Question: a worker is paid a regular rate of rs . 20 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 10 % higher than her regular rate . if she completed 70 surveys involving the use of her cellphone , how much did she get that week ?

<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>

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

<gadget id="calculator">20 * (1/10)</gadget>
<output>2</output>

<gadget id="calculator">70 * 2</gadget>
<output>140</output>

<gadget id="calculator">2_000 + 140</gadget>
<output>2_140</output>
<result>2_140</result>

Choices:
A. 2140
B. 1140
C. 550
D. 650
E. 750

add(multiply(20, 100), multiply(70, multiply(20, divide(10, const_100))))

Explanation: amount earned using her cell phone = 70 * 22 = 1540 earned for remaining surveys = 30 * 20 = 600 total earning = 2140 answer : a


Question: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 38 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?

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

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

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

<gadget id="calculator">80 * 2</gadget>
<output>160</output>

<gadget id="calculator">160 + 38</gadget>
<output>198</output>

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

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(1/10) + (2/25)</gadget>
<output>9/50 = around 0.18</output>

<gadget id="calculator">198 / (9/50)</gadget>
<output>1_100</output>

<gadget id="calculator">2_000 - 1_100</gadget>
<output>900</output>
<result>900</result>

Choices:
A. $ 700
B. $ 800
C. $ 900
D. $ 1100
E. $ 1200

subtract(multiply(multiply(const_100, 10), const_2), divide(add(multiply(multiply(10, 8), const_2), 38), add(divide(10, const_100), divide(8, const_100))))

Explanation: "0.1 x = 0.08 ( 2000 - x ) + 38 0.18 x = 198 x = 1100 then the amount invested at 8 % is $ 2000 - $ 1100 = $ 900 the answer is c ."


Question: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 42 kmph , find the speed of the stream ?

<gadget id="calculator">42 * 2</gadget>
<output>84</output>

<gadget id="calculator">84 / 3</gadget>
<output>28</output>

<gadget id="calculator">42 - 28</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 16 kmph
B. 18 kmph
C. 14 kmph
D. 79 kmph
E. 27 kmph

subtract(42, divide(multiply(42, const_2), const_3))

Explanation: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 42 / 3 = 14 kmph . answer : c"


Question: by selling an article at rs . 300 , a profit of 25 % is made . find its cost price ?

<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>

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

<gadget id="calculator">30_000 / 125</gadget>
<output>240</output>
<result>240</result>

Choices:
A. s . 486
B. s . 455
C. s . 240
D. s . 480
E. s . 489

divide(multiply(300, const_100), add(const_100, 25))

Explanation: "sp = 300 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 300 * [ 100 / ( 100 + 25 ) ] = 300 * [ 100 / 125 ] = rs . 240 answer : c"


Question: a batsman scores 26 runs and increases his average from 14 to 15 . find the runs to be made if he wants top increasing the average to 19 in the same match ?

<gadget id="calculator">26 - 15</gadget>
<output>11</output>

<gadget id="calculator">11 + 1</gadget>
<output>12</output>

<gadget id="calculator">19 * 12</gadget>
<output>228</output>

<gadget id="calculator">14 * 11</gadget>
<output>154</output>

<gadget id="calculator">228 - 154</gadget>
<output>74</output>
<result>74</result>

Choices:
A. 12
B. 18
C. 25
D. 74
E. 88

subtract(multiply(19, add(subtract(26, 15), const_1)), multiply(14, subtract(26, 15)))

Explanation: number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d


Question: a total of 520 players participated in a single tennis knock out tournament . what is the total number of matches played in the tournament ? ( knockout means if a player loses , he is out of the tournament ) . no match ends in a tie .

<gadget id="calculator">520 / 2</gadget>
<output>260</output>

<gadget id="calculator">260 / 2</gadget>
<output>130</output>

<gadget id="calculator">130 / 2</gadget>
<output>65</output>

<gadget id="calculator">260 + 130</gadget>
<output>390</output>

<gadget id="calculator">65 + 390</gadget>
<output>455</output>

<gadget id="calculator">65 / 2</gadget>
<output>65/2 = around 32.5</output>

<gadget id="calculator">455 + (65/2)</gadget>
<output>975/2 = around 487.5</output>

<gadget id="calculator">(65/2) / 2</gadget>
<output>65/4 = around 16.25</output>

<gadget id="calculator">(975/2) + (65/4)</gadget>
<output>2_015/4 = around 503.75</output>

<gadget id="calculator">(65/4) / 2</gadget>
<output>65/8 = around 8.125</output>

<gadget id="calculator">(2_015/4) + (65/8)</gadget>
<output>4_095/8 = around 511.875</output>

<gadget id="calculator">(65/8) / 2</gadget>
<output>65/16 = around 4.0625</output>

<gadget id="calculator">(4_095/8) + (65/16)</gadget>
<output>8_255/16 = around 515.9375</output>

<gadget id="calculator">(65/16) / 2</gadget>
<output>65/32 = around 2.03125</output>

<gadget id="calculator">(8_255/16) + (65/32)</gadget>
<output>16_575/32 = around 517.96875</output>

<gadget id="calculator">(65/32) / 2</gadget>
<output>65/64 = around 1.015625</output>

<gadget id="calculator">(16_575/32) + (65/64)</gadget>
<output>33_215/64 = around 518.984375</output>
<result>33_215/64 = around 518.984375</result>

Choices:
A. 511
B. 519
C. 256
D. 255
E. 1023

add(add(add(add(add(add(add(divide(divide(divide(520, const_2), const_2), const_2), add(divide(520, const_2), divide(divide(520, const_2), const_2))), divide(divide(divide(divide(520, const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2))

Explanation: there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b


Question: solving a linear equation with several occurrences of the variable , solve for w . simplify answer as much as possible . ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22

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

<gadget id="calculator">12 * 22</gadget>
<output>264</output>

<gadget id="calculator">8 * 6</gadget>
<output>48</output>

<gadget id="calculator">48 + 12</gadget>
<output>60</output>

<gadget id="calculator">264 - 60</gadget>
<output>204</output>

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

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

<gadget id="calculator">54 + 14</gadget>
<output>68</output>

<gadget id="calculator">204 / 68</gadget>
<output>3</output>
<result>3</result>

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

divide(subtract(multiply(multiply(2, 6), 22), add(multiply(8, 6), multiply(2, 6))), add(multiply(9, 6), multiply(7, const_2)))

Explanation: ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c


Question: two good train each 750 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .

<gadget id="calculator">45 + 30</gadget>
<output>75</output>

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

<gadget id="calculator">75 * (5/18)</gadget>
<output>125/6 = around 20.833333</output>

<gadget id="calculator">1 / (125/6)</gadget>
<output>6/125 = around 0.048</output>

<gadget id="calculator">750 * (6/125)</gadget>
<output>36</output>

<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 12 sec
B. 24 sec
C. 48 sec
D. 72 sec
E. none

multiply(multiply(750, inverse(multiply(add(45, 30), const_0_2778))), const_2)

Explanation: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 750 + 750 ) m = 1500 m . required time = ( 1500 x 6 / 125 ) sec = 72 sec . answer d"


Question: the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4800 sq cm . what is the ratio of the width and the area of the rectangle ?

<gadget id="calculator">3 * 4_800</gadget>
<output>14_400</output>

<gadget id="calculator">14_400 ** (1/2)</gadget>
<output>120</output>

<gadget id="calculator">120 / 2</gadget>
<output>60</output>

<gadget id="calculator">60 / 4_800</gadget>
<output>1/80 = around 0.0125</output>
<result>1/80 = around 0.0125</result>

Choices:
A. 1 : 72
B. 1 : 76
C. 1 : 80
D. 1 : 84
E. 1 : 88

divide(divide(sqrt(multiply(const_3, 4800)), const_2), 4800)

Explanation: let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4800 12 x ^ 2 = 4800 x ^ 2 = 400 x = 20 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 80 the answer is c .


Question: a work which could be finished in 7 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?

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

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

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

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

Choices:
A. 22
B. 20
C. 60
D. 71
E. 11

divide(multiply(multiply(3, const_2), 10), subtract(7, multiply(3, const_2)))

Explanation: "x - - - - - - - 7 ( x + 10 ) - - - - 6 x * 7 = ( x + 10 ) 6 x = 60 \ answer : c"


Question: if ( 6 ) ( x ^ 2 ) has 3 different prime factors , at most how many different prime factors does x have ?

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

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

Explanation: x can have at most 3 prime factors , namely the prime factors 2 and 3 , plus one other . if x had more than this number of prime factors , then ( 6 ) ( x ^ 2 ) would have more than 3 prime factors . the answer is c .


Question: a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 190 kilometers ?

<gadget id="calculator">190 / 20</gadget>
<output>19/2 = around 9.5</output>
<result>19/2 = around 9.5</result>

Choices:
A. 3.5 gallons
B. 9.5 gallons
C. 8.7 gallons
D. 4.5 gallons
E. 9.2 gallons

Explanation: each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 180 ã · 40 = 9.5 ã — 1 gallon = 9.5 gallons correct answer is b ) 9.5 gallons


Question: the list price of an article is rs . 66 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

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

<gadget id="calculator">66 * (1/10)</gadget>
<output>33/5 = around 6.6</output>

<gadget id="calculator">66 - (33/5)</gadget>
<output>297/5 = around 59.4</output>

<gadget id="calculator">(297/5) - 56.16</gadget>
<output>3.24</output>

<gadget id="calculator">3.24 / (297/5)</gadget>
<output>0.054545</output>

<gadget id="calculator">0.054545 * 100</gadget>
<output>5.4545</output>
<result>5.4545</result>

Choices:
A. 3.45 %
B. 4.45 %
C. 5.45 %
D. 6.45 %
E. 7.45 %

multiply(divide(subtract(subtract(66, multiply(66, divide(10, const_100))), 56.16), subtract(66, multiply(66, divide(10, const_100)))), const_100)

Explanation: "66 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 5.45 % answer : c"


Question: a trader marked the selling price of an article at 60 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :

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

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

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

<gadget id="calculator">100 + 60</gadget>
<output>160</output>

<gadget id="calculator">11 / 160</gadget>
<output>11/160 = around 0.06875</output>

<gadget id="calculator">100 * (11/160)</gadget>
<output>55/8 = around 6.875</output>
<result>55/8 = around 6.875</result>

Choices:
A. 10 %
B. 10.5 %
C. 6.8 %
D. 12.5 %
E. none

multiply(const_100, divide(add(multiply(add(const_2, const_3), const_2), 1), add(const_100, 60)))

Explanation: "sol . let c . p . = rs . 100 . then , marked price = rs . 160 , s . p . = rs . 99 . ∴ discount % = [ 11 / 160 * 100 ] % = 6.8 % answer c"


Question: a person saved $ 10 in buying an item on sale . if he spent $ 200 for the item , approximately how much percent he saved in the transaction ?

<gadget id="calculator">10 + 200</gadget>
<output>210</output>

<gadget id="calculator">10 / 210</gadget>
<output>1/21 = around 0.047619</output>

<gadget id="calculator">(1/21) * 100</gadget>
<output>100/21 = around 4.761905</output>

<gadget id="calculator">floor(100/21)</gadget>
<output>4</output>

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

Choices:
A. 8 %
B. 10 %
C. 2 %
D. 5 %
E. 6 %

add(floor(multiply(divide(10, add(10, 200)), const_100)), const_1)

Explanation: "actual price = 200 + 10 = $ 210 saving = 10 / 210 * 100 = 100 / 21 = 5 % approximately answer is d"


Question: a is 1.5 times as fast as b . a alone can do the work in 20 days . if a and b working together , in how many days will the work be completed ?

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

<gadget id="calculator">(1/20) / 1.5</gadget>
<output>0.033333</output>

<gadget id="calculator">(1/20) + 0.033333</gadget>
<output>0.083333</output>

<gadget id="calculator">1 / 0.083333</gadget>
<output>12.000048</output>
<result>12.000048</result>

Choices:
A. 23
B. 22
C. 12
D. 24
E. 25

divide(const_1, add(divide(const_1, 20), divide(divide(const_1, 20), 1.5)))

Explanation: a can finish 1 work in 20 days b can finish 1 / 1.5 work in 20 days - since a is 1.5 faster than b this means b can finish 1 work in 20 * 1.5 days = 30 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 30 / ( 20 + 30 ) = 20 * 30 / 50 = 12 days so answer is c


Question: if a speaks the truth 65 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time

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

<gadget id="calculator">20 * 5</gadget>
<output>100</output>

<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>

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

<gadget id="calculator">(13/20) * (3/5)</gadget>
<output>39/100 = around 0.39</output>
<result>39/100 = around 0.39</result>

Choices:
A. 0.39
B. 0.48
C. 0.41
D. 0.482
E. 0.411

multiply(divide(65, multiply(multiply(const_4, const_5), const_5)), divide(60, multiply(multiply(const_4, const_5), const_5)))

Explanation: "explanation : probability that a speaks truth is 65 / 100 = 0.65 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.65 × 0.6 = 0.39 answer : a"


Question: if a = 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?

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

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

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

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

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

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

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

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

Choices:
A. - 14
B. - 4
C. 0
D. 4
E. 14

negate(add(add(add(power(1, 2), power(1, 3)), power(1, 4)), power(1, 5)))

Explanation: if a = 1 , then putting values in equation = - [ ( 1 ) ^ 2 + ( 1 ) ^ 3 + ( 1 ^ 4 ) + ( 1 ^ 5 ) ] = - [ 1 + 1 + 1 + 1 ] = - 4 answer = b = - 4


Question: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 30 % ?

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

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

<gadget id="calculator">70 / (2/3)</gadget>
<output>105</output>

<gadget id="calculator">105 - 100</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 20 %
B. 29 %
C. 70 %
D. 27 %
E. 5 %

subtract(divide(subtract(const_100, 30), divide(2, 3)), const_100)

Explanation: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 70 2 / 3 sp 1 = 70 sp 1 = 105 100 - - - 105 = > 5 % answer : e"


Question: an astronomer noted that a grouping of red giant stars had an average solar mass of 8 m each , and a grouping of white dwarf stars had an average solar mass of 1.5 m each . if the astronomer calculated the total solar mass of both groupings to be 49 m , what total number of red giant stars and white dwarf stars did the astronomer note ?

<gadget id="calculator">2 + 4</gadget>
<output>6</output>

<gadget id="calculator">1.5 * 6</gadget>
<output>9</output>

<gadget id="calculator">49 - 9</gadget>
<output>40</output>

<gadget id="calculator">40 / 8</gadget>
<output>5</output>

<gadget id="calculator">5 + 6</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 10
B. 11
C. 12
D. 13
E. 14

add(divide(subtract(49, multiply(1.5, add(const_2, const_4))), 8), add(const_2, const_4))

Explanation: we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b


Question: village a ’ s population is 300 greater than village b ' s population . if village b ’ s population were reduced by 600 people , then village a ’ s population would be 4 times as large as village b ' s population . what is village b ' s current population ?

<gadget id="calculator">600 * 4</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 + 300</gadget>
<output>2_700</output>

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

<gadget id="calculator">2_700 / 3</gadget>
<output>900</output>
<result>900</result>

Choices:
A. 900
B. 1000
C. 1100
D. 1200
E. 1300

divide(add(multiply(600, 4), 300), subtract(4, const_1))

Explanation: a = b + 300 . a = 4 ( b - 600 ) . 4 ( b - 600 ) = b + 300 . 3 b = 2700 . b = 900 . the answer is a .


Question: a sum amounts to rs . 4851 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>

<gadget id="calculator">4_851 / (441/400)</gadget>
<output>4_400</output>
<result>4_400</result>

Choices:
A. s . 4000
B. s . 5000
C. s . 4400
D. s . 4800
E. s . 5800

divide(4851, power(add(divide(5, const_100), const_1), 2))

Explanation: "ci = 4851 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 4851 = p [ 21 / 20 ] ^ 2 4851 [ 20 / 21 ] ^ 2 4400 answer : c"


Question: the average monthly salary of 10 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?

<gadget id="calculator">1_600 + 100</gadget>
<output>1_700</output>

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

<gadget id="calculator">1_700 * 11</gadget>
<output>18_700</output>

<gadget id="calculator">1_600 * 10</gadget>
<output>16_000</output>

<gadget id="calculator">18_700 - 16_000</gadget>
<output>2_700</output>
<result>2_700</result>

Choices:
A. rs . 3601
B. rs . 3618
C. rs . 2700
D. rs . 3619
E. rs . 3610

subtract(multiply(add(1600, 100), add(10, const_1)), multiply(1600, 10))

Explanation: "manager ' s monthly salary = rs . ( 1700 * 11 - 1600 * 10 ) = rs . 2700 answer : c"


Question: if a lends rs . 1200 to b at 10 % per annum and b lends the same sum to c at 18 % per annum then the gain of b in a period of 2 years is ?

<gadget id="calculator">1_200 * 18</gadget>
<output>21_600</output>

<gadget id="calculator">21_600 * 2</gadget>
<output>43_200</output>

<gadget id="calculator">43_200 / 100</gadget>
<output>432</output>

<gadget id="calculator">1_200 * 10</gadget>
<output>12_000</output>

<gadget id="calculator">12_000 * 2</gadget>
<output>24_000</output>

<gadget id="calculator">24_000 / 100</gadget>
<output>240</output>

<gadget id="calculator">432 - 240</gadget>
<output>192</output>
<result>192</result>

Choices:
A. 190
B. 188
C. 192
D. 145
E. 188

subtract(divide(multiply(multiply(1200, 18), 2), const_100), divide(multiply(multiply(1200, 10), 2), const_100))

Explanation: "( 1200 * 8 * 2 ) / 100 = > 192 answer : c"


Question: if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 6 ?

<gadget id="calculator">96 / 2</gadget>
<output>48</output>

<gadget id="calculator">96 / 6</gadget>
<output>16</output>

<gadget id="calculator">48 + 16</gadget>
<output>64</output>

<gadget id="calculator">64 / 96</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>

Choices:
A. 2 / 3
B. 3 / 8
C. 1 / 2
D. 5 / 8
E. 3 / 4

divide(add(divide(96, 2), divide(96, 6)), 96)

Explanation: i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 6 = integer , therefore we have 48 / 96 numbers divisible by 6 o e o / 6 = not integer we can not forget multiples of 6 from 1 to 96 we have 16 numbers that are multiple of 8 therefore , 48 / 96 + 16 / 96 = 64 / 96 = 2 / 3 answer : a


Question: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5 ?

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

Choices:
A. 6
B. 7
C. 8
D. 9
E. 10

Explanation: "the numbers should be of the form 5 c + 3 . the minimum is 3 when c = 0 . the maximum is 48 when c = 9 . there are 10 such numbers . the answer is e ."


Question: 6 students wrote science exam . their average marks are 70 . 5 students got 65 , 75 , 55 , 72 and 69 marks respectively . therefore what is the marks of the sixth student ?

<gadget id="calculator">70 * 6</gadget>
<output>420</output>

<gadget id="calculator">65 + 75</gadget>
<output>140</output>

<gadget id="calculator">140 + 55</gadget>
<output>195</output>

<gadget id="calculator">195 + 72</gadget>
<output>267</output>

<gadget id="calculator">267 + 69</gadget>
<output>336</output>

<gadget id="calculator">420 - 336</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 84
B. 68
C. 85
D. 75
E. 42

Explanation: explanation total marks of 5 students = ( 65 + 75 + 55 + 72 + 69 ) = 336 required marks = [ ( 70 x 6 ) – 336 ] = ( 420 – 336 ) = 84 answer a


Question: a bowl was filled with 10 ounces of water , and 0.010 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?

<gadget id="calculator">50 * 0.01</gadget>
<output>0.5</output>

<gadget id="calculator">0.5 / 10</gadget>
<output>0.05</output>

<gadget id="calculator">0.05 * 100</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 0.004 %
B. 0.04 %
C. 0.40 %
D. 5 %
E. 40 %

multiply(divide(multiply(50, 0.010), 10), const_100)

Explanation: "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 010 * 100 / 2 = 1.0 / 2 = . 5 percent of the original amount of water evaporated during this period = ( . 5 / 10 ) * 100 % = 5 % answer d"


Question: the sum of 7 th and 23 rd term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0

<gadget id="calculator">8 + 15</gadget>
<output>23</output>

<gadget id="calculator">13 + 23</gadget>
<output>36</output>

<gadget id="calculator">7 + 23</gadget>
<output>30</output>

<gadget id="calculator">36 - 30</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 8
C. 10
D. 12
E. 14

Explanation: t 7 + t 23 = t 8 + t 15 + t 13 = > a + 6 d + a + 22 d = a + 7 d + a + 14 d + a + 12 d = > a + 5 d = 0 = > t 6 = 0 i . e . 6 th term is zero . answer : a


Question: let c be defined as the sum of all prime numbers between 0 and 35 . what is c / 3

<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">2 + 4</gadget>
<output>6</output>

<gadget id="calculator">2 ** 6</gadget>
<output>64</output>

<gadget id="calculator">(3/10) + 64</gadget>
<output>643/10 = around 64.3</output>
<result>643/10 = around 64.3</result>

Choices:
A. 155
B. 129
C. 64.3
D. 47
E. 43

add(divide(3, const_10), power(const_2, add(const_2, const_4)))

Explanation: prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 33 sum , c = 193 c / 3 = 64.3 answer c


Question: the speed of a boat in still water in 22 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :

<gadget id="calculator">22 + 5</gadget>
<output>27</output>

<gadget id="calculator">24 / 60</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">27 * (2/5)</gadget>
<output>54/5 = around 10.8</output>
<result>54/5 = around 10.8</result>

Choices:
A. 10.6
B. 10.2
C. 10.8
D. 10.4
E. 10.0

multiply(add(22, 5), divide(24, const_60))

Explanation: speed downstream = ( 22 + 5 ) = 27 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 27 = 10.8 km answer is c .


Question: a boat having a length 3 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

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

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

<gadget id="calculator">9 * (1/100)</gadget>
<output>9/100 = around 0.09</output>

<gadget id="calculator">(9/100) * 1_000</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 100 kg
B. 120 kg
C. 89 kg
D. 90 kg
E. 110 kg

multiply(multiply(multiply(3, 3), divide(1, const_100)), const_1000)

Explanation: "volume of water displaced = ( 3 x 3 x 0.01 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced x density of water = ( 0.09 x 1000 ) kg = 90 kg . answer : d"


Question: by selling 12 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

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

<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>

<gadget id="calculator">120 * (1/80)</gadget>
<output>3/2 = around 1.5</output>

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

<gadget id="calculator">(2/3) * 12</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8
B. 76
C. 17
D. 7
E. 77

multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 20)))), 12)

Explanation: "80 % - - - 12 120 % - - - ? 80 / 120 * 12 = 8 answer : a"


Question: walking with 4 / 5 of my usual speed , i miss the bus by 7 minutes . what is my usual time ?

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

<gadget id="calculator">7 / (5/4)</gadget>
<output>28/5 = around 5.6</output>

<gadget id="calculator">(28/5) * 5</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 16 min
B. 26 min
C. 28 min
D. 20 min
E. 12 min

Explanation: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 7 4 - - - - - - - - - ? è 28 answer : c"


Question: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 150 then sum is

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

<gadget id="calculator">(1/10) * (1/10)</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">150 / (1/100)</gadget>
<output>15_000</output>
<result>15_000</result>

Choices:
A. s . 15000
B. s . 15100
C. s . 15800
D. s . 16000
E. s . 16200

divide(150, multiply(divide(10, const_100), divide(10, const_100)))

Explanation: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 150 15000 answer : a"


Question: in one hour , a boat goes 8 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is :

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

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

Choices:
A. 3
B. 5
C. 8
D. 9
E. 10

Explanation: "solution speed in still water = 1 / 2 ( 8 + 2 ) km / hr = 5 kmph . answer b"


Question: coconuts were purchased at 150 per 100 and sold at 2 per coconut . if 2000 coconuts were sold , what was the total profit made ?

<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">2 - (3/2)</gadget>
<output>1/2 = around 0.5</output>

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

Choices:
A. 500
B. 1000
C. 1500
D. 2000
E. none of these

multiply(2000, subtract(2, divide(150, 100)))

Explanation: c . p . for one coconut = 150 ⁄ 100 = 3 ⁄ 2 s . p . for one coconut = 2 profit on one coconut = 2 - 3 ⁄ 2 = 1 ⁄ 2 ∴ profit on 2000 coconut = 1 ⁄ 2 × 2000 = 1000 answer b


Question: a train is 435 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length

<gadget id="calculator">435 + 140</gadget>
<output>575</output>

<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>

<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">575 / (25/2)</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 20 seconds
B. 30 seconds
C. 46 seconds
D. 50 seconds
E. none of these

divide(add(435, 140), divide(multiply(45, const_1000), const_3600))

Explanation: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 435 + 140 = 575 meter time = distance / speed = 575 ∗ 2 / 25 = 46 seconds option c"


Question: if the l . c . m of two numbers is 450 and their product is 22500 , find the h . c . f of the numbers .

<gadget id="calculator">22_500 / 450</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 50
B. 30
C. 125
D. 25
E. none of these

Explanation: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 22500 / 450 = 50 . answer : a"


Question: the area of a parallelogram is 72 cm ^ 2 and its altitude is twice the corresponding base . what is the length of the base ?

<gadget id="calculator">72 / 2</gadget>
<output>36</output>

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

Choices:
A. 1 cm
B. 3 cm
C. 6 cm
D. 4 cm
E. 2 cm

Explanation: let base = x cm height = 2 x cm area = x ã — 2 x = 2 x ^ 2 area = x ã — 2 x = 2 x ^ 2 area is given as 72 cm ^ 2 2 x ^ 2 = 72 x ^ 2 = 36 x = 6 cm answer : c


Question: martin buys a pencil and a notebook for 80 cents . at the same store , gloria buys a notebook and an eraser for $ 1.15 cents , and zachary buys a pencil and an eraser for 75 cents . how many cents would it cost to buy 3 pencils , 3 notebooks , and 3 erasers ? ( assume that there is no volume discount . )

<gadget id="calculator">1.15 * 100</gadget>
<output>115</output>

<gadget id="calculator">115 + 80</gadget>
<output>195</output>

<gadget id="calculator">195 + 75</gadget>
<output>270</output>

<gadget id="calculator">270 / 2</gadget>
<output>135</output>

<gadget id="calculator">135 * 3</gadget>
<output>405</output>
<result>405</result>

Choices:
A. 325
B. 345
C. 365
D. 385
E. 405

multiply(divide(add(add(multiply(1.15, const_100), 80), 75), const_2), 3)

Explanation: pencil + notebook = 80 notebook + eraser = 115 pencil + eraser = 75 let ' s add all three equations . 2 pencils + 2 notebooks + 2 erasers = 270 cents the cost to buy 3 of each would be ( 3 / 2 ) ( 270 ) = 405 the answer is e .


Question: when 200 is divided by positive integer x , the remainder is 3 . what is the remainder when 297 is divided by x ?

<gadget id="calculator">297 - 200</gadget>
<output>97</output>

<gadget id="calculator">100 - 97</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 2
B. 3
C. 4
D. 6
E. 8

Explanation: "f 200 / x leaves a reminder 3 then ( 200 - 3 ) i . e . 197 is divisible by x so ( 200 + 197 ) / x leaves a reminder rem ( 200 / x ) + rem ( 197 / x ) = > 3 + 0 = 3 answer : b"


Question: if a fast song has 160 beats per minute , and a slow song has 90 beats per minute , how many minutes total would you play a fast and a slow song to have a stream of music that had a total of 1020 beats ?

<gadget id="calculator">160 + 90</gadget>
<output>250</output>

<gadget id="calculator">1_020 / 250</gadget>
<output>102/25 = around 4.08</output>

<gadget id="calculator">(102/25) * 2</gadget>
<output>204/25 = around 8.16</output>

<gadget id="calculator">floor(204/25)</gadget>
<output>8</output>

<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. 10

add(floor(multiply(divide(1020, add(160, 90)), const_2)), const_1)

Explanation: we can determine quickly that total number should range between 1020 / 160 < = n < = 1020 / 90 , so ans should be between 6 and 12 . now solving the expression 160 a + 90 b = 1020 decreasing 1020 by multiples of 160 and checking divisibility of that number by 9 , we get fast song plays for 3 minutes and slow somg plays for 6 minutes , 3 * 160 + 6 * 90 = 1020 hence total number of minutes stream of music plays is 3 + 6 = 9 minutes ans d


Question: in a party every person shakes hands with every other person . if there were a total of 190 handshakes in the party then what is the number of persons present in the party ?

<gadget id="calculator">190 * 2</gadget>
<output>380</output>

<gadget id="calculator">380 * 4</gadget>
<output>1_520</output>

<gadget id="calculator">1_520 + 1</gadget>
<output>1_521</output>

<gadget id="calculator">1_521 ** (1/2)</gadget>
<output>39</output>

<gadget id="calculator">39 + 1</gadget>
<output>40</output>

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

Choices:
A. 15
B. 16
C. 17
D. 18
E. 20

divide(add(sqrt(add(multiply(multiply(190, const_2), const_4), const_1)), const_1), const_2)

Explanation: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 190 n ( n - 1 ) / 2 = 190 â ˆ ´ n = 20 answer : option e"


Question: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 30 years . what is deepak present age ?

<gadget id="calculator">30 - 6</gadget>
<output>24</output>

<gadget id="calculator">24 * 3</gadget>
<output>72</output>

<gadget id="calculator">72 / 4</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 18
B. 15
C. 77
D. 266
E. 182

Explanation: "present age is 4 x and 3 x , = > 4 x + 6 = 30 = > x = 6 so deepak age is = 3 ( 6 ) = 18 answer : a"


Question: what is remainder of the division ( 1525 * 1527 * 1529 ) / 12 ?

Choices:
A. 0
B. 1
C. 2
D. 3
E. 4

subtract(multiply(multiply(1525, 1527), 1529), subtract(multiply(multiply(1525, 1527), 1529), const_3))

Explanation: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : d"


Question: a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?

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

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

<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>

<gadget id="calculator">25 - (25/3)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) / 25</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>

Choices:
A. 8 %
B. 15 %
C. 45 %
D. 52 %
E. 67 %

multiply(divide(subtract(multiply(divide(5, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(5, 20), const_100)), const_100)

Explanation: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 5 / 20 = 1 / 4 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 5 / 20 ) x 12 = 3 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 12 = 1 we can plug 15 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 1 – 3 ) / 3 ] x 100 - 200 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 200 / 3 is just a bit less than ½ , we know that - 200 / 3 x 100 is about a 67 % decrease . answer e .


Question: in the first 10 overs of a cricket game , the run rate was only 5.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?

<gadget id="calculator">10 * 5.2</gadget>
<output>52</output>

<gadget id="calculator">282 - 52</gadget>
<output>230</output>

<gadget id="calculator">230 / 40</gadget>
<output>23/4 = around 5.75</output>
<result>23/4 = around 5.75</result>

Choices:
A. 6.25
B. 6.5
C. 6.75
D. 5.75
E. 8

divide(subtract(282, multiply(10, 5.2)), 40)

Explanation: "10 overs - run rate = 5.2 runs scored in first 10 overs = 52 remaining overs 40 total runs to be scored = 282 52 runs already scored 282 - 52 = 230 230 runs to be scored in 40 overs let required runrate be x 40 * x = 230 x = 230 / 40 x = 5.75 the required runrate is 5.75 answer : d"


Question: of the diplomats attending a summit conference , 30 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?

<gadget id="calculator">32 - 30</gadget>
<output>2</output>

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

<gadget id="calculator">10 / 100</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">2 / (1/10)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20
B. 96
C. 108
D. 120
E. 150

divide(subtract(32, 30), subtract(divide(20, const_100), divide(10, const_100)))

Explanation: "{ total } = { french } + { russian } - { both } + { neither } { total } = 30 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 20 . answer : a ."


Question: if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers is :

<gadget id="calculator">0.08 * 100</gadget>
<output>8</output>

<gadget id="calculator">0.2 * 100</gadget>
<output>20</output>

<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

Choices:
A. 2 : 3
B. 3 : 4
C. 2 : 5
D. 20 : 3
E. 30 : 7

divide(multiply(0.08, const_100), multiply(0.2, const_100))

Explanation: "0.2 a = 0.08 b - > a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 : . a : b = 2 : 5 answer : c"


Question: a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is

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

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

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

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

<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">12 * (2/3)</gadget>
<output>8</output>

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

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

<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 27
B. 87
C. 40
D. 18
E. 17

multiply(multiply(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), divide(40, const_60)), add(const_1, divide(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), 3)))

Explanation: explanation : let distance = x km and usual rate = y kmph . then , x / y - x / ( y + 3 ) = 40 / 60 - - > 2 y ( y + 3 ) = 9 x - - - - - ( i ) also , x / ( y - 2 ) - x / y = 40 / 60 - - > y ( y - 2 ) = 3 x - - - - - - - - ( ii ) on dividing ( i ) by ( ii ) , we get : x = 40 km . answer : c


Question: if the average of w , b , c , 14 and 15 is 12 . what is the average value of w , b , c and 29

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

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

<gadget id="calculator">60 - 15</gadget>
<output>45</output>

<gadget id="calculator">45 - 14</gadget>
<output>31</output>

<gadget id="calculator">31 + 29</gadget>
<output>60</output>

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

Choices:
A. 12
B. 13
C. 14
D. 15
E. 16

divide(add(subtract(subtract(multiply(add(const_1, const_4), 12), 15), 14), 29), const_4)

Explanation: w + b + c + 14 + 15 = 12 * 5 = 60 = > w + b + c = 60 - 29 = 31 w + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d


Question: set a of 8 positive integers may have the same element and have 40 . and set b of 8 positive integers must have different elements and have 40 . when m and n are the greatest possible differences between 40 and other elements ’ sums in set a and set b , respectively , m - n = ?

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

<gadget id="calculator">10 + 8</gadget>
<output>18</output>

<gadget id="calculator">40 - 18</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 21
B. 29
C. 23
D. 25
E. 26

Explanation: this is maximum - minimum . hence , 40 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 32 and 40 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 11 . so , 32 - 11 = 21 . the correct answer is a .


Question: after 6 games , team b had an average of 65 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?

<gadget id="calculator">6 * 65</gadget>
<output>390</output>

<gadget id="calculator">390 + 47</gadget>
<output>437</output>

<gadget id="calculator">500 - 437</gadget>
<output>63</output>
<result>63</result>

Choices:
A. 85
B. 74
C. 67
D. 63
E. 28

Explanation: "( 6 * 65 ) + 47 + x > 500 390 + 47 + x > 500 437 + x > 500 = > x > 63 option d"


Question: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 16 more transactions than cal . how much transactions did jade handled ?

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>

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

<gadget id="calculator">(9/10) * 110</gadget>
<output>99</output>

<gadget id="calculator">99 * 2</gadget>
<output>198</output>

<gadget id="calculator">198 / 3</gadget>
<output>66</output>

<gadget id="calculator">66 + 16</gadget>
<output>82</output>
<result>82</result>

Choices:
A. 80
B. 81
C. 82
D. 83
E. 84

add(divide(multiply(multiply(divide(90, const_100), add(10, const_100)), 2), 3), 16)

Explanation: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 16 = 82 jade handled = 82 transactions . answer : c"


Question: a man buys an article for $ 100 . and sells it for $ 125 . find the gain percent ?

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

<gadget id="calculator">125 / 1</gadget>
<output>125</output>

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

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

subtract(divide(125, divide(100, const_100)), const_100)

Explanation: "c . p . = $ 100 s . p . = $ 125 gain = $ 25 gain % = 25 / 100 * 100 = 25 % answer is c"


Question: list a consists of 12 consecutive integers . if - 4 is the least integer in list a , what is the range of positive integers in list a ?

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

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

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

Choices:
A. 5
B. 6
C. 7
D. 11
E. 12

subtract(subtract(12, add(4, const_1)), const_1)

Explanation: since - 4 is the least integer in list a , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .


Question: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 2 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?

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

<gadget id="calculator">180 * 1</gadget>
<output>180</output>

<gadget id="calculator">360 - 180</gadget>
<output>180</output>

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

<gadget id="calculator">180 + 36</gadget>
<output>216</output>
<result>216</result>

Choices:
A. 18
B. 144
C. 175
D. 216
E. 250

add(multiply(divide(360, 2), 1), divide(subtract(360, multiply(divide(360, 2), 1)), 5))

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 2 ) * 360 = 180 gallons . remaning paint = 180 gallons paint used in the second week = ( 1 / 5 ) * 180 = 36 gallons total paint used = 216 gallons . option d"


Question: if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 4 ?

<gadget id="calculator">96 / 2</gadget>
<output>48</output>

<gadget id="calculator">96 / 4</gadget>
<output>24</output>

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

<gadget id="calculator">72 / 96</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>

Choices:
A. 1 / 4
B. 3 / 8
C. 1 / 2
D. 5 / 8
E. 3 / 4

divide(add(divide(96, 2), divide(96, 4)), 96)

Explanation: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 4 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 4 = not integer we can not forget multiples of 8 from 1 to 96 we have 24 numbers that are multiple of 4 therefore , 48 / 96 + 24 / 96 = 72 / 96 = 3 / 4 answer : e"


Question: when y is divided by 288 , the remainder is 44 . what is the remainder when the same y is divided by 24 ?

<gadget id="calculator">44 % 24</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20
B. 21
C. 23
D. 25
E. 26

Explanation: y = 288 * a + 44 = ( 24 * 12 ) * a + 24 + 20 the answer is a .


Question: after decreasing 24 % in the price of an article costs rs . 1140 . find the actual cost of an article ?

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>

<gadget id="calculator">1_140 / (19/25)</gadget>
<output>1_500</output>
<result>1_500</result>

Choices:
A. 1500
B. 6789
C. 1200
D. 6151
E. 1421

divide(1140, subtract(const_1, divide(24, const_100)))

Explanation: "cp * ( 76 / 100 ) = 1140 cp = 15 * 100 = > cp = 1500 answer : a"


Question: a room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles . what will be the least number of square tiles required to cover the floor ?

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

<gadget id="calculator">500 + 44</gadget>
<output>544</output>

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

<gadget id="calculator">300 + 74</gadget>
<output>374</output>

<gadget id="calculator">544 * 374</gadget>
<output>203_456</output>

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

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

<gadget id="calculator">44 - 10</gadget>
<output>34</output>

<gadget id="calculator">34 * 34</gadget>
<output>1_156</output>

<gadget id="calculator">203_456 / 1_156</gadget>
<output>176</output>
<result>176</result>

Choices:
A. 176
B. 124
C. 224
D. 186
E. 190

divide(multiply(add(multiply(5, const_100), 44), add(multiply(3, const_100), 74)), multiply(subtract(44, add(multiply(const_2, const_4), const_2)), subtract(44, add(multiply(const_2, const_4), const_2))))

Explanation: "length = 5 m 44 cm = 544 cm breadth = 3 m 74 cm = 374 cm area = 544 * 374 hcf = 34 area of square = 34 * 34 cm 2 no of tiles req = 544 * 374 / 34 * 34 = 16 * 11 = 176 answer a"


Question: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 , is :

<gadget id="calculator">54 * 10</gadget>
<output>540</output>
<result>540</result>

Choices:
A. 504
B. 536
C. 544
D. 548
E. none of these

Explanation: "explanation : required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d"


Question: jonathan can type a 30 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?

<gadget id="calculator">30 / 24</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">30 / 40</gadget>
<output>3/4 = around 0.75</output>

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

<gadget id="calculator">(3/4) + 1</gadget>
<output>7/4 = around 1.75</output>

<gadget id="calculator">(5/4) + (7/4)</gadget>
<output>3</output>

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

Choices:
A. 5 minutes
B. 10 minutes
C. 15 minutes
D. 18 minutes
E. 20 minutes

Explanation: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 30 / 40 + 30 / 30 + 30 / 24 = 30 / x if you solve this equation , you get the same answer b ( 10 )"


Question: a box contains 10 tablets of medicine a and 17 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .

<gadget id="calculator">17 + 2</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 12
B. 15
C. 17
D. 19
E. 21

Explanation: "the worst case scenario will be if we remove all 17 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17 + 2 = 19 tablets . answer : d ."


Question: the milk level in a rectangular box measuring 60 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )

<gadget id="calculator">60 * 25</gadget>
<output>1_500</output>

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

<gadget id="calculator">1_500 * (1/2)</gadget>
<output>750</output>

<gadget id="calculator">750 * 7.5</gadget>
<output>5_625</output>
<result>5_625</result>

Choices:
A. 100
B. 250
C. 750
D. 5625
E. 5635

multiply(multiply(multiply(60, 25), divide(1, const_2)), 7.5)

Explanation: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 25 * 1 / 2 = 750 feet ^ 3 of milk must be removed , which equals to 750 * 7.5 = 5625 gallons . answer : d ."


Question: rhonda picked 2 pen from the table , if there were 7 pens on the table and 5 belongs to jill , what is the probability that the 2 pen she picked does not belong to jill ? .

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

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

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

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

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

<gadget id="calculator">(2/7) * (1/6)</gadget>
<output>1/21 = around 0.047619</output>
<result>1/21 = around 0.047619</result>

Choices:
A. 5 / 42
B. 2 / 42
C. 7 / 42
D. 2 / 7
E. 5 / 7

multiply(divide(subtract(7, 5), 7), divide(subtract(subtract(7, 5), const_1), subtract(7, const_1)))

Explanation: since jill owns 5 of the pen , the subset from which the 2 pens hould be chosen are the 2 pens not owned by jill fom the universe of 7 . the first pen can be one of the 2 from the 7 with probability 2 / 7 . the second pen can be one of the 1 from the 6 remaining with probability 1 / 6 , the total probability will be 2 / 7 × 1 / 6 . on cancellation , this comes to 2 / 42 . thus , the answer is b - 2 / 42 .


Question: country x taxes each of its citizens an amount equal to 13 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?

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

<gadget id="calculator">40 * 1_000</gadget>
<output>40_000</output>

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

<gadget id="calculator">8 * 1_000</gadget>
<output>8_000</output>

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

<gadget id="calculator">(13/100) * 40_000</gadget>
<output>5_200</output>

<gadget id="calculator">8_000 - 5_200</gadget>
<output>2_800</output>

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

<gadget id="calculator">2_800 / (1/5)</gadget>
<output>14_000</output>

<gadget id="calculator">40_000 + 14_000</gadget>
<output>54_000</output>
<result>54_000</result>

Choices:
A. $ 54,000
B. $ 56,000
C. $ 64,000
D. $ 66,667
E. $ 80,000

add(multiply(multiply(const_4, const_10), const_1000), divide(subtract(multiply(multiply(const_4, const_2), const_1000), multiply(divide(13, const_100), multiply(multiply(const_4, const_10), const_1000))), divide(20, const_100)))

Explanation: "equation is correct , so math must be a problem . 0.13 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,200 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,800 - - > x = 54,000 . answer : a ."


Question: the surface of a cube is 294 sq cm . find its volume ?

<gadget id="calculator">2 + 4</gadget>
<output>6</output>

<gadget id="calculator">294 / 6</gadget>
<output>49</output>

<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>

<gadget id="calculator">7 ** 3</gadget>
<output>343</output>
<result>343</result>

Choices:
A. 8 cc
B. 9 cc
C. 2 cc
D. 343 cc
E. 6 cc

Explanation: "6 a 2 = 294 = 6 * 49 a = 7 = > a 3 = 343 cc answer : d"


Question: the average marks of 20 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?

<gadget id="calculator">100 * 20</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 - 50</gadget>
<output>1_950</output>

<gadget id="calculator">1_950 + 10</gadget>
<output>1_960</output>

<gadget id="calculator">1_960 / 20</gadget>
<output>98</output>
<result>98</result>

Choices:
A. 78
B. 82
C. 98
D. 91
E. 85

divide(add(subtract(multiply(100, 20), 50), 10), 20)

Explanation: "correct avg marks = 100 + ( 10 - 50 ) / 20 avg = 100 - 2 = 98 answer is c"


Question: a parking garage rents parking spaces for $ 10 per week or $ 20 per month . how much does a person save in a year by renting by the month rather than by the week ?

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

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

<gadget id="calculator">50 + 2</gadget>
<output>52</output>

<gadget id="calculator">52 * 10</gadget>
<output>520</output>

<gadget id="calculator">20 * 12</gadget>
<output>240</output>

<gadget id="calculator">520 - 240</gadget>
<output>280</output>
<result>280</result>

Choices:
A. $ 140
B. $ 160
C. $ 220
D. $ 240
E. $ 280

subtract(multiply(add(multiply(10, add(const_3, const_2)), const_2), 10), multiply(20, const_12))

Explanation: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 20 = 240 $ 520 - 240 = 280 ans e"


Question: jerry travels 8 miles at an average speed of 40 miles per hour , stops for 14 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?

<gadget id="calculator">8 + 20</gadget>
<output>28</output>

<gadget id="calculator">8 / 40</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">14 / 60</gadget>
<output>7/30 = around 0.233333</output>

<gadget id="calculator">(1/5) + (7/30)</gadget>
<output>13/30 = around 0.433333</output>

<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(13/30) + (1/3)</gadget>
<output>23/30 = around 0.766667</output>

<gadget id="calculator">28 / (23/30)</gadget>
<output>840/23 = around 36.521739</output>
<result>840/23 = around 36.521739</result>

Choices:
A. 36
B. 42.5
C. 44
D. 50
E. 52.5

Explanation: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 14 minutes + ( 20 / 60 ) * 60 minutes = 46 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 46 / 60 ) hours = 28 * 60 / 46 = 36 miles per hour answer : option a"


Question: the total surface area of a cuboid length 12 m , breadth 10 m and height 8 m .

<gadget id="calculator">2 * (12 * 10 + 10 * 8 + 12 * 8)</gadget>
<output>592</output>
<result>592</result>

Choices:
A. 576
B. 566
C. 596
D. 556
E. 586

Explanation: total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c .


Question: 60 boys can complete a work in 24 days . how many men need to complete twice the work in 20 days

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

<gadget id="calculator">60 * 48</gadget>
<output>2_880</output>

<gadget id="calculator">2_880 / 20</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 144
B. 170
C. 180
D. 190
E. 200

divide(multiply(60, multiply(24, const_2)), 20)

Explanation: "one man can complete the work in 24 * 60 = 1440 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1440 m = 144 workers answer : a"


Question: jill has 21 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?

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

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

<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1 + (3/4)</gadget>
<output>7/4 = around 1.75</output>

<gadget id="calculator">21 / (7/4)</gadget>
<output>12</output>

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

Choices:
A. 3
B. 6
C. 9
D. 36
E. 14

multiply(divide(21, add(const_1, add(const_0_25, divide(const_1, const_2)))), const_3)

Explanation: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 21 1 3 / 4 w = 21 w = 12 the total number of jars = 3 w = 36 answer : d


Question: a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 20 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?

<gadget id="calculator">20 * 40</gadget>
<output>800</output>
<result>800</result>

Choices:
A. rs . 800
B. rs . 1500
C. rs . 1000
D. rs . 1200
E. none of these

Explanation: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 20 = rs . 185 cp on 40 metres = 185 x 40 = rs . 7400 profit earned on 40 metres cloth = rs . 8200 – rs . 7400 = rs . 800 . answer : option a"


Question: 24 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?

<gadget id="calculator">24 * 10</gadget>
<output>240</output>

<gadget id="calculator">240 / 40</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 10
B. 6
C. 4
D. 7
E. 5

Explanation: "required number of machines = 24 * 10 / 40 = 6 answer is b"


Question: in a company of 170 employees , 110 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 25 employees are males with college degree only , how many employees are females with advanced degrees ?

<gadget id="calculator">170 - 110</gadget>
<output>60</output>

<gadget id="calculator">60 - 25</gadget>
<output>35</output>

<gadget id="calculator">80 - 35</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 40
B. 45
C. 50
D. 55
E. 60

subtract(80, subtract(subtract(170, 110), 25))

Explanation: the number of males is 170 - 110 = 60 . the number of males with advanced degrees is 60 - 25 = 35 . the number of females with advanced degrees is 80 - 35 = 45 . the answer is b .


Question: at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 36 males did not bring gifts to the party , how many females did bring gifts ?

<gadget id="calculator">70 * 300</gadget>
<output>21_000</output>

<gadget id="calculator">21_000 / 100</gadget>
<output>210</output>

<gadget id="calculator">300 - 210</gadget>
<output>90</output>

<gadget id="calculator">90 - 36</gadget>
<output>54</output>

<gadget id="calculator">54 * 100</gadget>
<output>5_400</output>

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

<gadget id="calculator">5_400 / 60</gadget>
<output>90</output>

<gadget id="calculator">90 * 40</gadget>
<output>3_600</output>

<gadget id="calculator">3_600 / 100</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 18
B. 36
C. 42
D. 68
E. 70

divide(multiply(divide(multiply(subtract(subtract(300, divide(multiply(70, 300), const_100)), 36), const_100), subtract(const_100, 40)), 40), const_100)

Explanation: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 36 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b"


Question: if 8 a = 9 b and ab ≠ 0 , what is the ratio of a / 9 to b / 8 ?

<gadget id="calculator">8 * 9</gadget>
<output>72</output>

<gadget id="calculator">9 * 8</gadget>
<output>72</output>

<gadget id="calculator">72 / 72</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 64 / 81
B. 8 / 9
C. 1
D. 9 / 8
E. 81 / 64

Explanation: "if ab ≠ 0 then a and b has two integer sets of pair if a = 9 then b = 8 and if a = - 9 then b = - 8 also in fraction if a = 1 / 8 then b = 1 / 9 any of the pair we check the ratio 8 a / 9 b = 1 answer : c"


Question: in a theater , the first row has 17 seats and each row has 3 more seats than previous row . if the last row has 44 seats , what is the total number of seats in the theater ?

<gadget id="calculator">17 + 44</gadget>
<output>61</output>

<gadget id="calculator">61 / 2</gadget>
<output>61/2 = around 30.5</output>

<gadget id="calculator">44 - 17</gadget>
<output>27</output>

<gadget id="calculator">27 + 3</gadget>
<output>30</output>

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

<gadget id="calculator">(61/2) * 10</gadget>
<output>305</output>
<result>305</result>

Choices:
A. 265
B. 275
C. 285
D. 295
E. 305

multiply(divide(add(17, 44), const_2), divide(add(subtract(44, 17), 3), 3))

Explanation: "the number of seats in the theater is 17 + ( 17 + 3 ) + . . . + ( 17 + 27 ) = 10 ( 17 ) + 3 ( 1 + 2 + . . . + 9 ) = 10 ( 17 ) + 3 ( 9 ) ( 10 ) / 2 = 170 + 135 = 305 the answer is e ."


Question: the list price of an article is rs . 69 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

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

<gadget id="calculator">69 * (1/10)</gadget>
<output>69/10 = around 6.9</output>

<gadget id="calculator">69 - (69/10)</gadget>
<output>621/10 = around 62.1</output>

<gadget id="calculator">(621/10) - 56.16</gadget>
<output>5.94</output>

<gadget id="calculator">5.94 / (621/10)</gadget>
<output>0.095652</output>

<gadget id="calculator">0.095652 * 100</gadget>
<output>9.5652</output>
<result>9.5652</result>

Choices:
A. 9.33 %
B. 9.44 %
C. 9.45 %
D. 9.56 %
E. 9.67 %

multiply(divide(subtract(subtract(69, multiply(69, divide(10, const_100))), 56.16), subtract(69, multiply(69, divide(10, const_100)))), const_100)

Explanation: "69 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 9.56 % answer : d"


Question: how many seconds will a 200 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

<gadget id="calculator">63 - 3</gadget>
<output>60</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">200 / (50/3)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 26 sec
B. 30 sec
C. 12 sec
D. 19 sec
E. 12 sec

divide(200, multiply(subtract(63, 3), const_0_2778))

Explanation: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 200 * 3 / 50 = 12 sec . answer : c"


Question: the radius of a semi circle is 70 cm then its perimeter is ?

<gadget id="calculator">2 * pi * 70</gadget>
<output>140*pi = around 439.822972</output>

<gadget id="calculator">(140*pi) / 2</gadget>
<output>70*pi = around 219.911486</output>

<gadget id="calculator">70 * 2</gadget>
<output>140</output>

<gadget id="calculator">(70*pi) + 140</gadget>
<output>140 + 70*pi = around 359.911486</output>
<result>140 + 70*pi = around 359.911486</result>

Choices:
A. 32.8
B. 32.4
C. 360
D. 32.2
E. 32.9

add(divide(circumface(70), const_2), multiply(70, const_2))

Explanation: "diameter = 140 cm 1 / 2 * 22 / 7 * 140 + 140 = 360 answer : c"


Question: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets .

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

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

Choices:
A. 4
B. 36
C. 8
D. 10
E. 12

Explanation: i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 36 days to doing 6 w widgets . answer : b


Question: the cost price of a radio is rs . 1500 and it was sold for rs . 1230 , find the loss % ?

<gadget id="calculator">1_500 - 1_230</gadget>
<output>270</output>

<gadget id="calculator">270 / 1_500</gadget>
<output>9/50 = around 0.18</output>

<gadget id="calculator">(9/50) * 100</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 18 %
B. 19 %
C. 68 %
D. 19 %
E. 38 %

multiply(divide(subtract(1500, 1230), 1500), const_100)

Explanation: "1500 - - - - 270 100 - - - - ? = > 18 % answer : a"


Question: the sale price sarees listed for rs . 500 after successive discount is 10 % and 5 % is ?

<gadget id="calculator">500 * 10</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 / 100</gadget>
<output>50</output>

<gadget id="calculator">500 - 50</gadget>
<output>450</output>

<gadget id="calculator">450 * 5</gadget>
<output>2_250</output>

<gadget id="calculator">2_250 / 100</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">450 - (45/2)</gadget>
<output>855/2 = around 427.5</output>
<result>855/2 = around 427.5</result>

Choices:
A. 427.5
B. 277
C. 342
D. 882
E. 212

subtract(subtract(500, divide(multiply(500, 10), const_100)), divide(multiply(subtract(500, divide(multiply(500, 10), const_100)), 5), const_100))

Explanation: "500 * ( 90 / 100 ) * ( 95 / 100 ) = 427.5 answer : a"


Question: the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 350 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?

<gadget id="calculator">350 * 2</gadget>
<output>700</output>

<gadget id="calculator">700 / 5</gadget>
<output>140</output>

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

<gadget id="calculator">140 + 10</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 60
B. 90
C. 120
D. 150
E. 240

add(divide(multiply(350, 2), 5), multiply(2, 5))

Explanation: let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 350 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 3 / 5 x = 3 / 5 ( 250 ) = 150 the correct answer is d


Question: a can do a piece of work in 8 days and b alone can do it in 12 days . how much time will both take to finish the work ?

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

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

<gadget id="calculator">(1/8) + (1/12)</gadget>
<output>5/24 = around 0.208333</output>

<gadget id="calculator">1 / (5/24)</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>

Choices:
A. 4.8
B. 6.333
C. 7.333
D. 8.5
E. 9

divide(const_1, add(divide(const_1, 8), divide(const_1, 12)))

Explanation: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 8 x 12 / ( 8 + 12 ) = 96 / 20 = 4.8 days answer : a"


Question: the measurement of a rectangular box with lid is 25 cmx 6 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )

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

<gadget id="calculator">3 ** 3</gadget>
<output>27</output>

<gadget id="calculator">(4/3) * 27</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 288
B. 48
C. 36
D. 864
E. 964

multiply(divide(const_4, const_3), power(3, const_3))

Explanation: d = 6 , r = 2 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 3 * 3 * 3 = 36 π cm 3 answer : c


Question: a and b go around a circular track of length 150 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?

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

<gadget id="calculator">54 * (5/18)</gadget>
<output>15</output>

<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>

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

<gadget id="calculator">150 / 5</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30 sec
B. 198 sec
C. 178 sec
D. 665 sec
E. 276 sec

divide(150, subtract(multiply(54, const_0_2778), multiply(36, const_0_2778)))

Explanation: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 150 / ( 36 * 5 / 18 ) , 150 / ( 54 * 5 / 18 ) } = lcm ( 15 , 10 ) = 30 sec . answer : a"


Question: two trains of length 150 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?

<gadget id="calculator">150 + 280</gadget>
<output>430</output>

<gadget id="calculator">42 + 30</gadget>
<output>72</output>

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

<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>

<gadget id="calculator">430 / 20</gadget>
<output>43/2 = around 21.5</output>
<result>43/2 = around 21.5</result>

Choices:
A. 22 sec
B. 77 sec
C. 76 sec
D. 21.5 sec
E. 66 sec

Explanation: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 150 + 280 = 430 m . the time required = d / s = 430 / 20 = 21.5 sec . answer : d"


Question: source : knewton a cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . what is the maximum distance , in miles , that the cyclist could travel in 5 hours ?

<gadget id="calculator">14 * 5</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 42
B. 56
C. 70
D. 98
E. 140

Explanation: we are told that : generallya cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . is it possible the cyclist to travel with maximum speed for some time ? why not , if there is right terrain for that . so , if there is long enough terrain for the maximum speed of 14 mph then the maximum distance , in miles , that the cyclist could travel in 5 hours would be 5 * 14 = 70 miles . answer : c .


Question: the length of a rectangle is two - seventh of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 5929 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 25 units ?

<gadget id="calculator">5_929 ** (1/2)</gadget>
<output>77</output>

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

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

<gadget id="calculator">77 * (2/7)</gadget>
<output>22</output>

<gadget id="calculator">25 * 22</gadget>
<output>550</output>
<result>550</result>

Choices:
A. 660 sq . units
B. 440 sq . units
C. 770 sq . units
D. 550 sq . units
E. 220 sq . units

rectangle_area(25, multiply(sqrt(5929), divide(const_2, add(const_3, const_4))))

Explanation: given that the area of the square = 5929 sq . units = > side of square = â ˆ š 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d


Question: if 20 men take 15 days to to complete a job , in how many days can 25 men finish that work ?

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

<gadget id="calculator">300 / 25</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 66
C. 77
D. 8
E. 6

Explanation: ans . 12 days


Question: on a certain transatlantic crossing , 20 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?

<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">20 / (1/2)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 30 %
B. 40 %
C. 50 %
D. 60 %
E. 65 %

divide(20, subtract(const_1, divide(50, const_100)))

Explanation: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.2 t x = 0.4 t the answer is b ."


Question: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 7 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?

<gadget id="calculator">5 * 7</gadget>
<output>35</output>

<gadget id="calculator">35 / 60</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">60 * (7/12)</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 20 km
B. 35 km
C. 40 km
D. 50 km
E. 60 km

multiply(60, divide(multiply(5, 7), 60))

Explanation: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 7 = 35 km imo , correct answer is ` ` b . ' '"


Question: the fuel indicator in a car shows 1 / 5 th of the fuel tank as full . when 22 more liters of fuel are poured in to the tank , the indicator rests at the 3 / 4 of the full mark . find the capacity of the tank .

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

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

<gadget id="calculator">(3/4) - (1/5)</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">22 / (11/20)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 25 litres
B. 35 litres
C. 30 litres
D. 40 litres
E. none of these

divide(22, subtract(divide(3, 4), divide(1, 5)))

Explanation: x / 5 + 22 = 3 x / 4 = > x = 40 litres answer : d


Question: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 450 kilograms of pears that day , how many kilograms did he sell in the afternoon ?

<gadget id="calculator">450 / 3</gadget>
<output>150</output>

<gadget id="calculator">150 * 2</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 120
B. 180
C. 300
D. 280
E. 320

Explanation: 3 x = 450 x = 150 therefore , the salesman sold 150 kg in the morning and 2 ⋅ 150 = 300 kg in the afternoon . so answer is c .


Question: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 30 as remainder

<gadget id="calculator">1_365 - 30</gadget>
<output>1_335</output>

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

<gadget id="calculator">1_335 / 5</gadget>
<output>267</output>

<gadget id="calculator">267 * 6</gadget>
<output>1_602</output>

<gadget id="calculator">1_602 + 30</gadget>
<output>1_632</output>
<result>1_632</result>

Choices:
A. 1235
B. 1456
C. 1567
D. 1632
E. 1635

add(multiply(divide(subtract(1365, 30), subtract(6, const_1)), 6), 30)

Explanation: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 30 5 x = 1335 x = 267 large number = 267 + 1365 = 1632 d"


Question: a rectangle with width 8 and diagonal 30 . find the area ?

<gadget id="calculator">30 ** 2</gadget>
<output>900</output>

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

<gadget id="calculator">900 - 64</gadget>
<output>836</output>

<gadget id="calculator">836 ** (1/2)</gadget>
<output>2*sqrt(209) = around 28.913665</output>

<gadget id="calculator">(2*sqrt(209)) * 8</gadget>
<output>16*sqrt(209) = around 231.309317</output>
<result>16*sqrt(209) = around 231.309317</result>

Choices:
A. 240 square units
B. 180 square units
C. 100 square units
D. 150 square units
E. 160 square units

rectangle_area(sqrt(subtract(power(30, const_2), power(8, const_2))), 8)

Explanation: then the area is : 8 ' ' x 30 ' ' = 240 square inches , or 240 square units hence a


Question: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 35 miles per hour . how many miles from the station was train a overtaken by train b ?

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

<gadget id="calculator">35 - 30</gadget>
<output>5</output>

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

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

Choices:
A. 420
B. 450
C. 480
D. 510
E. 540

multiply(divide(multiply(30, const_2), subtract(35, 30)), 35)

Explanation: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 5 miles per hour . the time to catch up is 60 / 5 = 12 hours . in 12 hours , train a travels another 30 * 12 = 360 miles for a total of 420 miles . the answer is a ."


Question: a box contains 25 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is

<gadget id="calculator">25 - 4</gadget>
<output>21</output>

<gadget id="calculator">binomial(21, 2)</gadget>
<output>210</output>

<gadget id="calculator">binomial(25, 2)</gadget>
<output>300</output>

<gadget id="calculator">210 / 300</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>

Choices:
A. 3 / 10
B. 7 / 19
C. 12 / 19
D. 21 / 95
E. none

subtract(const_1, divide(choose(subtract(25, 4), const_2), choose(25, const_2)))

Explanation: "solution p ( none is defective ) = 21 c 2 / 25 c 2 = 7 / 10 p ( at least one is defective ) = ( 1 - 7 / 10 ) = 3 / 10 . answer a"


Question: how many prime numbers are between 28 / 3 and 86 / 6 ?

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

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

Explanation: "28 / 3 = 9 . xxx 86 / 6 = 14 . xxx so we need to find prime numbers between 9 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"


Question: in a school of 800 students , 44 % wear blue shirts , 28 % wear red shirts , 10 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?

<gadget id="calculator">44 / 100</gadget>
<output>11/25 = around 0.44</output>

<gadget id="calculator">(11/25) * 800</gadget>
<output>352</output>

<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">(7/25) * 800</gadget>
<output>224</output>

<gadget id="calculator">352 + 224</gadget>
<output>576</output>

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

<gadget id="calculator">(1/10) * 800</gadget>
<output>80</output>

<gadget id="calculator">576 + 80</gadget>
<output>656</output>

<gadget id="calculator">800 - 656</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 120
B. 132
C. 144
D. 156
E. 168

subtract(800, add(add(multiply(divide(44, const_100), 800), multiply(divide(28, const_100), 800)), multiply(divide(10, const_100), 800)))

Explanation: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 800 * 18 / 100 = 144 the answer is c ."


Question: in what ratio must rice of rs . 25 per kg be mixed with rice of rs . 12 per kg so that cost of mixture is rs . 20 per kg ?

<gadget id="calculator">20 - 12</gadget>
<output>8</output>

<gadget id="calculator">25 - 12</gadget>
<output>13</output>

<gadget id="calculator">8 / 13</gadget>
<output>8/13 = around 0.615385</output>

<gadget id="calculator">1 - (8/13)</gadget>
<output>5/13 = around 0.384615</output>

<gadget id="calculator">(8/13) / (5/13)</gadget>
<output>8/5 = around 1.6</output>
<result>8/5 = around 1.6</result>

Choices:
A. 8 : 5
B. 5 : 8
C. 20 : 25
D. 12 : 20
E. 25 : 12

divide(divide(subtract(20, 12), subtract(25, 12)), subtract(const_1, divide(subtract(20, 12), subtract(25, 12))))

Explanation: "( 20 - 12 ) / ( 25 - 20 = 8 / 5 = 8 : 5 answer : a"


Question: 10 men and 15 women together can complete a work in 4 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?

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

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

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

<gadget id="calculator">100 / 60</gadget>
<output>5/3 = around 1.666667</output>

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

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

Choices:
A. 100 days
B. 667 days
C. 177 days
D. 187 days
E. 225 days

multiply(divide(multiply(const_1, 100), subtract(multiply(const_1, 100), multiply(10, 4))), multiply(15, 4))

Explanation: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 4 15 women ' s 1 day work = ( 1 / 4 - 10 / 100 ) = 3 / 20 1 woman ' s 1 day work = 1 / 100 1 woman alone can complete the work in 100 days . answer : a"


Question: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 4 other contributions made before john ' s , what is the size of his donation ?

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

<gadget id="calculator">5 * 75</gadget>
<output>375</output>

<gadget id="calculator">5 * 50</gadget>
<output>250</output>

<gadget id="calculator">375 - 250</gadget>
<output>125</output>

<gadget id="calculator">125 + 50</gadget>
<output>175</output>
<result>175</result>

Choices:
A. $ 100
B. $ 175
C. $ 200
D. $ 250
E. $ 450

add(subtract(multiply(add(4, const_1), 75), multiply(add(4, const_1), 50)), 50)

Explanation: cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 4 people . so $ 100 . but , he also has to put in the average for himself ( the fiveth person ) , so add $ 75 . so $ 175 is your answer . answer b


Question: if 0.5 : x : : 5 : 8 , then x is equal to :

<gadget id="calculator">0.5 * 8</gadget>
<output>4</output>

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

Choices:
A. 1.12
B. 1.2
C. 1.25
D. 0.9
E. 0.8

Explanation: "( x * 5 ) = ( 0.5 * 8 ) x = 4 / 5 x = 0.8 answer = e"


Question: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what is the weight of the new person ?

<gadget id="calculator">2.5 * 8</gadget>
<output>20</output>

<gadget id="calculator">20 + 75</gadget>
<output>95</output>
<result>95</result>

Choices:
A. 75 kg
B. 85 kg
C. 95 kg
D. 65 kg
E. 55 kg

Explanation: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 75 + 20 ) kg = 95 kg the answer is c ."


Question: the radius of a wheel is 12.6 cm . what is the distance covered by the wheel in making 200 resolutions ?

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

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

<gadget id="calculator">21 + 1</gadget>
<output>22</output>

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">(22/7) * 12.6</gadget>
<output>39.6</output>

<gadget id="calculator">39.6 * 2</gadget>
<output>79.2</output>

<gadget id="calculator">79.2 * 200</gadget>
<output>15_840</output>

<gadget id="calculator">15_840 / 100</gadget>
<output>792/5 = around 158.4</output>
<result>792/5 = around 158.4</result>

Choices:
A. 158.210 m
B. 704 m
C. 153.256 m
D. 158.256 m
E. 204 m

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 12.6), const_2), 200), const_100)

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 200 resolutions . = 200 * 2 * 22 / 7 * 12.6 = 15825.6 cm = 158.256 m answer : d"


Question: on my sister ' s birthday , she was 143 cm in height , having grown 10 % since the year before . how tall was she the previous year ?

<gadget id="calculator">143 * 10</gadget>
<output>1_430</output>

<gadget id="calculator">1_430 / 100</gadget>
<output>143/10 = around 14.3</output>

<gadget id="calculator">143 - (143/10)</gadget>
<output>1_287/10 = around 128.7</output>
<result>1_287/10 = around 128.7</result>

Choices:
A. 140 cm
B. 136 cm
C. 130 cm
D. 127 cm
E. 125 cm

subtract(143, divide(multiply(143, 10), const_100))

Explanation: "let the previous year ' s height be x . 1.1 x = 143 x = 130 the answer is c ."


Question: the length of each side of an equilateral triangle having an area of 4 â ˆ š 3 cm 2 is ?

<gadget id="calculator">3 ** (1/2)</gadget>
<output>sqrt(3) = around 1.732051</output>

<gadget id="calculator">4 * (sqrt(3))</gadget>
<output>4*sqrt(3) = around 6.928203</output>

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

<gadget id="calculator">(1/2) * (1/2)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * (sqrt(3))</gadget>
<output>sqrt(3)/4 = around 0.433013</output>

<gadget id="calculator">(4*sqrt(3)) / (sqrt(3)/4)</gadget>
<output>16</output>

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

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

sqrt(divide(multiply(4, sqrt(3)), multiply(multiply(divide(const_1, 2), divide(const_1, 2)), sqrt(3))))

Explanation: explanation : â ˆ š 3 / 4 a 2 = 4 â ˆ š 3 - > a = 4 answer is d


Question: if the sides of a rectangle are increased by 25 % , what is the percentage increase in the area ?

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

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) ** 2</gadget>
<output>25/16 = around 1.5625</output>

<gadget id="calculator">(25/16) - 1</gadget>
<output>9/16 = around 0.5625</output>

<gadget id="calculator">(9/16) * 100</gadget>
<output>225/4 = around 56.25</output>
<result>225/4 = around 56.25</result>

Choices:
A. 54.25 %
B. 56.25 $
C. 53.25 %
D. 55.25 %
E. 58.25 %

multiply(subtract(power(add(divide(25, const_100), const_1), const_2), const_1), const_100)

Explanation: "if sides are a and b , after increase sides would be 1.25 a and 1.25 b . percentage increase in area = ( 1.25 a * 1.25 b - ab ) * 100 / ab = 56.25 % answer : b"


Question: the charge for a single room at hotel p is 30 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?

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

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

<gadget id="calculator">70 / 90</gadget>
<output>7/9 = around 0.777778</output>

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

<gadget id="calculator">100 - (700/9)</gadget>
<output>200/9 = around 22.222222</output>

<gadget id="calculator">(200/9) / (700/9)</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>

Choices:
A. 28 %
B. 20 %
C. 40 %
D. 50 %
E. 150 %

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

Explanation: "let rate in r = 100 x then p = 70 x g = 100 y p = 90 y thus 70 x = 90 y or x = 1.28 y ans r = 128 y so increase = 28 % answer : a"


Question: a trader marked the selling price of an article at 11 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :

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

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

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

<gadget id="calculator">100 + 11</gadget>
<output>111</output>

<gadget id="calculator">11 / 111</gadget>
<output>11/111 = around 0.099099</output>

<gadget id="calculator">100 * (11/111)</gadget>
<output>1_100/111 = around 9.90991</output>
<result>1_100/111 = around 9.90991</result>

Choices:
A. 10 %
B. 10.5 %
C. 9.9 %
D. 12.5 %
E. none

multiply(const_100, divide(add(multiply(add(const_2, const_3), const_2), 1), add(const_100, 11)))

Explanation: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 111 * 100 ] % = 9.9 % answer c"


Question: bottle r contains 250 capsules and costs $ 5.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?

<gadget id="calculator">2.99 / 130</gadget>
<output>0.023</output>

<gadget id="calculator">5.25 / 250</gadget>
<output>0.021</output>

<gadget id="calculator">0.023 - 0.021</gadget>
<output>0.002</output>
<result>0.002</result>

Choices:
A. $ 0.25
B. $ 0.12
C. $ 0.05
D. $ 0.03
E. $ 0.002

Explanation: cost per capsule in r is 5.25 / 250 = 0.525 / 25 = 0.021 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.002 the answer is e


Question: area of four walls of a room is 99 m 2 . the length and breadth of the room are 7.5 m and 3.5 m respectively . the height of the room is :

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

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

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

<gadget id="calculator">99 / 22</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>

Choices:
A. 2.5 m
B. 3.5 m
C. 1.5 m
D. 4.5 m
E. 5.5 m

divide(99, add(multiply(7.5, const_2), multiply(3.5, const_2)))

Explanation: 2 ( 7.5 + 3.5 ) × h = 99 2 ( 11 ) h = 99 22 h = 99 h = 99 / 22 = 9 / 2 = 4.5 m answer is d .


Question: x is a positive integer less than 300 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?

<gadget id="calculator">7 % 300</gadget>
<output>7</output>

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

<gadget id="calculator">3 % 300</gadget>
<output>3</output>

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

<gadget id="calculator">1 % 300</gadget>
<output>1</output>

<gadget id="calculator">24 - 1</gadget>
<output>23</output>
<result>23</result>

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

subtract(add(multiply(reminder(7, 300), 3), reminder(3, 300)), reminder(1, 300))

Explanation: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 300 n = 22.13 or n = 22 answer : - b"


Question: how many different ways can 2 students be seated in a row of 4 desks , so that there is always at least one empty desk between the students ?

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

<gadget id="calculator">factorial(3) / factorial(3 - 2)</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 2
B. 3
C. 4
D. 6
E. 12

Explanation: "total cases : 12 ( student one has 4 options and student two has three options , 4 x 3 = 12 ) non - favourable cases : 6 ( when two students sit together . students in desk 1 and desk 2 , in desk 2 and desk 3 , in desk 3 and desk 4 ) for each of these cases there are two possibilities because the positions can be interchanged . hence 2 x 3 = 6 . so favourable cases : 12 - 6 = 6 . answer : d"