . if monday ’ s temperature recorded as 39 degrees c , find the thursday ’ s temperature ?

<gadget id="calculator">36.7 * 3</gadget>
<output>110.1</output>

<gadget id="calculator">36.3 * 3</gadget>
<output>108.9</output>

<gadget id="calculator">108.9 - 39</gadget>
<output>69.9</output>

<gadget id="calculator">110.1 - 69.9</gadget>
<output>40.2</output>
<result>40.2</result>

Choices:
A. 60.2 degrees c
B. 50.2 degrees c
C. 40.2 degrees c
D. 70.2 degrees c
E. none of these

subtract(multiply(36.7, const_3), subtract(multiply(36.3, const_3), 39))

Explanation: explanation : mon + tue + wed temperature = 3 x 36.3 = 108.9 tue + wed temperature = 108.9 – 39 = 69.9 tue + wed + thu temperature = 3 x 36.7 = 110.1 so , thursday ’ s temperature = 110.1 – 69.9 = 40.2 degrees c answer : c


Question: a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 6 - digit numbers are palindromes ?

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

<gadget id="calculator">10 ** 3</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 / 2</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 400
B. 450
C. 500
D. 900
E. 2500

divide(power(const_10, divide(6, const_2)), const_2)

Explanation: "first recognize you only need to consider the first three digits ( because the second three are just the first three flipped ) there are 900 possibilities for the first three digits of a 6 digit number , 100 - 999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 900 = 500 answer : c"


Question: p , q and r have $ 6000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?

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

<gadget id="calculator">6_000 * 4</gadget>
<output>24_000</output>

<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>

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

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

<gadget id="calculator">4 + 3</gadget>
<output>7</output>

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

<gadget id="calculator">24_000 / 10</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. 2400
B. 2403
C. 3998
D. 2539
E. 1930

divide(multiply(6000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3)))

Explanation: "a 2400 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 6000 - r ) = > 3 r = 12000 - 2 r = > 5 r = 12000 = > r = 2400 ."


Question: light glows for every 15 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .

<gadget id="calculator">2 + 47</gadget>
<output>49</output>

<gadget id="calculator">2 + 60</gadget>
<output>62</output>

<gadget id="calculator">20 + 62</gadget>
<output>82</output>

<gadget id="calculator">82 * 60</gadget>
<output>4_920</output>

<gadget id="calculator">49 + 4_920</gadget>
<output>4_969</output>

<gadget id="calculator">4_969 / 15</gadget>
<output>4_969/15 = around 331.266667</output>
<result>4_969/15 = around 331.266667</result>

Choices:
A. 380 times
B. 381 times
C. 382 times
D. 392 times
E. 331 times

divide(add(add(const_2, 47), multiply(add(20, add(const_2, const_60)), const_60)), 15)

Explanation: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 15 ) = 331 times . answer : e"


Question: a boy goes to his school from his house at a speed of 3 km / hr and returns at a speed of 2 km / hr . if he takes 5 hours in going and coming . the distance between his house and school is :

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) + 1</gadget>
<output>5/2 = around 2.5</output>

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

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

Choices:
A. 4.5 km
B. 5.5 km
C. 6 km
D. 7 km
E. none

multiply(divide(5, add(divide(3, 2), const_1)), 3)

Explanation: "sol . average speed = [ 2 * 3 * 2 / 3 + 2 ] km / hr = 12 / 5 km / hr . distance travelled = [ 12 / 5 * 5 ] km = 12 km . ∴ distance between house and school = [ 12 / 2 ] km = 6 km . answer c"


Question: of the 120 passengers on flight 750 , 60 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?

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

<gadget id="calculator">120 * (3/5)</gadget>
<output>72</output>

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

<gadget id="calculator">120 * (1/10)</gadget>
<output>12</output>

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

<gadget id="calculator">12 - 4</gadget>
<output>8</output>

<gadget id="calculator">72 - 8</gadget>
<output>64</output>
<result>64</result>

Choices:
A. 44
B. 48
C. 50
D. 64
E. 56

subtract(multiply(120, divide(60, const_100)), subtract(multiply(120, divide(10, const_100)), divide(multiply(120, divide(10, const_100)), 3)))

Explanation: "number of passengers on flight = 120 number of female passengers = . 6 * 120 = 72 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 72 - 8 = 64 answer d"


Question: the ratio of radius of a circle and the side of a square is 2 : 7 . find the ratio of their areas :

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

<gadget id="calculator">(2/7) ** 2</gadget>
<output>4/49 = around 0.081633</output>
<result>4/49 = around 0.081633</result>

Choices:
A. 2 : 1
B. 4 : 7
C. 8 : 77
D. 4 : 49
E. none

Explanation: "radius / side = 2 / 7 â ‡ ’ area of circle / area of square = 4 / 49 answer : d"


Question: how many kilograms of sugar costing rs . 9 per kg must be mixed with 27 kg of sugar costing rs . 7 per kg so that there may be a gain of 10 % by selling the mixture at rs . 9.24 per kg ?

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

<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">9.24 / (11/10)</gadget>
<output>8.4</output>

<gadget id="calculator">27 * 8.4</gadget>
<output>226.8</output>

<gadget id="calculator">27 * 7</gadget>
<output>189</output>

<gadget id="calculator">226.8 - 189</gadget>
<output>37.8</output>

<gadget id="calculator">9 - 8.4</gadget>
<output>0.6</output>

<gadget id="calculator">37.8 / 0.6</gadget>
<output>63</output>
<result>63</result>

Choices:
A. 33
B. 39
C. 38
D. 63
E. 01

divide(subtract(multiply(27, divide(9.24, add(divide(10, const_100), const_1))), multiply(27, 7)), subtract(9, divide(9.24, add(divide(10, const_100), const_1))))

Explanation: by the rule of alligation : c . p . of 1 kg sugar of 1 st kind c . p . of 1 kg sugar of 2 nd kind { \ color { blue } \ therefore } ratio of quantities of 1 st and 2 nd kind = 14 : 6 = 7 : 3 . let x kg of sugar of 1 st kind be mixed with 27 kg of 2 nd kind . then , 7 : 3 = x : 27 or x = ( 7 x 27 / 3 ) = 63 kg . answer : d ) 63 kg


Question: a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?

<gadget id="calculator">1_020 - 820</gadget>
<output>200</output>

<gadget id="calculator">200 / 5</gadget>
<output>40</output>

<gadget id="calculator">40 * 2</gadget>
<output>80</output>

<gadget id="calculator">820 - 80</gadget>
<output>740</output>
<result>740</result>

Choices:
A. rs . 440
B. rs . 500
C. rs . 540
D. rs . 740
E. rs . 840

subtract(820, multiply(divide(subtract(1020, 820), 5), 2))

Explanation: "s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 5 * 2 = rs . 80 . principal = ( 820 - 80 ) = rs . 740 . answer : d"


Question: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 60 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?

<gadget id="calculator">7 + 15</gadget>
<output>22</output>

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

<gadget id="calculator">(11/50) + 1</gadget>
<output>61/50 = around 1.22</output>

<gadget id="calculator">60 / (61/50)</gadget>
<output>3_000/61 = around 49.180328</output>
<result>3_000/61 = around 49.180328</result>

Choices:
A. 39.55 $
B. 40.63 $
C. 41.63 $
D. 42.15 $
E. 48.7 $

divide(60, add(divide(add(7, 15), const_100), const_1))

Explanation: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 60 x = 48.7 hence , the correct option is e"


Question: for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 21000 , my total savings for the two - year is

<gadget id="calculator">21_000 * 5</gadget>
<output>105_000</output>

<gadget id="calculator">105_000 / 3</gadget>
<output>35_000</output>

<gadget id="calculator">42_000 - 35_000</gadget>
<output>7_000</output>

<gadget id="calculator">42_000 * 4</gadget>
<output>168_000</output>

<gadget id="calculator">168_000 / 7</gadget>
<output>24_000</output>

<gadget id="calculator">24_000 - 21_000</gadget>
<output>3_000</output>

<gadget id="calculator">7_000 + 3_000</gadget>
<output>10_000</output>
<result>10_000</result>

Choices:
A. rs . 8000
B. rs . 9000
C. rs . 9800
D. rs . 9900
E. rs . 10000

add(subtract(42000, divide(multiply(21000, 5), 3)), subtract(divide(multiply(42000, 4), 7), 21000))

Explanation: sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 21000 + 35000 ) = 66000 - s 6000 = rs . 10000 e


Question: a boat can travel with a speed of 12 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 68 km downstream .

<gadget id="calculator">12 + 4</gadget>
<output>16</output>

<gadget id="calculator">68 / 16</gadget>
<output>17/4 = around 4.25</output>
<result>17/4 = around 4.25</result>

Choices:
A. 4.25 hr
B. 5.25 hr
C. 8.25 hr
D. 2.25 hr
E. 2.50 hr

Explanation: "speed of boat in still water = 12 km / hr speed of the stream = 4 km / hr speed downstream = ( 12 + 4 ) = 16 km / hr time taken to travel 68 km downstream = 68 ⁄ 16 = 17 ⁄ 4 = 4.25 hours answer is a"


Question: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if saran and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?

<gadget id="calculator">80 * 0.02</gadget>
<output>1.6</output>

<gadget id="calculator">2 * 1.6</gadget>
<output>3.2</output>

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

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">160 * (3/4)</gadget>
<output>120</output>

<gadget id="calculator">120 * 0.02</gadget>
<output>2.4</output>

<gadget id="calculator">3.2 - 2.4</gadget>
<output>0.8</output>

<gadget id="calculator">0.8 / 2</gadget>
<output>0.4</output>
<result>0.4</result>

Choices:
A. $ 0.32
B. $ 0.40
C. $ 0.45
D. $ 0.48
E. $ 0.54

divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2)

Explanation: if saran and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combinedno discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) .


Question: p is able to do a piece of work in 10 days and q can do the same work in 12 days . if they can work together for 5 days , what is the fraction of work left ?

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

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

<gadget id="calculator">(1/12) + (1/10)</gadget>
<output>11/60 = around 0.183333</output>

<gadget id="calculator">(11/60) * 5</gadget>
<output>11/12 = around 0.916667</output>

<gadget id="calculator">1 - (11/12)</gadget>
<output>1/12 = around 0.083333</output>
<result>1/12 = around 0.083333</result>

Choices:
A. 7 / 12
B. 5 / 12
C. 1 / 12
D. 3 / 12
E. 1 / 2

subtract(const_1, multiply(add(divide(const_1, 12), divide(const_1, 10)), 5))

Explanation: "explanation : amount of work p can do in 1 day = 1 / 10 amount of work q can do in 1 day = 1 / 12 amount of work p and q can do in 1 day = 1 / 10 + 1 / 12 = 11 / 60 amount of work p and q can together do in 5 days = 5 × ( 11 / 60 ) = 11 / 12 fraction of work left = 1 – 11 / 12 = 1 / 12 answer : option c"


Question: find the area of a parallelogram with base 24 cm and height 12 cm ?

<gadget id="calculator">24 * 12</gadget>
<output>288</output>
<result>288</result>

Choices:
A. 297 cm 2
B. 384 cm 2
C. 672 cm 2
D. 267 cm 2
E. 288 cm 2

Explanation: "area of a parallelogram = base * height = 24 * 12 = 288 cm 2 answer : e"


Question: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 2 / 3 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?

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

<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">1 - (1/6)</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">(1/3) * (5/6)</gadget>
<output>5/18 = around 0.277778</output>
<result>5/18 = around 0.277778</result>

Choices:
A. 5 / 27
B. 2 / 9
C. 1 / 3
D. 4 / 9
E. 2 / 7

multiply(subtract(1, divide(2, 3)), subtract(1, divide(subtract(1, divide(2, 3)), 2)))

Explanation: p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 2 / 3 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 2 / 3 = 1 / 3 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 1 / 3 = 1 / 6 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 2 / 3 * 1 / 6 = 2 / 7 ans e


Question: a glass was filled with 10 ounces of water , and 0.05 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?

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

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

<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 0.002 %
B. 0.02 %
C. 0.2 %
D. 2 %
E. 10 %

multiply(divide(multiply(0.05, 20), 10), const_100)

Explanation: "we are given that 0.05 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.05 by 20 . this gives us : 0.05 x 20 = 1 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 1 / 10 ) x 100 % ( 10 / 100 ) x 100 % = 10 % answer e"


Question: a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital

<gadget id="calculator">3_500 * 12</gadget>
<output>42_000</output>

<gadget id="calculator">42_000 * 3</gadget>
<output>126_000</output>

<gadget id="calculator">12 - 5</gadget>
<output>7</output>

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

<gadget id="calculator">126_000 / 14</gadget>
<output>9_000</output>
<result>9_000</result>

Choices:
A. rs 9000
B. rs 7000
C. rs 5000
D. rs 4000
E. none of these

divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 5), 2))

Explanation: "explanation : let b contribution is x . 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = rs 9000 option a"


Question: a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?

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

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

<gadget id="calculator">(1/5) - (1/10)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 / (1/10)</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 20 hr
B. 10 hr
C. 5 hr
D. 4 hr
E. 15 hr

divide(const_1, subtract(divide(const_1, 5), divide(const_1, 10)))

Explanation: "net part filled in 1 hour 1 / 5 - 1 / 10 = 1 / 10 the cistern will be filled in 10 hr answer is b"


Question: the mall charges 50 cents for the first hour of parking and $ 3 for each additional hour until the customer reaches 4 hours , after that the parking fee is $ 1 per hour . if a certain customer parked his in the mall for 7 hours and 30 minutes , how much is he going to pay ?

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

<gadget id="calculator">7 - 4</gadget>
<output>3</output>

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

<gadget id="calculator">3 + (1/2)</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">(7/2) * 1</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">9 + (7/2)</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) + (1/2)</gadget>
<output>13</output>
<result>13</result>

Choices:
A. $ 11.5 .
B. $ 12 .
C. $ 13 .
D. $ 14.5
E. $ 15 .

add(add(multiply(3, 3), multiply(add(subtract(7, 4), divide(50, const_100)), 1)), divide(50, const_100))

Explanation: charges for 7 hours = ( first hour @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( 1 @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.5 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.50 ) charges for 7 hours = $ 13 hence correct answer must be ( c )


Question: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40000 , the amount invested by y is

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

<gadget id="calculator">40_000 * 5</gadget>
<output>200_000</output>

<gadget id="calculator">200_000 / 2</gadget>
<output>100_000</output>

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

<gadget id="calculator">100_000 * (3/5)</gadget>
<output>60_000</output>
<result>60_000</result>

Choices:
A. 33488
B. 63809
C. 60000
D. 37887
E. 77824

multiply(divide(multiply(40000, add(2, 3)), 2), divide(3, add(2, 3)))

Explanation: explanation : suppose y invested rs . y . then 40000 / y = 2 / 3 or y = 60000 . answer : c ) 60000


Question: an article with cost price of 245 is sold at 34 % profit . what is the selling price ?

<gadget id="calculator">34 / 100</gadget>
<output>17/50 = around 0.34</output>

<gadget id="calculator">245 * (17/50)</gadget>
<output>833/10 = around 83.3</output>

<gadget id="calculator">245 + (833/10)</gadget>
<output>3_283/10 = around 328.3</output>
<result>3_283/10 = around 328.3</result>

Choices:
A. 328
B. 320
C. 300
D. 207
E. 310

add(245, multiply(245, divide(34, const_100)))

Explanation: sp = 1.34 * 245 = 328 answer : a


Question: two stations p and q are 155 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?

<gadget id="calculator">155 + 25</gadget>
<output>180</output>

<gadget id="calculator">20 + 25</gadget>
<output>45</output>

<gadget id="calculator">180 / 45</gadget>
<output>4</output>

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

Choices:
A. 10 am
B. 12 am
C. 10.30 am
D. 12.30 am
E. 11 am

Explanation: "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 155 = > 20 x + 25 ( x - 1 ) = 155 = > 45 x = 180 = > x = 4 means , they meet after 3 hours after 7 am , ie , they meet at 11 am answer is e ."


Question: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?

<gadget id="calculator">26 + 3</gadget>
<output>29</output>

<gadget id="calculator">26 + 29</gadget>
<output>55</output>

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

<gadget id="calculator">55 - 9</gadget>
<output>46</output>

<gadget id="calculator">46 / 2</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 23 years
B. 20 years
C. 25 years
D. 22 years
E. 28 years

divide(subtract(add(26, add(26, 3)), multiply(3, 3)), const_2)

Explanation: "a 23 years let the average age of the whole team by x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . so , average age of the team is 23 years"


Question: the number of students in each section of a school is 24 . after admitting new students , 3 new sections were started . now , the total number of sections is 16 and there are 21 students in each section . the number of new students admitted is :

<gadget id="calculator">21 * 16</gadget>
<output>336</output>

<gadget id="calculator">16 - 3</gadget>
<output>13</output>

<gadget id="calculator">24 * 13</gadget>
<output>312</output>

<gadget id="calculator">336 - 312</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 12
B. 42
C. 24
D. 28
E. 26

subtract(multiply(21, 16), multiply(24, subtract(16, 3)))

Explanation: original number of sections = 16 - 3 = 13 original number of students = 24 x 13 = 312 present number of students = 21 x 16 = 336 number of new students admitted = 336 - 312 = 24 so the answer is option c ) 24 .


Question: simplify : 81 x 81 + 68 x 68 - 2 x 81 x 68 .

<gadget id="calculator">81 + 81</gadget>
<output>162</output>
<result>162</result>

Choices:
A. 169
B. 159
C. 189
D. 179
E. 219

Explanation: = ( 81 ) ^ 2 + ( 68 ) ^ 2 – 2 x 81 x 68 = a ^ 2 + b ^ 2 – 2 ab , where a = 81 , b = 68 = ( a - b ) ^ 2 = ( 81 – 68 ) ^ 2 = ( 13 ) ^ 2 = 169 . answer is a .


Question: - 24 * 29 + 1240 = ?

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

<gadget id="calculator">(-24) * 29</gadget>
<output>-696</output>

<gadget id="calculator">(-696) + 1_240</gadget>
<output>544</output>
<result>544</result>

Choices:
A. - 544
B. 584
C. 544
D. 345
E. none of these

Explanation: "= > - 24 * ( 30 - 1 ) + 1240 ; = > - ( 24 * 30 ) + 24 + 1240 ; = > - 720 + 1264 = 544 . correct option : c"


Question: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13750 ?

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

<gadget id="calculator">12 - 4</gadget>
<output>8</output>

<gadget id="calculator">48_000 * 8</gadget>
<output>384_000</output>

<gadget id="calculator">36_000 * 12</gadget>
<output>432_000</output>

<gadget id="calculator">42_000 * 12</gadget>
<output>504_000</output>

<gadget id="calculator">432_000 + 504_000</gadget>
<output>936_000</output>

<gadget id="calculator">936_000 + 384_000</gadget>
<output>1_320_000</output>

<gadget id="calculator">13_750 / 1_320_000</gadget>
<output>1/96 = around 0.010417</output>

<gadget id="calculator">384_000 * (1/96)</gadget>
<output>4_000</output>
<result>4_000</result>

Choices:
A. 3200
B. 4000
C. 3250
D. 3825
E. 3985

multiply(multiply(48000, subtract(multiply(const_3, const_4), const_4)), divide(13750, add(add(multiply(36000, multiply(const_3, const_4)), multiply(42000, multiply(const_3, const_4))), multiply(48000, subtract(multiply(const_3, const_4), const_4)))))

Explanation: ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13750 × 16 / 55 = rs . 4000 . share of z in the profit is rs . 4000 . option b


Question: machine a and machine b are each used to manufacture 550 sprockets . it takes machine a 10 hours longer to produce 550 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?

<gadget id="calculator">10 * 550</gadget>
<output>5_500</output>

<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">5_500 * (11/10)</gadget>
<output>6_050</output>

<gadget id="calculator">550 * (11/10)</gadget>
<output>605</output>

<gadget id="calculator">605 - 550</gadget>
<output>55</output>

<gadget id="calculator">6_050 / 55</gadget>
<output>110</output>

<gadget id="calculator">550 / 110</gadget>
<output>5</output>
<result>5</result>

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

divide(550, divide(multiply(multiply(10, 550), divide(add(const_100, 10), const_100)), subtract(multiply(550, divide(add(const_100, 10), const_100)), 550)))

Explanation: "machine b : takes x hours to produce 550 sprockets machine a : takes ( x + 10 ) hours to produce 550 sprockets machine b : in 1 hour , b makes 550 / x sprockets machine a : in 1 hour , a makes 550 / ( x + 10 ) sprockets equating : 1.1 ( 550 / ( x + 10 ) ) = 550 / x 605 / ( x + 10 ) = 550 / x 605 x = 550 x + 5500 55 x = 5500 x = 100 a makes 550 / ( 110 ) = 5 sprockets per hour answer : b"


Question: how long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 120 m in length ?

<gadget id="calculator">100 + 120</gadget>
<output>220</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">220 / (50/3)</gadget>
<output>66/5 = around 13.2</output>
<result>66/5 = around 13.2</result>

Choices:
A. 15.8 sec
B. 13.2 sec
C. 12.4 sec
D. 16.8 sec
E. 11.8 sec

Explanation: "b 13.2 sec d = 100 + 120 = 220 m s = 60 * 5 / 18 = 50 / 3 t = 220 * 3 / 50 = 13.2 sec answer is b"


Question: a rainstorm increased the amount of water stored in state j reservoirs from 5 billion gallons to 7.5 billion gallons . if the storm increased the amount of water in the reservoirs to 55 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?

<gadget id="calculator">7.5 * 100</gadget>
<output>750</output>

<gadget id="calculator">750 / 55</gadget>
<output>150/11 = around 13.636364</output>

<gadget id="calculator">(150/11) / 2</gadget>
<output>75/11 = around 6.818182</output>
<result>75/11 = around 6.818182</result>

Choices:
A. 6.9
B. 1.4
C. 2.5
D. 3.0
E. 4.4

divide(divide(multiply(7.5, const_100), 55), const_2)

Explanation: after the reservoir is filled to 7.5 gallons the amount of water is at 55 % - which means that 45 % of the reservoir is empty . to figure out what that 45 % is approximate : 7.5 gallons / 55 percent = x gallons / 45 percent , therefore , x = 6.136 gallons , answer choices e , b , c , d are below 6.136 . we know that the reservoir must be short more than 6.136 gallons , therefore , the only possible choice is a .


Question: kathleen can paint a room in 2 hours , and anthony can paint an identical room in 3 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?

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

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/2) + (1/3)</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">1 / (5/6)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) * 2</gadget>
<output>12/5 = around 2.4</output>
<result>12/5 = around 2.4</result>

Choices:
A. 8 / 15
B. 4 / 3
C. 12 / 5
D. 9 / 4
E. 15 / 4

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

Explanation: "( 1 / 2 + 1 / 3 ) t = 2 t = 12 / 5 answer : c"


Question: a parallelogram has a base that is four time the size of it ' s height . the total area of this parallelogram is 2,304 sq ft . what is the height of the parallelogram ?

<gadget id="calculator">1_000 * 2</gadget>
<output>2_000</output>

<gadget id="calculator">100 * 3</gadget>
<output>300</output>

<gadget id="calculator">2_000 + 300</gadget>
<output>2_300</output>

<gadget id="calculator">2_300 + 4</gadget>
<output>2_304</output>

<gadget id="calculator">2_304 / 4</gadget>
<output>576</output>

<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 19
B. 23
C. 24
D. 16
E. 17

sqrt(divide(add(add(multiply(const_1000, const_2), multiply(const_100, const_3)), const_4), const_4))

Explanation: 4 x * x = 2304 = > x = 24 answer : c


Question: how long does a train 150 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?

<gadget id="calculator">150 + 170</gadget>
<output>320</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">320 / (50/3)</gadget>
<output>96/5 = around 19.2</output>
<result>96/5 = around 19.2</result>

Choices:
A. 16.5
B. 19.2
C. 16.4
D. 16.8
E. 16.1

Explanation: "d = 150 + 170 = 320 m s = 60 * 5 / 18 = 50 / 3 t = 320 * 3 / 50 = 19.2 sec answer : b"


Question: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 4 , 7 } . what is the probability that the median of the set will increase but the range still remains the same ?

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

Choices:
A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

Explanation: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 4 ) / 2 = 3.5 , thus the number selected must be 4 or greater . for the range to remain the same , the number must be between 2 and 7 inclusive . to satisfy both conditions , the number selected must be 4 , 5 , 6 , or 7 . the probability is 4 / 10 = 0.4 the answer is c ."


Question: a student chose a number , multiplied it by 6 , then subtracted 250 from the result and got 122 . what was the number he chose ?

<gadget id="calculator">122 + 250</gadget>
<output>372</output>

<gadget id="calculator">372 / 6</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 59
B. 60
C. 61
D. 62
E. 63

Explanation: "let x be the number he chose , then 6 ⋅ x − 250 = 122 6 x = 372 x = 62 correct answer d"


Question: if the average marks of 3 batches of 55 , 60 and 45 students respectively is 40 , 62 , 58 , then the average marks of all the students is

<gadget id="calculator">55 * 40</gadget>
<output>2_200</output>

<gadget id="calculator">60 * 62</gadget>
<output>3_720</output>

<gadget id="calculator">2_200 + 3_720</gadget>
<output>5_920</output>

<gadget id="calculator">40 * 58</gadget>
<output>2_320</output>

<gadget id="calculator">5_920 + 2_320</gadget>
<output>8_240</output>

<gadget id="calculator">55 + 60</gadget>
<output>115</output>

<gadget id="calculator">115 + 45</gadget>
<output>160</output>

<gadget id="calculator">8_240 / 160</gadget>
<output>103/2 = around 51.5</output>
<result>103/2 = around 51.5</result>

Choices:
A. 54.48
B. 53.31
C. 54.6
D. 54.58
E. none of these

divide(add(add(multiply(55, 40), multiply(60, 62)), multiply(40, 58)), add(add(55, 60), 45))

Explanation: explanation : ( 55 ã — 40 ) + ( 60 ã — 62 ) + ( 45 ã — 58 ) / 55 + 60 + 45 8530 / 160 = 53.3 option b


Question: in an election contested by two parties , party d secured 12 % of the total votes more than party r . if party r got 132000 votes , by how many votes did it lose the election ?

<gadget id="calculator">100 - 12</gadget>
<output>88</output>

<gadget id="calculator">88 / 2</gadget>
<output>44</output>

<gadget id="calculator">132_000 / 44</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 * 12</gadget>
<output>36_000</output>
<result>36_000</result>

Choices:
A. 240000
B. 300000
C. 168000
D. 36000
E. 24,000

multiply(divide(132000, divide(subtract(const_100, 12), const_2)), 12)

Explanation: explanatory answer let the percentage of the total votes secured by party d be x % then the percentage of total votes secured by party r = ( x - 12 ) % as there are only two parties contesting in the election , the sum total of the votes secured by the two parties should total up to 100 % i . e . , x + x - 12 = 100 2 x - 12 = 100 or 2 x = 112 or x = 56 % . if party d got 56 % of the votes , then party got ( 56 - 12 ) = 44 % of the total votes . 44 % of the total votes = 132,000 i . e . , 44 / 100 * t = 132,000 = > t = 132000 * 100 / 44 = 300,000 votes . the margin by which party r lost the election = 12 % of the total votes = 12 % of 300,000 = 36,000 . the correct choice is ( d )


Question: in measuring the sides of a rectangle , one side is taken 4 % in excess , and the other 3 % in deficit . find the error percent in the area calculated from these measurements .

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

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

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">1 - (3/25)</gadget>
<output>22/25 = around 0.88</output>
<result>22/25 = around 0.88</result>

Choices:
A. 0.11 %
B. 0.7 %
C. 0.4 %
D. 0.6 %
E. 0.88 %

subtract(subtract(4, 3), divide(multiply(4, 3), const_100))

Explanation: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 26 / 25 ) x ( 32 / 33 ) y = ( 344 / 341 ) ( xy ) error in measurement = ( 344 / 341 ) xy - xy = ( 3 / 341 ) xy error percentage = [ ( 3 / 341 ) xy ( 1 / xy ) 100 ] % = ( 22 / 25 ) % = 0.88 % . answer is e ."


Question: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many e ways can the test be completed if every question is unanswered ?

<gadget id="calculator">5 ** 4</gadget>
<output>625</output>
<result>625</result>

Choices:
A. 24
B. 120
C. 625
D. 720
E. 1024

Explanation: "5 choices for each of the 4 questions , thus total e of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."


Question: a and b undertake to do a piece of work for $ 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a ?

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

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

<gadget id="calculator">24 * (1/6)</gadget>
<output>4</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">(1/6) + (1/8)</gadget>
<output>7/24 = around 0.291667</output>

<gadget id="calculator">(1/3) - (7/24)</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">24 * (1/24)</gadget>
<output>1</output>

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

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

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

<gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * 600</gadget>
<output>300</output>
<result>300</result>

Choices:
A. $ 100
B. $ 150
C. $ 300
D. $ 250
E. $ 350

multiply(divide(multiply(multiply(3, 8), inverse(6)), add(add(multiply(multiply(3, 8), subtract(inverse(3), add(inverse(6), inverse(8)))), multiply(multiply(3, 8), inverse(6))), multiply(multiply(3, 8), inverse(8)))), 600)

Explanation: c ' s 1 day work = ( 1 / 3 ) - ( 1 / 6 + 1 / 8 ) = 1 / 24 a : b : c = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 a ' s share = 600 * 4 / 8 = $ 300 answer is c


Question: two employees x and y are paid a total of rs . 660 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

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

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

<gadget id="calculator">660 * 10</gadget>
<output>6_600</output>

<gadget id="calculator">10 + 1</gadget>
<output>11</output>

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

<gadget id="calculator">6_600 / 22</gadget>
<output>300</output>
<result>300</result>

Choices:
A. s . 150
B. s . 200
C. s . 250
D. s . 350
E. s . 300

divide(multiply(660, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 660 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 660 â ‡ ’ y [ 12 / 10 + 1 ] = 660 â ‡ ’ 22 y / 10 = 660 â ‡ ’ 22 y = 6600 â ‡ ’ y = 6600 / 22 = 600 / 2 = rs . 300 e"


Question: a 250 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?

<gadget id="calculator">120 + 80</gadget>
<output>200</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>

<gadget id="calculator">(500/9) * 9</gadget>
<output>500</output>

<gadget id="calculator">500 - 250</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 230 m
B. 240 m
C. 250 m
D. 260 m
E. 270 m

subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 250)

Explanation: "speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 250 + x therefore , d = speed * time thus 250 + x = 500 / 9 * 9 x = 500 - 250 = 250 m answer : c"


Question: the value of x + x ( xx ) when x = 7

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

<gadget id="calculator">7 * 49</gadget>
<output>343</output>

<gadget id="calculator">343 + 7</gadget>
<output>350</output>
<result>350</result>

Choices:
A. 350
B. 346
C. 358
D. 336
E. 364

Explanation: x + x ( xx ) put the value of x = 7 in the above expression we get , 7 + 7 ( 77 ) = 7 + 7 ( 7 ã — 7 ) = 7 + 7 ( 49 ) = 7 + 343 = 350 the answer is ( a )


Question: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 11 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?

<gadget id="calculator">40 * 2</gadget>
<output>80</output>

<gadget id="calculator">12 * 1</gadget>
<output>12</output>

<gadget id="calculator">12 + 11</gadget>
<output>23</output>

<gadget id="calculator">23 + 2</gadget>
<output>25</output>

<gadget id="calculator">40 - 25</gadget>
<output>15</output>

<gadget id="calculator">15 - 1</gadget>
<output>14</output>

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

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

<gadget id="calculator">12 + 22</gadget>
<output>34</output>

<gadget id="calculator">42 + 34</gadget>
<output>76</output>

<gadget id="calculator">80 - 76</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 3
B. 4
C. 5
D. 6
E. 7

subtract(multiply(40, 2), add(multiply(subtract(subtract(40, add(add(multiply(12, 1), 11), 2)), 1), 3), add(multiply(12, 1), multiply(11, 2))))

Explanation: "the class borrowed a total of 40 * 2 = 80 books . the 25 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 11 * 2 = 34 . to maximize the number of books borrowed by 1 student , let ' s assume that 14 students borrowed 3 books and 1 student borrowed the rest . 80 - 34 - 3 * 14 = 4 the maximum number of books borrowed by any student is 4 . the answer is b ."


Question: if ( t - 8 ) is a factor of t ^ 2 - kt - 45 , then k =

<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 16
B. 12
C. 2
D. 6
E. 14

Explanation: t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 12 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) b


Question: set a contains all the even numbers between 12 and 50 inclusive . set b contains all the even numbers between 112 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?

<gadget id="calculator">112 - 12</gadget>
<output>100</output>

<gadget id="calculator">50 - 12</gadget>
<output>38</output>

<gadget id="calculator">38 / 2</gadget>
<output>19</output>

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

<gadget id="calculator">100 * 20</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 2000
B. 2550
C. 5050
D. 6275
E. 11325

multiply(subtract(112, 12), add(divide(subtract(50, 12), const_2), const_1))

Explanation: set a contains 12,14 , 16 . . . 50 set b contains 112 , 114 , 116 . . . 150 number of terms in each set = 20 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 20 = 2000 answer a


Question: how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 15 inches than that of a rectangular sheet of paper measuring 7.5 inches by 11 inches ?

<gadget id="calculator">11 * 15</gadget>
<output>165</output>

<gadget id="calculator">165 * 2</gadget>
<output>330</output>

<gadget id="calculator">7.5 * 11</gadget>
<output>82.5</output>

<gadget id="calculator">82.5 * 2</gadget>
<output>165</output>

<gadget id="calculator">330 - 165</gadget>
<output>165</output>

<gadget id="calculator">165 / 165</gadget>
<output>1</output>

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

Choices:
A. 50 %
B. 87 %
C. 100 %
D. 187 %
E. 200 %

multiply(divide(subtract(multiply(rectangle_area(11, 15), const_2), multiply(rectangle_area(7.5, 11), const_2)), rectangle_area(11, 15)), const_100)

Explanation: "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 15 is twice 7.5 then the area will be double which means 100 % greater . the answer is c ."


Question: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 30 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?

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

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">30 * (1/3)</gadget>
<output>10</output>

<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 13
B. 30
C. 50
D. 51
E. 52

multiply(multiply(30, divide(1, add(1, 2))), add(1, 2))

Explanation: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 30 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 15 cents . fraction of spirit is 1 / 2 . 15 = k * ( 1 / 2 ) k = 30 cost per liter = 30 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 30 * ( 1 / 3 ) * 3 = 50 cents b . 30 cents"


Question: you need to print a document of the area 216 sq cm . condition is 3 cm margin is to be left at both top & bottom and 2 cm at the sides . what is the optimized size of your paper ?

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

<gadget id="calculator">216 / 9</gadget>
<output>24</output>

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

<gadget id="calculator">24 - 6</gadget>
<output>18</output>

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

<gadget id="calculator">9 - 4</gadget>
<output>5</output>

<gadget id="calculator">18 * 5</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 60 sq . cm
B. 70 sq . cm
C. 95 sq . cm
D. 80 sq . cm
E. 90 sq . cm

multiply(subtract(divide(216, power(const_3, const_2)), multiply(3, const_2)), subtract(power(const_3, const_2), multiply(2, const_2)))

Explanation: let us consider it is a rectangle . so area = 24 * 9 = 216 sq . cm now ( 24 - 3 * 2 ) * ( 9 - 2 * 2 ) = 18 * 5 = 90 sq . cm answer : e


Question: if x / y = 5 / 3 , then ( x + y ) / ( x - y ) = ?

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

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

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

Choices:
A. 4
B. 1 / 5
C. - 1 / 6
D. - 1 / 5
E. - 5

Explanation: "any x and y satisfying x / y = 5 / 3 should give the same value for ( x + y ) / ( x - y ) . say x = 5 and y = 3 , then ( x + y ) / ( x - y ) = ( 5 + 3 ) / ( 5 - 3 ) = 4 . answer : a ."


Question: a number , when 35 is subtracted from it , reduces to its 80 percent . what is 4 - fifth of that number ?

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

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">35 * 5</gadget>
<output>175</output>

<gadget id="calculator">(4/5) * 175</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 130
B. 155
C. 490
D. 140
E. 160

multiply(divide(4, add(const_4, const_1)), multiply(35, add(const_4, const_1)))

Explanation: explanation : x - 35 = 80 x / 100 = > x = 175 = > 4 x / 5 = 4 x 175 / 5 = 140 . answer d


Question: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 40 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?

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

<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(7/5) * (7/10)</gadget>
<output>49/50 = around 0.98</output>

<gadget id="calculator">(49/50) - 1</gadget>
<output>-1/50 = around -0.02</output>

<gadget id="calculator">(-1/50) * 100</gadget>
<output>-2</output>
<result>-2</result>

Choices:
A. − 5 %
B. − 2 %
C. 15 %
D. 20 %
E. 80 %

multiply(subtract(multiply(add(const_1, divide(40, const_100)), subtract(const_1, divide(30, const_100))), const_1), const_100)

Explanation: "the actual answer is obtained by multiplying 140 % by 70 % and subtracting 100 % from this total . that is : 140 % × 70 % = 98 % ; 98 % − 100 % = - 2 % . answer : b"


Question: a library has an average of 425 visitors on sundays and 325 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :

<gadget id="calculator">3 + 4</gadget>
<output>7</output>

<gadget id="calculator">30 / 7</gadget>
<output>30/7 = around 4.285714</output>

<gadget id="calculator">floor(30/7)</gadget>
<output>4</output>

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

<gadget id="calculator">5 * 425</gadget>
<output>2_125</output>

<gadget id="calculator">30 - 5</gadget>
<output>25</output>

<gadget id="calculator">25 * 325</gadget>
<output>8_125</output>

<gadget id="calculator">2_125 + 8_125</gadget>
<output>10_250</output>

<gadget id="calculator">10_250 / 30</gadget>
<output>1_025/3 = around 341.666667</output>
<result>1_025/3 = around 341.666667</result>

Choices:
A. 140
B. 240
C. 260
D. 280
E. 340

divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 425), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 325)), 30)

Explanation: explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 415 * 5 + 325 * 25 ) / 30 = 10200 / 30 = 340 answer : e ) 340


Question: the sector of a circle has radius of 14 cm and its perimeter 50 cm . find its central angel ?

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

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

<gadget id="calculator">4 + 3</gadget>
<output>7</output>

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">2 * (22/7)</gadget>
<output>44/7 = around 6.285714</output>

<gadget id="calculator">(44/7) * 14</gadget>
<output>88</output>
<result>88</result>

Choices:
A. 180 o
B. 225 o
C. 270 o
D. 150 o
E. 90 o

multiply(multiply(const_2, divide(multiply(subtract(14, const_3), const_2), add(const_4, const_3))), 14)

Explanation: lte central angle = x perimeter of the sector = length of the arc + 2 ( radius ) 50 = ( x / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) 50 = 88 x / 360 + 28 88 x / 360 = 22 88 x = 7920 x = 90 answer : e