Question: of the diplomats who attended a summit conference : 20 spoke japanese , 32 did not speak russian and 20 % of the diplomats spoke neither japanese nor russian . if 10 % of the diplomats spoke both japanese and russian , then how many diplomats attended the conference ?

<gadget id="calculator">32 - 20</gadget>
<output>12</output>

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

<gadget id="calculator">80 + 10</gadget>
<output>90</output>

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

<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>

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

Choices:
A. 70
B. 96
C. 108
D. 120
E. 150

divide(subtract(32, 20), subtract(const_1, divide(add(subtract(const_100, 20), 10), const_100)))

Explanation: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer


Question: if n = 2.0423 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?

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

<gadget id="calculator">20 + 3</gadget>
<output>23</output>

<gadget id="calculator">23 / 100</gadget>
<output>23/100 = around 0.23</output>

<gadget id="calculator">(23/100) / 100</gadget>
<output>23/10_000 = around 0.0023</output>

<gadget id="calculator">2.0423 - (23/10_000)</gadget>
<output>2.04</output>

<gadget id="calculator">2.04 - 2.0423</gadget>
<output>-0.0023</output>
<result>-0.0023</result>

Choices:
A. - 0.0053
B. - 0.0023
C. 0.0007
D. 0.0047
E. 0.0153

subtract(subtract(2.0423, divide(divide(add(multiply(const_2, const_10), const_3), const_100), const_100)), 2.0423)

Explanation: n * = 2.04 n * - n = 2.04 - 2.0423 - 0.0023 answer : b


Question: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 49 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?

<gadget id="calculator">72 / 60</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) * 35</gadget>
<output>42</output>

<gadget id="calculator">49 - 35</gadget>
<output>14</output>

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

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

Choices:
A. 105
B. 120
C. 140
D. 147
E. 168

multiply(35, divide(multiply(divide(72, const_60), 35), subtract(49, 35)))

Explanation: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 49 t or 5 t + 6 = 7 t or t = 3 distance travelled by car x from the time car y began traveling until both cars stopped is 35 x 3 = 105 miles answer : - a"


Question: in a restaurant , the profit is 160 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?

<gadget id="calculator">160 / 100</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">100 * (8/5)</gadget>
<output>160</output>

<gadget id="calculator">160 + 100</gadget>
<output>260</output>

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

<gadget id="calculator">1 + (3/25)</gadget>
<output>28/25 = around 1.12</output>

<gadget id="calculator">100 * (28/25)</gadget>
<output>112</output>

<gadget id="calculator">260 - 112</gadget>
<output>148</output>

<gadget id="calculator">148 / 260</gadget>
<output>37/65 = around 0.569231</output>

<gadget id="calculator">100 * (37/65)</gadget>
<output>740/13 = around 56.923077</output>
<result>740/13 = around 56.923077</result>

Choices:
A. 30 %
B. 57 %
C. 90 %
D. 100 %
E. none of these

multiply(const_100, divide(subtract(add(multiply(const_100, divide(160, const_100)), const_100), multiply(const_100, add(const_1, divide(12, const_100)))), add(multiply(const_100, divide(160, const_100)), const_100)))

Explanation: "explanation : let c . p . = rs . 100 . then , profit = rs . 160 , s . p . = rs . 260 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 260 . profit = rs . ( 260 - 112 ) = rs . 148 . required percentage = ( 148 / 260 * 100 ) % = 57 % appox answer : b"


Question: 25 * 25 * 25 * 25 * 25 = 5 ^ ?

<gadget id="calculator">max(5, 10)</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 4
B. 6
C. 5
D. 3
E. 10

Explanation: "solution : 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 = 5 ^ ( 2 + 2 + 2 + 2 + 2 ) = 5 ^ 10 answer : e"


Question: what quantity of water should taken out to concentrate 21 liters of 40 % acidic liquid to 60 % acidic liquid ?

<gadget id="calculator">21 * 40</gadget>
<output>840</output>

<gadget id="calculator">840 / 60</gadget>
<output>14</output>

<gadget id="calculator">21 - 14</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 5 liters
B. 10 liters
C. 7 liters
D. 8 liters
E. 6 liters

subtract(21, divide(multiply(21, 40), 60))

Explanation: "required answer is = 21 ( 60 - 40 ) / 60 = 7 liters answer is c"


Question: a and b together can do a work in 6 days . if a alone can do it in 10 days . in how many days can b alone do it ?

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

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

<gadget id="calculator">(1/6) - (1/10)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">1 / (1/15)</gadget>
<output>15</output>

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

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

<gadget id="calculator">15 + (2/5)</gadget>
<output>77/5 = around 15.4</output>
<result>77/5 = around 15.4</result>

Choices:
A. 10
B. 15
C. 77
D. 55
E. 21

add(inverse(subtract(divide(const_1, 6), divide(const_1, 10))), divide(const_2, add(const_2, const_3)))

Explanation: "1 / 6 – 1 / 10 = 1 / 15 = > 15 answer : b"


Question: sam and nik start from a and b respectively at the same time and travel towards each other at constant speeds along the same route . sam meets nik at point c on the road which is 600 m away from starting point a and 400 m away from point b . the speed of sam is 50 m / m ( meter / minute ) . how much time did sam take to cover the distance between a and b ?

<gadget id="calculator">600 + 400</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 / 50</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 10 minutes
B. 15 minutes
C. 20 minutes
D. 22 minutes
E. 17 minutes

Explanation: total distance from a to b - a - c = 600 m , b - c = 400 m ; therefore a - b = 1000 m ; vs = 50 m / m ; therefore , t = 1000 / 50 = 20 minutes . option c


Question: subtract . simplify your answer and write it as a proper fraction or as a whole or mixed number . 4 / 5 - 1 / 5 =

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

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

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

Explanation: here ' s how to subtract 1 / 5 from 4 / 5 : 4 / 5 − 1 / 5 since our denominators match , we can subtract the numerators . 4 − 1 = 3 so the answer is : 3 / 5 answer : c


Question: ratio between two numbers is 3 : 4 and their sum is 420 . find the smaller number ?

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

<gadget id="calculator">420 / 7</gadget>
<output>60</output>

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

Choices:
A. 378
B. 180
C. 820
D. 734
E. 840

Explanation: explanation : 3 x + 4 x = 420 x = 60 = > 3 x = 180 answer : option b


Question: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 30 , what is the greatest possible value of q minus r ?

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

<gadget id="calculator">30 % 9</gadget>
<output>3</output>

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

Choices:
A. 23
B. 24
C. 25
D. 26
E. 27

multiply(reminder(30, subtract(const_10, const_1)), subtract(const_10, const_1))

Explanation: a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 30 . the greatest multiple of 9 which is less than 30 is 27 . the answer is e .


Question: in a vehicle ' s repair shed , 3 men and 8 boys can do a piece of work in 15 days ; 4 men and 9 boys can do the same work in 12 days . then , 5 men and 5 boys can do double the amount of this work in :

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

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

<gadget id="calculator">17 * 15</gadget>
<output>255</output>

<gadget id="calculator">15 + 5</gadget>
<output>20</output>

<gadget id="calculator">255 / 20</gadget>
<output>51/4 = around 12.75</output>

<gadget id="calculator">(51/4) * 2</gadget>
<output>51/2 = around 25.5</output>

<gadget id="calculator">floor(51/2)</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 20 days
B. 33 days
C. 24 days
D. 28 days
E. none of these

floor(multiply(divide(multiply(add(multiply(3, 3), 8), 15), add(15, 5)), const_2))

Explanation: explanation : solution : ( 3 * 15 ) men + ( 8 * 15 ) boys = ( 4 * 12 ) men + ( 9 * 12 ) boys 45 m + 120 b = 48 m + 108 b < = > 3 m = 12 b = > 1 m = 4 b . . ' . 3 m + 8 b = ( 3 * 4 ) b + 8 b = 20 b . 5 m + 5 b = ( 5 * 4 ) b + 5 b = 25 b . let the required number of days be x . now , more boys , less days ( ip ) more work , more days ( dp ) boys 25 : 20 } : : 15 : x work 1 : 2 . ' . ( 25 * 1 * x ) = ( 20 * 2 * 15 ) = > x = 40 * 15 / 25 = 24 . answer : c


Question: increasing the original price of an article by 8 percent and then increasing the new price by 8 percent is equivalent to increasing the original price by

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

<gadget id="calculator">1 + (2/25)</gadget>
<output>27/25 = around 1.08</output>

<gadget id="calculator">(27/25) * (27/25)</gadget>
<output>729/625 = around 1.1664</output>

<gadget id="calculator">(729/625) - 1</gadget>
<output>104/625 = around 0.1664</output>

<gadget id="calculator">100 * (104/625)</gadget>
<output>416/25 = around 16.64</output>
<result>416/25 = around 16.64</result>

Choices:
A. 16.16 %
B. 16.32 %
C. 16.64 %
D. 17.26 %
E. 18.56 %

multiply(const_100, subtract(multiply(add(const_1, divide(8, const_100)), add(const_1, divide(8, const_100))), const_1))

Explanation: "1.08 * 1.08 * x = 1.1664 * x the answer is c ."


Question: if 6 women can color 180 m long cloth in 3 days , then 5 women can color 200 m long cloth in ?

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

<gadget id="calculator">180 / 18</gadget>
<output>10</output>

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

<gadget id="calculator">200 / 50</gadget>
<output>4</output>
<result>4</result>

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

divide(200, multiply(5, divide(180, multiply(6, 3))))

Explanation: the length of cloth painted by one woman in one day = 180 / 6 × 3 = 10 m no . of days required to paint 200 m cloth by 5 women = 200 / 5 × 10 = 4 days answer : c


Question: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 210 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?

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

<gadget id="calculator">32 * (3/4)</gadget>
<output>24</output>

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

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

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

<gadget id="calculator">240 + 210</gadget>
<output>450</output>

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

<gadget id="calculator">7 * 32</gadget>
<output>224</output>

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

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

<gadget id="calculator">(5/4) * 3</gadget>
<output>15/4 = around 3.75</output>

<gadget id="calculator">(15/4) * 32</gadget>
<output>120</output>

<gadget id="calculator">224 + 120</gadget>
<output>344</output>

<gadget id="calculator">450 / 344</gadget>
<output>225/172 = around 1.30814</output>

<gadget id="calculator">(225/172) * (5/4)</gadget>
<output>1_125/688 = around 1.635174</output>
<result>1_125/688 = around 1.635174</result>

Choices:
A. $ 1.50
B. $ 1.64
C. $ 2.25
D. $ 2.50
E. $ 3.25

multiply(divide(add(multiply(multiply(32, divide(75, const_100)), multiply(add(const_4, 1), const_2)), 210), add(multiply(subtract(multiply(add(const_4, 1), const_2), 3), 32), multiply(multiply(divide(add(const_100, 25), const_100), 3), 32))), divide(add(const_100, 25), const_100))

Explanation: "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 210 - - > x = 1.308 . 1.25 x = ~ 1.64 . answer : b ."


Question: the price of a certain painting increased by 30 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?

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

<gadget id="calculator">15 * 30</gadget>
<output>450</output>

<gadget id="calculator">450 / 100</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">15 - (9/2)</gadget>
<output>21/2 = around 10.5</output>

<gadget id="calculator">(21/2) + 100</gadget>
<output>221/2 = around 110.5</output>
<result>221/2 = around 110.5</result>

Choices:
A. 102 %
B. 105 %
C. 110.5 %
D. 112.5 %
E. 100 %

add(subtract(subtract(30, 15), divide(multiply(15, 30), const_100)), const_100)

Explanation: easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.15 = 130 * 0.85 = 110.5 hence required answer = ( 110.5 / 100 ) * 100 % = 110.5 % answer is c .


Question: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 27 more than the correct answer . find the number .

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

<gadget id="calculator">27 * (4/5)</gadget>
<output>108/5 = around 21.6</output>

<gadget id="calculator">(108/5) * (4/5)</gadget>
<output>432/25 = around 17.28</output>

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

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

<gadget id="calculator">(432/25) / (9/25)</gadget>
<output>48</output>

<gadget id="calculator">48 / (4/5)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 40
B. 50
C. 60
D. 70
E. 80

divide(divide(multiply(multiply(27, divide(4, 5)), divide(4, 5)), subtract(const_1, multiply(divide(4, 5), divide(4, 5)))), divide(4, 5))

Explanation: let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 27 25 x = 16 x + 540 9 x = 540 x = 60 the answer is c .


Question: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 150 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?

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

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

<gadget id="calculator">150 * (9/10)</gadget>
<output>135</output>

<gadget id="calculator">135 * (9/10)</gadget>
<output>243/2 = around 121.5</output>

<gadget id="calculator">(243/2) * (9/10)</gadget>
<output>2_187/20 = around 109.35</output>
<result>2_187/20 = around 109.35</result>

Choices:
A. 110
B. 146
C. 152
D. 162
E. 170

multiply(multiply(multiply(150, subtract(1, divide(1, 10))), subtract(1, divide(1, 10))), subtract(1, divide(1, 10)))

Explanation: "the probability of survival for each of the first 3 months of life is 1 - 1 / 10 = 9 / 10 , so of 150 newborn 150 * 9 / 10 * 9 / 10 * 9 / 10 = ~ 110 is expected to survive . answer : a ."


Question: the units digit of ( 35 ) ^ ( 7 ) + ( 93 ) ^ ( 45 ) is :

<gadget id="calculator">45 % 4</gadget>
<output>1</output>

<gadget id="calculator">1 * 93</gadget>
<output>93</output>

<gadget id="calculator">93 % 10</gadget>
<output>3</output>

<gadget id="calculator">35 % 10</gadget>
<output>5</output>

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

Choices:
A. 2
B. 4
C. 6
D. 8
E. 0

add(reminder(multiply(reminder(45, const_4), 93), const_10), reminder(35, const_10))

Explanation: "any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . done . the second term takes a little more work . we can ignore the tens digit , and just treat this base as 3 . here is the units digit patter for the powers of 3 . 3 ^ 45 has a units digit of 3 of course 5 + 3 = 8 , d"


Question: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 7 : 3 . if 70 % of the toyota bought and 30 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?

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

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

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

<gadget id="calculator">100 - 42</gadget>
<output>58</output>
<result>58</result>

Choices:
A. 76 %
B. 58 %
C. 68 %
D. 89 %
E. 49 %

subtract(const_100, add(multiply(7, 3), multiply(3, 7)))

Explanation: let total no of vehicles bought be 100 , toyota 70 and honda 30 , so total number of suv ' s bought for toyota and honda respectively 70 * 70 / 100 = 49 and 30 * 30 / 100 = 9 so total 58 suv ' s were bought out of 100 vehicles bought . . so required % is 58 % answer : b


Question: a can do a piece of work in 10 days , b in 15 days . they work for 5 days . the rest of work finished by c in 2 days . if they get rs 1500 for the whole work , the daily wages of b and c are ?

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

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

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

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

<gadget id="calculator">1 - (5/6)</gadget>
<output>1/6 = around 0.166667</output>

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

<gadget id="calculator">(1/12) * 2</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1_500 * (1/6)</gadget>
<output>250</output>

<gadget id="calculator">250 / 2</gadget>
<output>125</output>

<gadget id="calculator">(1/15) * 5</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 1_500</gadget>
<output>500</output>

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

<gadget id="calculator">125 + 100</gadget>
<output>225</output>
<result>225</result>

Choices:
A. 225
B. 276
C. 126
D. 187
E. 1267

add(divide(multiply(1500, multiply(divide(subtract(const_1, multiply(5, add(divide(const_1, 10), divide(const_1, 15)))), 2), 2)), 2), divide(multiply(multiply(divide(const_1, 15), 5), 1500), 5))

Explanation: explanation : let the total work = 30 units . then capacity of a = 3 units , b = 2 units . now they worked for 5 days . so they must have completed 25 units . rest of the work 5 units done by c in 2 days . so c capacity = 5 / 2 = 2.5 units . given that toatal wages are rs . 1500 for 30 units . so for 1 unit of work they get rs . 50 . now b and c per day work = ( 2 + 2.5 ) = 4.5 units . so their daily wages = 4.5 × 50 = rs . 225 answer : a


Question: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 20 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?

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

<gadget id="calculator">50 / (1/2)</gadget>
<output>100</output>

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

<gadget id="calculator">100 * (1/5)</gadget>
<output>20</output>

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

Choices:
A. $ 20
B. $ 40
C. $ 50
D. $ 80
E. $ 100

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

Explanation: cost + profit = income ( selling price ) profit now = 0.5 x or x - 50 0.5 x = x - 50 50 = 0.5 x x = 100 $ is selling price so , profit before was 0.2 * 100 = 20 $ cost = 100 - 20 = 80 $ answer : d


Question: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 900 responses are needed , what is the minimum number of questionnaires that should be mailed ?

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

<gadget id="calculator">900 / (3/5)</gadget>
<output>1_500</output>
<result>1_500</result>

Choices:
A. 1300
B. 1350
C. 1400
D. 1450
E. 1500

Explanation: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 900 x = 1500 the answer is e ."


Question: find the value o f 72519 x 9999 = m ?

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>

<gadget id="calculator">9_995 * 72_519</gadget>
<output>724_827_405</output>
<result>724_827_405</result>

Choices:
A. 434539873
B. 355797990
C. 435453490
D. m = 725117481
E. 873430134

Explanation: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"


Question: ( 4 ! ) ^ n is a factor of 12 ! , but ( 4 ! ) ^ ( n + 1 ) is not factor of 12 ! . what is the value of n ?

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

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

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

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

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

subtract(add(add(1, 4), divide(12, 12)), const_3)

Explanation: 12 ! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 4 ! = 24 question can be rephrased as how many 24 ' s are there in 12 ! 12 * 2 = 24 4 * 6 = 24 3 * 8 = 24 value of n = 3 answer : c


Question: a motorcyclist goes from bombay to pune , a distance of 256 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?

<gadget id="calculator">256 / 32</gadget>
<output>8</output>

<gadget id="calculator">256 / 8</gadget>
<output>32</output>

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

<gadget id="calculator">256 / 5</gadget>
<output>256/5 = around 51.2</output>

<gadget id="calculator">32 / (256/5)</gadget>
<output>5/8 = around 0.625</output>
<result>5/8 = around 0.625</result>

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

divide(divide(256, divide(256, 32)), divide(256, subtract(divide(256, 32), const_3)))

Explanation: "t = 256 / 32 = 8 h t = 8 - 3 = 5 time ratio = 8 : 5 speed ratio = 5 : 8 answer : e"


Question: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years x in which the population would be doubled assuming there is no emigration or immigration is

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

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

<gadget id="calculator">39.4 - 19.4</gadget>
<output>20</output>

<gadget id="calculator">20 / 1_000</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">(1/50) * 100</gadget>
<output>2</output>

<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 20
B. x = 25
C. x = 30
D. x = 35
E. 40

divide(subtract(const_100, multiply(const_10, const_3)), multiply(divide(subtract(39.4, 19.4), 1000), const_100))

Explanation: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."


Question: when the positive integer y is divided by 9 , the remainder is 5 . what is the remainder when 3 y is divided by 9 ?

<gadget id="calculator">9 + 5</gadget>
<output>14</output>

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

<gadget id="calculator">42 % 9</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 0
B. 1
C. 3
D. 4
E. 6

Explanation: lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y = 9 k + 5 multiplying by 3 will give 3 y = 27 k + 15 we can also write 3 y = 27 k + 9 + 6 now 27 k and 9 are divisible by 9 leaving the remainder as 6 hence e is the answer .


Question: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 70 th number in this set ?

<gadget id="calculator">70 - 1</gadget>
<output>69</output>

<gadget id="calculator">69 * 8</gadget>
<output>552</output>

<gadget id="calculator">552 + 5</gadget>
<output>557</output>
<result>557</result>

Choices:
A. 557
B. 608
C. 613
D. 616
E. 621

add(multiply(subtract(70, const_1), 8), 5)

Explanation: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 70 th number = 8 * ( 70 - 1 ) + 5 = 557 answer = a"


Question: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 122 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?

<gadget id="calculator">122 - 120</gadget>
<output>2</output>

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

<gadget id="calculator">4 / 120</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">120 / (1/30)</gadget>
<output>3_600</output>
<result>3_600</result>

Choices:
A. 600
B. 720
C. 1080
D. 2200
E. 3600

divide(120, divide(multiply(const_2, subtract(122, 120)), 120))

Explanation: "$ 120 for 2 years = $ 60 per year . extra $ 2 yearned with the compound interest is the percent yearned on percent . so , $ 2 is yearned on $ 60 , which means that the interest = 30 % . this on the other hand means that half of the savings = 60 * 30 = $ 1800 . twice of that = $ 3,600 . answer : e ."


Question: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 29 m * 2 m * 0.75 m ?

<gadget id="calculator">29 * 100</gadget>
<output>2_900</output>

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

<gadget id="calculator">2_900 * 200</gadget>
<output>580_000</output>

<gadget id="calculator">0.75 * 100</gadget>
<output>75</output>

<gadget id="calculator">580_000 * 75</gadget>
<output>43_500_000</output>

<gadget id="calculator">43_500_000 / 20</gadget>
<output>2_175_000</output>

<gadget id="calculator">2_175_000 / 10</gadget>
<output>217_500</output>

<gadget id="calculator">217_500 / 7.5</gadget>
<output>29_000</output>
<result>29_000</result>

Choices:
A. 29000
B. 27908
C. 78902
D. 25000
E. 27991

divide(divide(divide(multiply(multiply(multiply(29, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5)

Explanation: "29 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 29 = 1 / 100 * x = > x = 29000 answer : a"


Question: on a map , 1 inch represents 28 miles . how many b inches would be necessary to represent a distance of 383.6 miles ?

<gadget id="calculator">383.6 / 28</gadget>
<output>13.7</output>
<result>13.7</result>

Choices:
A. 5.2
B. 7.4
C. 13.7
D. 21.2
E. 28.7

Explanation: b inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c


Question: a worker is paid a regular rate of rs . 30 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 20 % higher than her regular rate . if she completed 50 surveys involving the use of her cellphone , how much did she get that week ?

<gadget id="calculator">30 * 100</gadget>
<output>3_000</output>

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

<gadget id="calculator">30 * (1/5)</gadget>
<output>6</output>

<gadget id="calculator">50 * 6</gadget>
<output>300</output>

<gadget id="calculator">3_000 + 300</gadget>
<output>3_300</output>
<result>3_300</result>

Choices:
A. 2200
B. 1100
C. 2500
D. 2800
E. 3300

add(multiply(30, 100), multiply(50, multiply(30, divide(20, 100))))

Explanation: "amount earned using her cell phone = 50 * 36 = 1800 earned for remaining surveys = 50 * 30 = 1500 total earning = 3300 answer : e"


Question: a man goes from a to b at a speed of 20 kmph and comes back to a at a speed of 30 kmph . find his average speed for the entire journey ?

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

<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 11
B. 24
C. 55
D. 66
E. 71

Explanation: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 20 ) + ( d / 30 ) ] = ( 2 d ) / [ 5 d / 60 ) = > 24 kmph . answer : b"


Question: find the maximum value of the function f ( x ) = x − 5 if x is a number between - 5 and 13 .

<gadget id="calculator">13 - 5</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. none

Explanation: solution : since f ( x ) is a linear function whose slope is 1 , a positive number , it is strictly increasing for all x . therefore its maximal value is reached for the largest value of x , x = 13 and f ( x ) = 13 - 5 = 8 . answer c


Question: a shopkeeper sold 30 articles at the cost price of 35 articles . then find the profit % or lost %

<gadget id="calculator">35 - 30</gadget>
<output>5</output>

<gadget id="calculator">5 / 30</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) * 100</gadget>
<output>50/3 = around 16.666667</output>
<result>50/3 = around 16.666667</result>

Choices:
A. 12 %
B. 15 %
C. 16.67 %
D. 18 %
E. 22 %

multiply(divide(subtract(35, 30), 30), const_100)

Explanation: "here 30 articles selling price = 35 articles cost price so the difference = 35 - 30 = 5 % of profit = 5 * 100 / 30 = 16.67 % correct option is c"


Question: a cycle is bought for rs . 900 and sold for rs . 1140 , find the gain percent ?

<gadget id="calculator">1_140 - 900</gadget>
<output>240</output>

<gadget id="calculator">240 / 900</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">(4/15) * 100</gadget>
<output>80/3 = around 26.666667</output>
<result>80/3 = around 26.666667</result>

Choices:
A. 11
B. 27
C. 99
D. 77
E. 18

multiply(divide(subtract(1140, 900), 900), const_100)

Explanation: "900 - - - - 240 100 - - - - ? = > 27 % answer : b"


Question: the average of 5 quantities is 12 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?

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

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

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

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

Choices:
A. 24
B. 10
C. 8
D. 9.5
E. none of these

divide(subtract(multiply(5, 12), multiply(3, 4)), 2)

Explanation: "answer : a ( 5 x 12 - 3 x 4 ) / 2 = 24"


Question: a trained covered x km at 30 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .

<gadget id="calculator">30 * 3</gadget>
<output>90</output>

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

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

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

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

<gadget id="calculator">90 / 4</gadget>
<output>45/2 = around 22.5</output>
<result>45/2 = around 22.5</result>

Choices:
A. 22.5
B. 99
C. 24
D. 66
E. 887

divide(multiply(30, 3), add(divide(30, 30), divide(multiply(2, 30), 20)))

Explanation: "total time taken = x / 30 + 2 x / 20 hours = 2 x / 15 hours average speed = 3 x / ( 2 x / 15 ) = 22.5 kmph answer : a"


Question: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 28,000 is made ?

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

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

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

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

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

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

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

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

<gadget id="calculator">500 * 100</gadget>
<output>50_000</output>

<gadget id="calculator">100_000 + 50_000</gadget>
<output>150_000</output>

<gadget id="calculator">(16/25) * 150_000</gadget>
<output>96_000</output>

<gadget id="calculator">20 + 2</gadget>
<output>22</output>

<gadget id="calculator">22 * 100</gadget>
<output>2_200</output>

<gadget id="calculator">2_200 * 10</gadget>
<output>22_000</output>

<gadget id="calculator">96_000 + 22_000</gadget>
<output>118_000</output>
<result>118_000</result>

Choices:
A. 328897
B. 120000
C. 877888
D. 124000
E. 188871

add(multiply(multiply(subtract(1, divide(20, const_100)), subtract(1, divide(20, const_100))), add(multiply(multiply(const_100, const_100), sqrt(const_100)), multiply(multiply(divide(sqrt(const_100), const_2), const_100), const_100))), multiply(multiply(add(20, const_2), const_100), sqrt(const_100)))

Explanation: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 28,000 is made = 96,000 + 28,000 = rs . 1 , 24,000 answer : d"


Question: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 60 and the turban . find the price of the turban .

<gadget id="calculator">90 - 60</gadget>
<output>30</output>

<gadget id="calculator">12 - 9</gadget>
<output>3</output>

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

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

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

Choices:
A. 27
B. 30
C. 29
D. 10
E. 11

subtract(multiply(divide(subtract(90, 60), subtract(const_12, 9)), const_12), 90)

Explanation: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 60 . thus , 3434 ( 90 + x ) = 60 + x or 270 + 3 x = 240 + 4 x or x = 30 answer : b"


Question: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1450 ?

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

<gadget id="calculator">15 + 3</gadget>
<output>18</output>

<gadget id="calculator">18 / 5</gadget>
<output>18/5 = around 3.6</output>

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

<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>

<gadget id="calculator">(9/50) + 1</gadget>
<output>59/50 = around 1.18</output>

<gadget id="calculator">1_450 / (59/50)</gadget>
<output>72_500/59 = around 1_228.813559</output>
<result>72_500/59 = around 1_228.813559</result>

Choices:
A. rs . 1000
B. rs . 1250
C. rs . 1010
D. rs . 10000
E. none of these

divide(1450, add(divide(multiply(divide(add(multiply(3, 5), 3), 5), 5), const_100), const_1))

Explanation: "explanation : 1450 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1250 answer : option b"


Question: how many seconds will a 600 metre 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">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">63 - 3</gadget>
<output>60</output>

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

<gadget id="calculator">600 / (50/3)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 25
B. 36
C. 40
D. 45
E. 50

divide(600, multiply(const_0_2778, subtract(63, 3)))

Explanation: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 600 * 3 / 50 = 36 sec answer : b"


Question: a ship 450 m long is running at a speed of 24 km / hr . in what time will it pass a bridge 900 m long ?

<gadget id="calculator">450 + 900</gadget>
<output>1_350</output>

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

<gadget id="calculator">24 * (5/18)</gadget>
<output>20/3 = around 6.666667</output>

<gadget id="calculator">1_350 / (20/3)</gadget>
<output>405/2 = around 202.5</output>
<result>405/2 = around 202.5</result>

Choices:
A. 202.5 sec
B. 205.5 sec
C. 200 sec
D. 1350 sec
E. 900 sec

Explanation: total length = 450 + 900 = 1350 speed = 24 km / h = ( 24 * 5 ) / 18 = 20 / 3 m / s time = ( 1350 * 3 ) / 20 = 202.5 sec . answer : a


Question: p has $ 32 more than what q and r together would have had if both b and c had 1 / 6 of what p has . how much does p have ?

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

<gadget id="calculator">(1/6) * 2</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">32 / (2/3)</gadget>
<output>48</output>
<result>48</result>

Choices:
A. $ 44
B. $ 48
C. $ 52
D. $ 56
E. $ 60

divide(32, subtract(1, multiply(divide(1, 6), const_2)))

Explanation: "p = ( 2 / 6 ) * p + 32 ( 4 / 6 ) * p = 32 p = 48 the answer is b ."


Question: a salt manufacturing company produced a total of 2000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?

<gadget id="calculator">2_000 * 2</gadget>
<output>4_000</output>

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

<gadget id="calculator">11 * 100</gadget>
<output>1_100</output>

<gadget id="calculator">4_000 + 1_100</gadget>
<output>5_100</output>

<gadget id="calculator">5_100 * 12</gadget>
<output>61_200</output>

<gadget id="calculator">61_200 / 2</gadget>
<output>30_600</output>

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

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

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

<gadget id="calculator">300 + 60</gadget>
<output>360</output>

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

<gadget id="calculator">360 + 5</gadget>
<output>365</output>

<gadget id="calculator">30_600 / 365</gadget>
<output>6_120/73 = around 83.835616</output>
<result>6_120/73 = around 83.835616</result>

Choices:
A. 80
B. 85
C. 83
D. 95
E. 00

divide(divide(multiply(add(multiply(2000, const_2), multiply(subtract(const_12, const_1), 100)), const_12), const_2), add(add(multiply(const_3, 100), multiply(multiply(const_2, const_3), const_10)), add(const_2, const_3)))

Explanation: "total production of salt by the company in that year = 2000 + 2100 + 2200 + . . . . + 3100 = 30600 . average monthly production of salt for that year = 30600 / 365 â ‰ ˆ 84 answer : c"


Question: how many terminating zeroes e does 200 ! have ?

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

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

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

<gadget id="calculator">200 / 25</gadget>
<output>8</output>

<gadget id="calculator">40 + 8</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 40
B. 48
C. 49
D. 55
E. 64

add(divide(200, add(const_4, const_1)), divide(200, multiply(add(const_4, const_1), add(const_4, const_1))))

Explanation: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c


Question: the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 16 years old . what is the value of n ?

<gadget id="calculator">32 - 16</gadget>
<output>16</output>

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

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

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

divide(subtract(32, 16), subtract(16, 14))

Explanation: "14 n + 32 = 16 ( n + 1 ) 2 n = 16 n = 8 the answer is d ."


Question: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 216 . find the principal ?

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

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

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

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

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

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

<gadget id="calculator">216 / (1/25)</gadget>
<output>5_400</output>
<result>5_400</result>

Choices:
A. 2277
B. 2667
C. 5400
D. 2766
E. 1811

divide(216, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1)))

Explanation: "p = 216 ( 100 / 5 ) ^ 2 = > p = 5400 answer : c"


Question: a train running at the speed of 60 km / hr crosses a pole in 15 sec . what is the length of the train ?

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>

<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) * 15</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 287
B. 699
C. 250
D. 168
E. 150

multiply(divide(multiply(60, const_1000), const_3600), 15)

Explanation: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 250 m answer : c"


Question: rewrite ( 10 ^ 38 ) – 85 as a base 10 integer , what is the sum of the digits in that integer ?

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

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

<gadget id="calculator">36 * 9</gadget>
<output>324</output>

<gadget id="calculator">324 + 1</gadget>
<output>325</output>

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

<gadget id="calculator">325 + 5</gadget>
<output>330</output>
<result>330</result>

Choices:
A. 354
B. 357
C. 330
D. 370
E. 360

add(add(multiply(subtract(38, const_2), subtract(const_10, const_1)), const_1), add(const_2, const_3))

Explanation: we know that ( 10 ^ 38 ) is ending 00 , so ( 10 ^ 38 ) – 85 = 9 . . . . 9915 total number of digits in ( 10 ^ 38 ) – 85 is 38 , or 36 digits of 9 and two digits 1 and 5 . answer choice is 36 * 9 + 6 = 330 answer is c 330


Question: he average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?

<gadget id="calculator">23 + 4</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 26
B. 27
C. 88
D. 99
E. 12

Explanation: sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b


Question: a man buy a book in rs 50 & sale it rs 70 . what is the rate of profit ? ? ?

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

<gadget id="calculator">20 / 50</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 10 %
B. 40 %
C. 30 %
D. 25 %
E. 28 %

multiply(divide(subtract(70, 50), 50), const_100)

Explanation: "cp = 50 sp = 70 profit = 70 - 50 = 20 % = 20 / 50 * 100 = 40 % answer : b"


Question: a tank is filled by 3 pipes a , b , c in 6 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?

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

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

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

<gadget id="calculator">7 * 6</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 25 hr
B. 42 hr
C. 40 hr
D. 20 hr
E. 50 hr

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

Explanation: suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 6 7 / x = 1 / 6 x = 42 hours answer is b


Question: first column specifies the no of days prior to departure information . second column specifies the percentage discount offered . 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % 14 - 29 days = = > 25 % 30 days or more = = > 40 % the table above shows the discount structure for advanced purchase of tickets at a particular airline . a passenger bought a ticket at this airline for $ 1050 . the ticket agent informed her that , had she purchased the ticket one day later , she would have paid $ 210 more . how many days before her departure did she purchase her ticket .

<gadget id="calculator">7 * 4</gadget>
<output>28</output>

<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 6
B. 7
C. 13
D. 14
E. 29

Explanation: first i figured out the percentage change from the immediate previous amount for each of the period . thus it comes - 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % ( 90 % of the price ) 14 - 29 days = = > 17 % ( approx ) ( went from 90 % to 75 % ) 30 days or more = = > 20 % ( went from 75 % to 60 % ) if the passenger had to pay the extra amount , she had to pay = ( 210 + 1050 ) = 1260 now 210 is somehow between 10 % and 20 % of 1260 . so 17 % is the choice here . correct ans : 14 days answer : d


Question: a no . when divided by 158 gives a remainder 50 , what remainder will be obtainedby dividingthe same no . 16 ?

<gadget id="calculator">158 + 50</gadget>
<output>208</output>

<gadget id="calculator">208 / 16</gadget>
<output>13</output>
<result>13</result>

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

Explanation: "158 + 50 = 208 / 16 = 13 ( remainder ) d"


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

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

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

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

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

<gadget id="calculator">12 + 16</gadget>
<output>28</output>

<gadget id="calculator">2 ** 5</gadget>
<output>32</output>

<gadget id="calculator">28 + 32</gadget>
<output>60</output>

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

Choices:
A. - 14
B. - 60
C. 0
D. 4
E. 14

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

Explanation: "if a = - 1 , then putting values in equation = - [ ( 2 ) ^ 2 + ( 2 ) ^ 3 + ( 2 ^ 4 ) + ( 2 ^ 5 ) ] = - [ 4 + 8 + 16 + 32 ] = - 60 answer = b = - 60"


Question: a clock shows the time as 9 a . m . if the minute hand gains 7 minutes every hour , how many minutes will the clock gain by 6 p . m . ?

<gadget id="calculator">3 + 6</gadget>
<output>9</output>

<gadget id="calculator">9 * 7</gadget>
<output>63</output>
<result>63</result>

Choices:
A. 30 min
B. 35 min
C. 63 min
D. 50 min
E. 55 min

Explanation: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 7 = 63 minutes . answer : c"


Question: how much interest will $ 10,000 earn in 9 months at an annual rate of 4 % ?

<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>

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

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

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

<gadget id="calculator">400 * (3/4)</gadget>
<output>300</output>
<result>300</result>

Choices:
A. $ 300
B. $ 350
C. $ 450
D. $ 550
E. $ 650

multiply(multiply(power(const_100, const_2), divide(4, const_100)), divide(const_3, const_4))

Explanation: soln : - 9 months = 3 / 4 of year ; 4 % = 4 / 100 = 1 / 25 ; $ 10,000 ( principal ) * 1 / 25 ( interest rate ) * 3 / 4 ( time ) = $ 300 . answer : a


Question: if the perimeter of a rectangular garden is 700 m , its length when its breadth is 100 m is ?

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

<gadget id="calculator">350 - 100</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 299 m
B. 777 m
C. 200 m
D. 250 m
E. 128 m

Explanation: "2 ( l + 100 ) = 700 = > l = 250 m answer : d"


Question: you have been given a physical balance and 7 weights of 40 , 42 , 36 , 33 , 47 , 52 and 67 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 169 kgs .

<gadget id="calculator">42 + 36</gadget>
<output>78</output>

<gadget id="calculator">78 + 33</gadget>
<output>111</output>

<gadget id="calculator">111 + 52</gadget>
<output>163</output>
<result>163</result>

Choices:
A. 163
B. 166
C. 162
D. 164
E. 165

Explanation: "67 + 52 + 47 = 166 answer : e"


Question: a shopkeeper loses 15 % , if an article is sold for rs . 102 . what should be the selling price of the article to gain 20 % ?

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

<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">102 / (17/20)</gadget>
<output>120</output>

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

<gadget id="calculator">120 * (1/5)</gadget>
<output>24</output>

<gadget id="calculator">120 + 24</gadget>
<output>144</output>
<result>144</result>

Choices:
A. rs . 146
B. rs . 144
C. rs . 129
D. rs . 123
E. rs . 128

add(divide(102, subtract(const_1, divide(15, const_100))), multiply(divide(102, subtract(const_1, divide(15, const_100))), divide(20, const_100)))

Explanation: "given that sp = rs . 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = rs . 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = rs . 144 answer : b"


Question: sum of the squares of 3 no . ' s is 62 and the sum of their products taken two at a time is 131 . find the sum ?

<gadget id="calculator">131 * 2</gadget>
<output>262</output>

<gadget id="calculator">262 + 62</gadget>
<output>324</output>

<gadget id="calculator">324 ** (1/2)</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 20
B. 24
C. 26
D. 18
E. 30

Explanation: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 62 + 2 * 131 a + b + c = √ 324 = 18 d"


Question: some persons can do a piece of work in 12 days . two times the number of these people will do half of that work in ?

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

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

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

Choices:
A. 3
B. 4
C. 5
D. 6
E. 8

multiply(multiply(12, divide(const_1, const_2)), divide(const_1, const_2))

Explanation: "12 / ( 2 * 2 ) = 3 days answer : a"


Question: how many multiples of 4 are there between 12 and 92 , inclusive ?

<gadget id="calculator">92 - 12</gadget>
<output>80</output>

<gadget id="calculator">80 / 4</gadget>
<output>20</output>

<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<result>21</result>

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

add(divide(subtract(92, 12), 4), const_1)

Explanation: "the multiples of 4 are from 4 * 3 up to 4 * 23 . 23 - 3 + 1 = 21 . the answer is a ."


Question: a metered rikshaw charges rs 13.50 for the first 1 km and 2.50 per 1 / 3 km there after . what would the charge if this rikshaw is hired for 13 kms ? in approx ? ?

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

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

<gadget id="calculator">12 / (1/3)</gadget>
<output>36</output>

<gadget id="calculator">36 * 2.5</gadget>
<output>90</output>

<gadget id="calculator">13.5 + 90</gadget>
<output>103.5</output>
<result>103.5</result>

Choices:
A. 103.5 rs
B. 104.5 rs
C. 105.5 rs
D. 106.5 rs
E. 107.5 rs

add(13.5, multiply(divide(subtract(13, 1), divide(1, 3)), 2.5))

Explanation: for 1 st km : rs . 13.50 ramaining distance : 13 - 1 = 12 km 1 / 3 km costs 2.5 rs 1 km costs ( 2.5 * 3 ) remaining 12 km costs ( 2.5 * 3 ) * 12 = 90 rs total cost = 90 + 13.5 = 103.5 rs answer : a


Question: two pipes a and b separately fill in 15 / 2 min and 5 min respactively and third pipe c can empty of 14 l / m if all the pipes are open when the cistern is full , it is emptied in 1 hr . how many litres does the cistern hold ?

<gadget id="calculator">14 * 60</gadget>
<output>840</output>

<gadget id="calculator">2 / 15</gadget>
<output>2/15 = around 0.133333</output>

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

<gadget id="calculator">(2/15) + (1/5)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 60</gadget>
<output>20</output>

<gadget id="calculator">20 + 1</gadget>
<output>21</output>

<gadget id="calculator">840 / 21</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40
B. 30
C. 50
D. 80
E. 54

divide(multiply(14, const_60), add(multiply(add(divide(2, 15), divide(1, 5)), const_60), 1))

Explanation: let total water in cistern = x liter speed of a = 2 x / 15 l / m ( speed = liter / time ) speed of b = x / 5 l / m speed of c = 14 l / m according to question x + ( x / 5 + 2 x / 15 ) * 60 = 60 * 14 x + = 60 * 14 x = 40 liter answer : a


Question: a fruit seller sells mangoes at the rate of rs . 12 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 15 % ?

<gadget id="calculator">100 + 15</gadget>
<output>115</output>

<gadget id="calculator">12 * 115</gadget>
<output>1_380</output>

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

<gadget id="calculator">1_380 / 90</gadget>
<output>46/3 = around 15.333333</output>
<result>46/3 = around 15.333333</result>

Choices:
A. rs . 11.81
B. rs . 12
C. rs . 15.33
D. rs . 12.31
E. none

divide(multiply(12, add(const_100, 15)), subtract(const_100, 10))

Explanation: "solution 90 : 12 = 115 : x x = ( 12 ã — 115 / 90 ) = rs . 15.33 hence , s . p per kg = rs . 15.33 answer c"


Question: two numbers have a h . c . f of 20 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?

<gadget id="calculator">2_560 / 20</gadget>
<output>128</output>
<result>128</result>

Choices:
A. 140
B. 150
C. 160
D. 128
E. 180

Explanation: l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 20 = 128 . answer : d


Question: a cylindrical bucket of height 36 cm and radius 21 cm is filled with sand . the bucket is emptied on the ground and a conical heap of sand is formed , the height of the heap being 12 cm . the radius of the heap at the base is :

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

<gadget id="calculator">441 * 36</gadget>
<output>15_876</output>

<gadget id="calculator">15_876 / 4</gadget>
<output>3_969</output>

<gadget id="calculator">3_969 ** (1/2)</gadget>
<output>63</output>
<result>63</result>

Choices:
A. 63 cm
B. 53 cm
C. 56 cm
D. 66 cm
E. none of these

sqrt(divide(multiply(multiply(21, 21), 36), const_4))

Explanation: volume of the bucket = volume of the sand emptied volume of sand = π ( 21 ) 2 × 36 let r be the radius of the conical heap . then , 1 ⁄ 3 π r 2 × 12 = π ( 21 ) 2 × 36 or r 2 = ( 21 ) 2 × 9 or r = 21 × 3 = 63 answer a


Question: a man opens a shop . he buys water bottles for 50 cents each , fruit for 25 cents each , and snacks for a dollar each . he wants to start a bundle of selling a bottle a water , 3 snacks and 2 fruits for d dollars . every 5 th bundle sold will be sold for 2 dollars and a complimentary snack at the owner ' s expense . what should he charge at least to not lose any money ?

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

<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>

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

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

<gadget id="calculator">4 + (1/2)</gadget>
<output>9/2 = around 4.5</output>

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

<gadget id="calculator">(9/2) + (1/10)</gadget>
<output>23/5 = around 4.6</output>
<result>23/5 = around 4.6</result>

Choices:
A. 4.6
B. 3.0
C. 4.1
D. 3.2
E. 2.9

add(add(add(multiply(3, const_1), multiply(2, divide(5, const_10))), divide(5, const_10)), divide(const_1, const_10))

Explanation: w = 0.50 f = 0.25 s = 1.00 b = w + 2 f + 3 s = 4.00 they pay , he pays 4 , net loss 0 fifth bundle = 2 they pay , he pays 5 , net loss 3 dollars 3 / 5 = 60 cents . charging 60 more cents on each bundle will be safe . answer : a


Question: a person is traveling at 75 km / hr and reached his destiny in 4 hr then find the distance ?

<gadget id="calculator">75 * 4</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 300 km
B. 200 km
C. 250 km
D. 400 km
E. 220 km

Explanation: "t = 4 hrs d = t * s = 75 * 4 = 300 km answer is a"


Question: a box contains 11 apples , 10 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?

<gadget id="calculator">0.5 * 10</gadget>
<output>5</output>

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

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

Explanation: p ( choosing a red apple 6 times in a row ) = 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 11 < 0.5 the answer is d .


Question: if the price of a certain computer increased 30 percent from x dollars to 351 dollars , then 2 x =

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

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

<gadget id="calculator">351 / (13/10)</gadget>
<output>270</output>

<gadget id="calculator">270 * 2</gadget>
<output>540</output>
<result>540</result>

Choices:
A. 540
B. 570
C. 619
D. 649
E. 700

multiply(divide(351, divide(add(const_100, 30), const_100)), 2)

Explanation: "before price increase price = x after 30 % price increase price = x + ( 30 / 100 ) * x = 1.3 x = 351 ( given ) i . e . x = 351 / 1.3 = $ 270 i . e . 2 x = 2 * 270 = 540 answer : option a"


Question: in the mundane goblet competition , 6 teams compete in a “ round robin ” format : that is , each team plays every other team exactly once . a team gets 3 points for a win , 1 point for a tie ( a draw ) , and 0 points for a loss . what is the difference between the maximum total points and the minimum total points that can be gained by all teams ( added together ) in the mundane goblet competition ?

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

<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 15
B. 30
C. 45
D. 60
E. 75

Explanation: no oa yet : my method : max points : a b c d e f 15 12 9 6 3 0 = 45 points min points a b c d e f 5 5 5 5 5 5 = 30 45 - 30 = 15 points = = = = > ( a ) ans


Question: a can do a job in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?

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

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

<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>

<gadget id="calculator">4 * (7/60)</gadget>
<output>7/15 = around 0.466667</output>

<gadget id="calculator">1 - (7/15)</gadget>
<output>8/15 = around 0.533333</output>
<result>8/15 = around 0.533333</result>

Choices:
A. 2 / 15
B. 8 / 15
C. 3 / 11
D. 1 / 12
E. 6 / 13

subtract(const_1, multiply(4, add(divide(const_1, 15), divide(const_1, 20))))

Explanation: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 4 days work = 7 / 60 * 4 = 7 / 15 remaining work = 1 - 7 / 15 = 8 / 15 answer is b"


Question: diana is painting statues . she has 3 / 6 of a gallon of paint remaining . each statue requires 1 / 6 gallon of paint . how many statues can she paint ?

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

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

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

Choices:
A. 3
B. 20
C. 28
D. 14
E. 19

Explanation: "number of statues = all the paint ÷ amount used per statue = 3 / 6 ÷ 1 / 6 = 3 / 6 * 6 / 1 = 3 / 1 = 3 answer is a ."


Question: jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 5 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 9 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?

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

<gadget id="calculator">240 / 8</gadget>
<output>30</output>

<gadget id="calculator">30 * 9</gadget>
<output>270</output>
<result>270</result>

Choices:
A. 180
B. 210
C. 240
D. 270
E. 300

Explanation: the relative speed of jack and christina is 5 + 3 = 8 feet per second . the distance between them is 240 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 8 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 9 * 30 = 270 feet . answer : d .


Question: the average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .

<gadget id="calculator">16 * 50.25</gadget>
<output>804</output>

<gadget id="calculator">8 * 45.15</gadget>
<output>361.2</output>

<gadget id="calculator">804 + 361.2</gadget>
<output>1_165.2</output>

<gadget id="calculator">16 + 8</gadget>
<output>24</output>

<gadget id="calculator">1_165.2 / 24</gadget>
<output>48.55</output>
<result>48.55</result>

Choices:
A. 47.55 kg
B. 48 kg
C. 48.55 kg
D. 49.25 kg
E. 59.25 kg

Explanation: "16 * 50.25 + 8 * 45.15 / 24 = 48.55 answer : c"


Question: how much water should be added to 13 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?

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

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

<gadget id="calculator">(3/4) * 20</gadget>
<output>15</output>

<gadget id="calculator">20 - 15</gadget>
<output>5</output>

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

<gadget id="calculator">40 - 13</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 25 liters
B. 27 liters
C. 30 liters
D. 32 liters
E. 35 liters

subtract(divide(multiply(const_2, const_100), subtract(20, multiply(divide(75, const_100), 20))), 13)

Explanation: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 13 + x ) ) ) 2 = 5 % * ( 13 + x ) - - - - - - - - > x = 27 ans b"


Question: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.7 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :

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

<gadget id="calculator">16.7 - 15.8</gadget>
<output>0.9</output>

<gadget id="calculator">0.4 / 0.9</gadget>
<output>0.444444</output>
<result>0.444444</result>

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

Explanation: "let the ratio be k : 1 . then , k * 16.7 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.7 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.9 = 4 / 9 required ratio = 4 / 9 : 1 = 4 : 9 . answer : e"


Question: a number when divided by a divisor leaves a remainder of 30 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?

<gadget id="calculator">30 + 11</gadget>
<output>41</output>
<result>41</result>

Choices:
A. 12
B. 13
C. 35
D. 43
E. 59

Explanation: let the number is n , the divisor = d , i will make the two equations - n = xd + 30 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 43 as d is also integer and 43 is a prime number , the d should be 43 to satisfy the above equation . hence answer is ' d '


Question: a student got twice as many sums wrong as he got right . if he attempted 36 sums in all , how many did he solve correctly ?

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

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

Choices:
A. 12
B. 16
C. 18
D. 24
E. 26

Explanation: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 36 3 x = 36 x = 12 . answer : a"


Question: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 8 ounces of corn syrup , how many ounces of water does it contain ?

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

<gadget id="calculator">(1/12) * 3</gadget>
<output>1/4 = around 0.25</output>

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

<gadget id="calculator">(1/30) / 2</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">(1/4) / (1/60)</gadget>
<output>15</output>

<gadget id="calculator">15 * 8</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 45
B. 50
C. 55
D. 60
E. 120

multiply(divide(multiply(divide(1, 12), const_3), divide(divide(1, 30), const_2)), 8)

Explanation: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 8 * 180 / 12 = 120 ounces of water e"


Question: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability q this college graduate has a graduate degree ?

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

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

<gadget id="calculator">(1/8) / (2/3)</gadget>
<output>3/16 = around 0.1875</output>

<gadget id="calculator">(3/16) + 1</gadget>
<output>19/16 = around 1.1875</output>

<gadget id="calculator">(3/16) / (19/16)</gadget>
<output>3/19 = around 0.157895</output>
<result>3/19 = around 0.157895</result>

Choices:
A. 1 / 11
B. 1 / 12
C. 1 / 13
D. 3 / 19
E. 3 / 43

divide(divide(divide(1, 8), divide(2, 3)), add(divide(divide(1, 8), divide(2, 3)), 1))

Explanation: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability of cgd / ( cg ) q - > 3 / 19 answer d"


Question: solution y is 20 percent liquid x and 80 percent water . if 2 kilograms of water evaporate from 8 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?

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

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

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

<gadget id="calculator">(8/5) + (2/5)</gadget>
<output>2</output>

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">8 * (4/5)</gadget>
<output>32/5 = around 6.4</output>

<gadget id="calculator">(32/5) - 2</gadget>
<output>22/5 = around 4.4</output>

<gadget id="calculator">2 * (4/5)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(22/5) + (8/5)</gadget>
<output>6</output>

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

<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 20 %
B. 21 1 / 2 %
C. 22 %
D. 24 %
E. 25 %

multiply(const_100, divide(add(multiply(8, divide(20, const_100)), multiply(2, divide(20, const_100))), add(add(multiply(8, divide(20, const_100)), multiply(2, divide(20, const_100))), add(subtract(multiply(8, divide(80, const_100)), 2), multiply(2, divide(80, const_100))))))

Explanation: "in 8 kilograms of solution y there are 0.2 * 8 = 1.6 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.2 * 2 = 0.4 kilograms of solution x are added , so in the new solution of 8 kilograms there are 1.6 + 0.4 = 2 kilograms of solution x , which is 2 / 8 * 100 = 25 % of this new solution . answer : e ."


Question: 20.036 divided by 0.04 gives :

<gadget id="calculator">20.036 / 0.04</gadget>
<output>500.9</output>
<result>500.9</result>

Choices:
A. 50.09
B. 5.06
C. 50.06
D. 100.9
E. 500.9

Explanation: "= 20.036 / 0.04 = 2003.6 / 4 = 500.9 answer is e ."


Question: the ratio between the sale price and the cost price of an article is 12 : 7 . what is the ratio between the profit and the cost price of that article ?

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

<gadget id="calculator">5 / 7</gadget>
<output>5/7 = around 0.714286</output>
<result>5/7 = around 0.714286</result>

Choices:
A. 2 : 9
B. 2 : 5
C. 3 : 6
D. 5 : 7
E. 2 : 1

Explanation: "let c . p . = rs . 7 x and s . p . = rs . 12 x . then , gain = rs . 5 x required ratio = 5 x : 7 x = 5 : 7 answer : d"


Question: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6800 ?

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

<gadget id="calculator">6 * 6_800</gadget>
<output>40_800</output>

<gadget id="calculator">6_435 + 6_927</gadget>
<output>13_362</output>

<gadget id="calculator">13_362 + 6_855</gadget>
<output>20_217</output>

<gadget id="calculator">20_217 + 7_230</gadget>
<output>27_447</output>

<gadget id="calculator">27_447 + 6_562</gadget>
<output>34_009</output>

<gadget id="calculator">40_800 - 34_009</gadget>
<output>6_791</output>
<result>6_791</result>

Choices:
A. s . 4991
B. s . 5991
C. s . 6001
D. s . 6791
E. s . 7991

Explanation: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6800 * 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 . answer : d"


Question: sakshi can do a piece of work in 12 days . tanya is 20 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is ?

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

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

<gadget id="calculator">12 / (6/5)</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 10
B. 12
C. 14
D. 16
E. 18

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

Explanation: "ratio of times taken by sakshi and tanys = 120 : 100 = 6 : 5 suppose tanya takes x days to do the work . 6 : 5 : : 12 : x = > x = 10 days . hence , tanya takes 10 days to complete the work . answer : a"


Question: a river 4 m deep and 40 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?

<gadget id="calculator">4 * 40</gadget>
<output>160</output>

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

<gadget id="calculator">160 * 4_000</gadget>
<output>640_000</output>

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

<gadget id="calculator">640_000 / 60</gadget>
<output>32_000/3 = around 10_666.666667</output>
<result>32_000/3 = around 10_666.666667</result>

Choices:
A. 10666
B. 11678
C. 12345
D. 10678
E. 19099

divide(multiply(multiply(4, 40), multiply(4, const_1000)), multiply(const_1, const_60))

Explanation: "( 4000 * 4 * 40 ) / 60 = 10666 m 3 answer : a"


Question: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water is :

<gadget id="calculator">11 + 5</gadget>
<output>16</output>

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

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

Explanation: "solution speed in still water = 1 / 2 ( 11 + 5 ) kmph = 8 kmph . answer c"


Question: what least number should be subtracted from 1398 so that the remainder when divided by 7 , 9 , and 11 will leave in each case the same remainder 5 ?

<gadget id="calculator">7 * 9</gadget>
<output>63</output>

<gadget id="calculator">63 * 11</gadget>
<output>693</output>

<gadget id="calculator">693 * 2</gadget>
<output>1_386</output>

<gadget id="calculator">1_386 + 5</gadget>
<output>1_391</output>

<gadget id="calculator">1_398 - 1_391</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 6
B. 7
C. 8
D. 10
E. 11

subtract(1398, add(multiply(multiply(multiply(7, 9), 11), const_2), 5))

Explanation: "the lcm of 7 , 9 , and 11 is 693 . the next multiple is 2 * 693 = 1386 . 1386 + { remainder } = 1386 + 5 = 1391 , which is 7 less than 1398 . answer : b ."


Question: if the sides of a triangle are 32 cm , 27 cm and 12 cm , what is its area ?

<gadget id="calculator">27 * 12</gadget>
<output>324</output>

<gadget id="calculator">324 / 2</gadget>
<output>162</output>
<result>162</result>

Choices:
A. 120 cm 2
B. 112 cm 2
C. 162 cm 2
D. 666 cm 2
E. 886 cm 2

Explanation: "the triangle with sides 32 cm , 27 cm and 12 cm is right angled , where the hypotenuse is 32 cm . area of the triangle = 1 / 2 * 27 * 12 = 162 cm 2 answer : c"


Question: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1233 . find the number to be multiplied .

<gadget id="calculator">43 - 34</gadget>
<output>9</output>

<gadget id="calculator">1_233 / 9</gadget>
<output>137</output>
<result>137</result>

Choices:
A. 130
B. 132
C. 134
D. 137
E. 138

Explanation: "let the required number be x . then , 43 x – 34 x = 1233 or 9 x = 1233 or x = 137 . required number = 137 . answer : d"


Question: two letters from the word barkhint are selected at random . what is the probability that at least one of the selected letters is a consonant ?

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

<gadget id="calculator">binomial(8, 2)</gadget>
<output>28</output>

<gadget id="calculator">binomial(2, 2)</gadget>
<output>1</output>

<gadget id="calculator">28 - 1</gadget>
<output>27</output>

<gadget id="calculator">27 / 28</gadget>
<output>27/28 = around 0.964286</output>
<result>27/28 = around 0.964286</result>

Choices:
A. 30 / 28
B. 40 / 28
C. 25 / 28
D. 27 / 28
E. 32 / 28

divide(subtract(choose(multiply(const_2, const_4), const_2), choose(const_2, const_2)), choose(multiply(const_2, const_4), const_2))

Explanation: there are 6 consonants and 2 vowels in barkhint . probability that at least one of the selected letters is a consonant = 1 - ( probability of both vowels ) probability of both vowels = 2 c 2 / 8 c 2 = 1 / 28 so , answer is 1 - 1 / 28 = 27 / 28 answer : d


Question: if ( a + b ) = 4 , ( b + c ) = 8 and ( c + d ) = 3 , what is the value of ( a + d ) ?

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

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

Choices:
A. 16 .
B. 8 .
C. 7 .
D. 2 .
E. - 1 .

Explanation: "given a + b = 4 b + c = 8 c + d = 3 then ( a + b ) - ( b + c ) + ( c + d ) = 4 - 8 + 3 = - 1 option e . . ."


Question: ( 69842 x 69842 - 30158 x 30158 ) / ( 69842 - 30158 ) = ?

Choices:
A. 100000
B. 69842
C. 39684
D. 30158
E. none

Explanation: answer given expression = [ ( 69842 ) 2 - ( 30158 ) 2 ] / [ ( 69842 - 30158 ) ] = [ ( 69842 - 30158 ) ( 69842 + 30158 ) ] / ( 60842 - 30158 ) = 100000 correct option : a


Question: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 6 seconds . the length of the faster train is

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

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

<gadget id="calculator">81 * (5/18)</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">(45/2) * 6</gadget>
<output>135</output>
<result>135</result>

Choices:
A. 80 m
B. 100 m
C. 120 m
D. 135 m
E. none

multiply(multiply(add(36, 45), const_0_2778), 6)

Explanation: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 6 ) m = 135 m . answer d"


Question: 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?

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

<gadget id="calculator">80 - 8</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 15 %
B. 20 %
C. 25 %
D. 69 %
E. 75 %

Explanation: initially 92 % and 8 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 92 so , the required % is [ ( 3 / 4 ) ∗ 92 / 100 ] ∗ 100 = 69 % answer : d


Question: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 20 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?

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

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

<gadget id="calculator">(4/5) * (1/5)</gadget>
<output>4/25 = around 0.16</output>

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

<gadget id="calculator">(4/25) / (1/10)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(8/5) * 100</gadget>
<output>160</output>
<result>160</result>

Choices:
A. 80 %
B. 160 %
C. 120 %
D. 124.2 %
E. 138 %

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

Explanation: "0,16 r = x / 100 * 0.1 r answer b"


Question: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 750 ( before payroll deductions ) ?

<gadget id="calculator">12.5 * 40</gadget>
<output>500</output>

<gadget id="calculator">750 - 500</gadget>
<output>250</output>

<gadget id="calculator">250 / 0.16</gadget>
<output>1_562.5</output>
<result>1_562.5</result>

Choices:
A. 1600
B. 1625
C. 1650
D. 1655
E. 1675

Explanation: "total pay = 40 * $ 12.50 + $ 0.16 * x = 760 x = 260 / 0.16 = 1625 the answer is b ."


Question: 2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened to fillthe tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?

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

<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>

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

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

<gadget id="calculator">(1/20) + (1/30)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(4/3) / (1/12)</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 10 hrs
B. 12 hrs
C. 16 hrs
D. 18 hrs
E. 20 hrs

divide(add(const_1, divide(const_1, const_3)), add(inverse(20), inverse(30)))

Explanation: 1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c


Question: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 15 . the larger of the two numbers is :

<gadget id="calculator">23 * 15</gadget>
<output>345</output>
<result>345</result>

Choices:
A. 276
B. 299
C. 322
D. 345
E. 354

Explanation: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 15 ) . larger number = ( 23 x 15 ) = 345 . answer : option d"


Question: an assembly line produces 15 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?

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

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

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

<gadget id="calculator">120 / 5</gadget>
<output>24</output>
<result>24</result>

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

divide(multiply(60, const_2), add(divide(60, 15), const_1))

Explanation: "the time to produce the first 60 cogs is 60 / 15 = 4 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 5 hours = 24 cogs per hour . the answer is c ."


Question: 210 students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?

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

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

<gadget id="calculator">80 + 90</gadget>
<output>170</output>

<gadget id="calculator">210 - 170</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 25
B. 40
C. 50
D. 60
E. 75

subtract(210, add(add(60, divide(60, const_3)), 90))

Explanation: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .


Question: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 19 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?

<gadget id="calculator">19 ** 2</gadget>
<output>361</output>

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

<gadget id="calculator">361 - 289</gadget>
<output>72</output>

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

Choices:
A. 36
B. 4
C. 16
D. 38
E. 40

divide(subtract(power(19, const_2), power(17, const_2)), const_2)

Explanation: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 19 ^ 2 / 2 - 17 ^ 2 / 2 = 72 / 2 = 36 ans a ."


Question: increasing the original price of a certain item by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by what percent ?

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

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

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

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

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

Choices:
A. 31.25
B. 37.5
C. 50.0
D. 52.5
E. 44.0

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

Explanation: "we ' re told that the original price of an item is increased by 20 % and then that price is increased by 20 % . . . . if . . . . starting value = $ 100 + 20 % = 100 + . 20 ( 100 ) = 120 + 20 % = 120 + . 20 ( 120 ) = 120 + 24 = 144 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 44 / 100 = 44 % final answer : e"


Question: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 63 ounces of this substance ?

<gadget id="calculator">48 / 112</gadget>
<output>3/7 = around 0.428571</output>

<gadget id="calculator">(3/7) * 63</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 27
B. 36
C. 42
D. 64
E. 147

Explanation: "112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 112 ) * 63 = 27 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 63 will have a volume a little more than 24 , that is 27 answer : a"


Question: if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 266 m , what is its area ?

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

<gadget id="calculator">266 - 46</gadget>
<output>220</output>

<gadget id="calculator">220 / 4</gadget>
<output>55</output>

<gadget id="calculator">55 + 23</gadget>
<output>78</output>

<gadget id="calculator">78 * 55</gadget>
<output>4_290</output>
<result>4_290</result>

Choices:
A. 4290
B. 2535
C. 2530
D. 2515
E. 2520

rectangle_area(add(divide(subtract(266, multiply(const_2, 23)), const_4), 23), divide(subtract(266, multiply(const_2, 23)), const_4))

Explanation: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 266 m ⇒ breadth = 55 m length = 55 + 23 = 78 m area = 78 × 55 = 4290 m 2 answer is a ."


Question: the chance of rain on any given day in tel - aviv is 50 % . what is the probability z that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?

<gadget id="calculator">binomial(6, 4)</gadget>
<output>15</output>

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

<gadget id="calculator">(1/2) ** 4</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/16) * (1/4)</gadget>
<output>1/64 = around 0.015625</output>

<gadget id="calculator">1 / (1/64)</gadget>
<output>64</output>

<gadget id="calculator">15 / 64</gadget>
<output>15/64 = around 0.234375</output>
<result>15/64 = around 0.234375</result>

Choices:
A. 15 / 64
B. 30 / 64
C. 1 / 2
D. 1 / 4
E. 52 / 64

divide(choose(6, 4), inverse(multiply(power(divide(const_1, const_2), 4), power(divide(const_1, const_2), const_2))))

Explanation: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days z = 15 / 64 ans a it is ."


Question: little john had $ 7.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?

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

<gadget id="calculator">1.05 + 2</gadget>
<output>3.05</output>

<gadget id="calculator">7.1 - 3.05</gadget>
<output>4.05</output>
<result>4.05</result>

Choices:
A. $ 4.85
B. $ 4.15
C. $ 4.65
D. $ 4.55
E. $ 4.05

Explanation: "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 7.10 - 3.05 = $ 4.05 answer : e"


Question: in a class of 32 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?

<gadget id="calculator">32 * 2</gadget>
<output>64</output>

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

<gadget id="calculator">12 + 10</gadget>
<output>22</output>

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

<gadget id="calculator">32 - 24</gadget>
<output>8</output>

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

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

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

<gadget id="calculator">12 + 20</gadget>
<output>32</output>

<gadget id="calculator">21 + 32</gadget>
<output>53</output>

<gadget id="calculator">64 - 53</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 3
B. 5
C. 8
D. 11
E. 15

subtract(multiply(32, 2), add(multiply(subtract(subtract(32, add(add(multiply(12, 1), 10), 2)), 1), 3), add(multiply(12, 1), multiply(10, 2))))

Explanation: "total # of students = 32 avg # of books per student = 2 total # of books = 32 * 2 = 64 # of student borrowed at least 3 books = 32 - 2 - 12 - 10 = 8 # of books borrowed by above 8 students = 60 - ( 12 * 1 ) + ( 10 * 2 ) = 32 considering that 7 out of above 8 students borrowed only 3 books , # of books borrowed = 7 * 3 = 21 so maximum # of books borrowed by any single student = 32 - 21 = 11 option d"


Question: the average of 10 numbers is calculated as 21 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?

<gadget id="calculator">36 - 26</gadget>
<output>10</output>

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

<gadget id="calculator">21 + 1</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 16
B. 18
C. 19
D. 22
E. 24

Explanation: "explanation : 10 * 21 + 36 – 26 = 220 = > 220 / 10 = 22 d )"


Question: - 45 * 29 + 108 = ?

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

<gadget id="calculator">(-45) * 29</gadget>
<output>-1_305</output>

<gadget id="calculator">(-1_305) + 108</gadget>
<output>-1_197</output>
<result>-1_197</result>

Choices:
A. 1197
B. 1897
C. - 1197
D. - 1900
E. none of these

Explanation: "= > - 45 * ( 30 - 1 ) + 108 ; = > - ( 45 * 30 ) + 45 + 108 ; = > - 1350 + 153 = - 1197 . correct option : c"


Question: in a family gathering , there is a basket in which there are oranges , bananas and apples . half of the people in the family eat oranges , half of the other half eat bananas and the rest eat apples . if the number of people who eat oranges are 10 less than the total number of people , find the number of people in the gathering .

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

Choices:
A. 5
B. 10
C. 15
D. 20
E. 25

Explanation: let the number of people who eat oranges be x . then , total number of people = x + ( x / 2 ) + ( x / 2 ) = 2 x = > 2 x - 10 = x = > x = 10 = > total number of people were 2 x = 20 option d


Question: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 15 km / hr . for how many minutes does the bus stop per hour ?

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

<gadget id="calculator">15 / 60</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * 60</gadget>
<output>15</output>

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

Choices:
A. 22
B. 88
C. 77
D. 20
E. 45

subtract(multiply(const_1, const_60), multiply(divide(15, 60), const_60))

Explanation: "in 1 hr , the bus covers 60 km without stoppages and 15 km with stoppages . stoppage time = time take to travel ( 60 - 15 ) km i . e 45 km at 60 km / hr . stoppage time = 45 / 60 hrs = 45 min . answer : e"


Question: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 20 kmph and prasanna moves southward at a speed of 30 kmph . how far will be prasanna from laxmi after 60 minutes ?

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

Choices:
A. 11
B. 50
C. 28
D. 27
E. 18

Explanation: explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 20 kmph x 1 hr = 20 km total southward prasanna ' s distance = 30 kmph x 1 hr = 30 km total distance between prasanna and laxmi is = 20 + 30 = 50 km . answer : b


Question: there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 4 / 5 th of the speed of the train . how many kilometers will the car cover in 7 hours ?

<gadget id="calculator">320 / 5</gadget>
<output>64</output>

<gadget id="calculator">64 * 5</gadget>
<output>320</output>

<gadget id="calculator">320 / 4</gadget>
<output>80</output>

<gadget id="calculator">80 * 15</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 / 16</gadget>
<output>75</output>

<gadget id="calculator">75 * 7</gadget>
<output>525</output>
<result>525</result>

Choices:
A. 375
B. 425
C. 475
D. 525
E. 575

multiply(divide(multiply(divide(multiply(divide(320, 5), 5), 4), 15), 16), 7)

Explanation: the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 5 ) / 4 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 7 hours is 75 × 7 = 525 km the answer is d .


Question: ( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a then what is the units digit for a / ( ( 13 ! ) ^ 4 ) =

<gadget id="calculator">13 - 3</gadget>
<output>10</output>

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

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

Explanation: ( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a solving it , we get a / ( ( 13 ! ) ^ 4 ) = ( ( 13 ! ) ^ 4 - 1 ) last digit of ( 13 ! ) ^ 4 will be 0 . so last digit of ( ( 13 ! ) ^ 4 - 1 ) will be 9 . answer : c


Question: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6358 , how much amount did raghu invest ?

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

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

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

<gadget id="calculator">(9/10) * (11/10)</gadget>
<output>99/100 = around 0.99</output>

<gadget id="calculator">(99/100) + (9/10)</gadget>
<output>189/100 = around 1.89</output>

<gadget id="calculator">(189/100) + 1</gadget>
<output>289/100 = around 2.89</output>

<gadget id="calculator">6_358 / (289/100)</gadget>
<output>2_200</output>
<result>2_200</result>

Choices:
A. 1287
B. 2200
C. 2000
D. 1129
E. 1192

divide(6358, add(add(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(10, const_100))), subtract(const_1, divide(10, const_100))), const_1))

Explanation: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6358 = x = 6358 / 2.89 = 2200 therefore , amount invested by raghu is rs . 2200 . answer : b"