Question: calculate the area of a triangle , if the sides of are 39 cm , 36 cm and 15 cm , what is its area ?

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

<gadget id="calculator">18 * 15</gadget>
<output>270</output>
<result>270</result>

Choices:
A. 570 cm 2
B. 370 cm 2
C. 170 cm 2
D. 271 cm 2
E. 270 cm 2

Explanation: "the triangle with sides 39 cm , 36 cm and 15 is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : e"


Question: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 20 hours . how much time he would have saved if the direction of tide has not changed ?

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

<gadget id="calculator">20 - 4</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 2
B. 8
C. 1
D. 6
E. 16

Explanation: "explanation : he covered 5 km in 1 hour , so he might cover 20 km in 4 hours . but he took 20 hours . he would have saved 20 â € “ 4 = 16 hours . answer : e"


Question: a man can do a job in 15 days . his father takes 20 days and his son finishes it in 15 days . how long will they take to complete the job if they all work together ?

<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">(1/15) + (7/60)</gadget>
<output>11/60 = around 0.183333</output>

<gadget id="calculator">1 / (11/60)</gadget>
<output>60/11 = around 5.454545</output>
<result>60/11 = around 5.454545</result>

Choices:
A. 6.3
B. 6.9
C. 5.5
D. 6.1
E. 6.2

divide(const_1, add(divide(const_1, 15), add(divide(const_1, 15), divide(const_1, 20))))

Explanation: "1 day work of the three persons = ( 1 / 15 + 1 / 20 + 1 / 15 ) = 11 / 60 so , all three together will complete the work in 300 / 47 = 5.5 days . answer : c"


Question: how long does a train 250 meters long running at the rate of 72 km / hr take to cross a bridge 150 meters in length ?

<gadget id="calculator">250 + 150</gadget>
<output>400</output>

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

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

<gadget id="calculator">400 / 20</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 10 sec
B. 20 sec
C. 25 sec
D. 30 sec
E. 35 sec

Explanation: "distance = length of train + length of bridge = 250 + 150 = 400 speed = 72 km / hr = 72 * 5 / 18 = 20 m / s required time = 400 / 20 = 20 seconds answer is b"


Question: the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 10 cents less than the price of commodity y ?

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

<gadget id="calculator">7.3 - 5.2</gadget>
<output>2.1</output>

<gadget id="calculator">(1/10) + 2.1</gadget>
<output>2.2</output>

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

<gadget id="calculator">(9/20) - 2.1</gadget>
<output>-1.65</output>

<gadget id="calculator">2.2 / (-1.65)</gadget>
<output>-1.333333</output>

<gadget id="calculator">2_001 + (-1.333333)</gadget>
<output>1_999.666667</output>
<result>1_999.666667</result>

Choices:
A. 2008
B. 2009
C. 2010
D. 2011
E. 2012

add(2001, divide(add(divide(10, const_100), subtract(7.30, 5.20)), subtract(divide(45, const_100), subtract(7.30, 5.20))))

Explanation: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 10 cents less than commodity y . $ 2.00 / 25 cents = 8 years the answer is 2001 + 8 years = 2009 . the answer is b ."


Question: if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 , then find the total number of items the wholesaler distributes ?

<gadget id="calculator">100 * 4</gadget>
<output>400</output>

<gadget id="calculator">400 + 100</gadget>
<output>500</output>

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

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

<gadget id="calculator">60 + 7</gadget>
<output>67</output>

<gadget id="calculator">500 + 67</gadget>
<output>567</output>
<result>567</result>

Choices:
A. 567
B. 167
C. 267
D. 467
E. 667

add(add(multiply(const_100, const_4), const_100), add(multiply(15, const_4), add(const_4, const_3)))

Explanation: here , a : b : c : d = 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 1 ) l . c . m of 12 : 13 : 15 : 2 is 780 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 12 ) x 780 = 65 b = ( 1 / 13 ) x 780 = 60 c = ( 1 / 15 ) x 780 = 52 d = ( 1 / 2 ) x 780 = 390 3 ) total number of toys = ( 65 x + 60 x + 52 x + 390 x ) = 567 x minimum number of pens ( x ) = 1 therefore , total number of items = 567 items . correct option : a


Question: john makes $ 50 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?

<gadget id="calculator">60 - 50</gadget>
<output>10</output>

<gadget id="calculator">10 / 50</gadget>
<output>1/5 = around 0.2</output>

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

Choices:
A. 16 %
B. 16.66 %
C. 17.9 %
D. 18.12 %
E. 20 %

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

Explanation: "increase = ( 10 / 50 ) * 100 = ( 1 / 5 ) * 100 = 20 % . e"


Question: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 90 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?

<gadget id="calculator">420 - 312</gadget>
<output>108</output>

<gadget id="calculator">250 * 90</gadget>
<output>22_500</output>

<gadget id="calculator">22_500 / 100</gadget>
<output>225</output>

<gadget id="calculator">250 - 225</gadget>
<output>25</output>

<gadget id="calculator">108 - 25</gadget>
<output>83</output>
<result>83</result>

Choices:
A. 69 .
B. 83 .
C. 81
D. 91
E. 108

subtract(subtract(420, 312), subtract(250, divide(multiply(250, 90), const_100)))

Explanation: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 90 % of 250 = 225 are boys who play soccer . girls who play soccer = 25 . total girls who do not play soccer = 108 - 25 = 83 . correct option : b"


Question: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 14 , what was the price before the first discount ?

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

<gadget id="calculator">10_000 * 14</gadget>
<output>140_000</output>

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

<gadget id="calculator">75 * 100</gadget>
<output>7_500</output>

<gadget id="calculator">75 * 25</gadget>
<output>1_875</output>

<gadget id="calculator">7_500 - 1_875</gadget>
<output>5_625</output>

<gadget id="calculator">140_000 / 5_625</gadget>
<output>224/9 = around 24.888889</output>
<result>224/9 = around 24.888889</result>

Choices:
A. $ 45.10
B. $ 34.31
C. $ 24.88
D. $ 67.54
E. $ 65.23

divide(multiply(multiply(const_100, const_100), 14), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25)))

Explanation: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 14 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 14 solve for x x = $ 24.88 correct answer c"


Question: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1690 . the perimeter of the plot is ?

<gadget id="calculator">1_690 / 6.5</gadget>
<output>260</output>

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

<gadget id="calculator">130 - 10</gadget>
<output>120</output>

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

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

<gadget id="calculator">60 + 70</gadget>
<output>130</output>

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

Choices:
A. 126
B. 156
C. 190
D. 321
E. 260

multiply(add(divide(subtract(divide(divide(1690, 6.5), const_2), 10), const_2), add(divide(subtract(divide(divide(1690, 6.5), const_2), 10), const_2), 10)), const_2)

Explanation: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1650 x = 60 required perimeter = 2 ( 60 + 70 ) = 260 e"


Question: the average weight of 4 person ' s increases by 1.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?

<gadget id="calculator">4 * 1.5</gadget>
<output>6</output>

<gadget id="calculator">6 + 95</gadget>
<output>101</output>
<result>101</result>

Choices:
A. 101 kg
B. 103.4 kg
C. 105 kg
D. data inadequate
E. none of these

Explanation: "total weight increased = ( 4 x 1.5 ) kg = 6 kg . weight of new person = ( 95 + 6 ) kg = 101 kg . answer : option a"


Question: each of the three people individually can complete a certain job in 3 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?

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

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

<gadget id="calculator">(1/5) + (1/6)</gadget>
<output>11/30 = around 0.366667</output>
<result>11/30 = around 0.366667</result>

Choices:
A. 4 / 15
B. 7 / 30
C. 11 / 30
D. 7 / 18
E. 5 / 18

Explanation: "the two slowest people work at rates of 1 / 5 and 1 / 6 of the job per hour . the sum of these rates is 1 / 5 + 1 / 6 = 11 / 30 of the job per hour . the answer is c ."


Question: the average of 5 consecutive odd numbers a , b , c , d and e is 33 . what percent of a is d ?

<gadget id="calculator">33 * 5</gadget>
<output>165</output>

<gadget id="calculator">165 / 5</gadget>
<output>33</output>

<gadget id="calculator">33 + 2</gadget>
<output>35</output>

<gadget id="calculator">35 + 2</gadget>
<output>37</output>

<gadget id="calculator">37 + 2</gadget>
<output>39</output>

<gadget id="calculator">33 / 39</gadget>
<output>11/13 = around 0.846154</output>

<gadget id="calculator">100 * (11/13)</gadget>
<output>1_100/13 = around 84.615385</output>
<result>1_100/13 = around 84.615385</result>

Choices:
A. 86.8
B. 88.6
C. 89.2
D. 90.1
E. 92.2

multiply(const_100, divide(divide(multiply(33, 5), 5), add(add(add(divide(multiply(33, 5), 5), const_2), const_2), const_2)))

Explanation: explanation : in such a case the middle number ( c ) is the average ∴ c = 33 and a = 31 and d = 35 required percentage = 31 / 35 x 100 = 88.6 answer : option b


Question: daniel went to a shop and bought things worth rs . 25 , out of which 60 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?

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

<gadget id="calculator">25 - (3/5)</gadget>
<output>122/5 = around 24.4</output>

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

<gadget id="calculator">(122/5) - 10</gadget>
<output>72/5 = around 14.4</output>
<result>72/5 = around 14.4</result>

Choices:
A. 14.4
B. 20
C. 21.3
D. 21.5
E. 22

subtract(subtract(25, divide(60, const_100)), divide(60, 6))

Explanation: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 60 paise = rs . 60 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 60 / 100 − x ) 6 / 100 = 60 / 100 ⇒ 6 ( 25 − 0.6 − x ) = 60 ⇒ ( 25 − 0.6 − x ) = 10 ⇒ x = 25 − 0.6 − 10 = 14.4 a"


Question: the volumes of two cubes are in the ratio 27 : 125 , what shall be the ratio of their surface areas ?

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

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

<gadget id="calculator">6 * (3 ** 2)</gadget>
<output>54</output>

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

<gadget id="calculator">125 / 5</gadget>
<output>25</output>

<gadget id="calculator">125 / 25</gadget>
<output>5</output>

<gadget id="calculator">6 * (5 ** 2)</gadget>
<output>150</output>

<gadget id="calculator">54 / 150</gadget>
<output>9/25 = around 0.36</output>
<result>9/25 = around 0.36</result>

Choices:
A. 6 : 25
B. 3 : 5
C. 9 : 25
D. 16 : 25
E. 19 : 25

divide(surface_cube(divide(divide(27, const_3), const_3)), surface_cube(divide(125, divide(125, add(const_4, const_1)))))

Explanation: a 13 : a 23 = 27 : 125 a 1 : a 2 = 3 : 5 6 a 12 : 6 a 22 a 12 : a 22 = 9 : 25 answer : c


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

<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>

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

<gadget id="calculator">factorial(5)</gadget>
<output>120</output>

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

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

<gadget id="calculator">5_040 / 240</gadget>
<output>21</output>

<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>

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

<gadget id="calculator">factorial(6)</gadget>
<output>720</output>

<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>

<gadget id="calculator">40_320 / 1_440</gadget>
<output>28</output>

<gadget id="calculator">21 + 28</gadget>
<output>49</output>

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

<gadget id="calculator">factorial(15)</gadget>
<output>1_307_674_368_000</output>

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

<gadget id="calculator">factorial(13)</gadget>
<output>6_227_020_800</output>

<gadget id="calculator">6_227_020_800 * 2</gadget>
<output>12_454_041_600</output>

<gadget id="calculator">1_307_674_368_000 / 12_454_041_600</gadget>
<output>105</output>

<gadget id="calculator">49 / 105</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>

Choices:
A. 7 / 15
B. 2 / 8
C. 7 / 11
D. 13 / 5
E. 87

divide(add(divide(factorial(7), multiply(factorial(subtract(7, const_2)), factorial(const_2))), divide(factorial(8), multiply(factorial(subtract(8, const_2)), factorial(const_2)))), divide(factorial(add(7, 8)), multiply(factorial(subtract(add(7, 8), const_2)), factorial(const_2))))

Explanation: explanation : drawing two balls of same color from seven green balls can be done in â  · c â ‚ ‚ ways . similarly from eight white balls two can be drawn in â  ¸ c â ‚ ‚ ways . p = â  · c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ + â  ¸ c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ = 7 / 15 a


Question: two trains of equal length , running with the speeds of 60 and 40 kmph , take 75 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?

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

<gadget id="calculator">60 - 40</gadget>
<output>20</output>

<gadget id="calculator">(5/18) * 20</gadget>
<output>50/9 = around 5.555556</output>

<gadget id="calculator">(50/9) * 75</gadget>
<output>1_250/3 = around 416.666667</output>

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

<gadget id="calculator">(5/18) * 100</gadget>
<output>250/9 = around 27.777778</output>

<gadget id="calculator">1 / (250/9)</gadget>
<output>9/250 = around 0.036</output>

<gadget id="calculator">(1_250/3) * (9/250)</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 15 sec
B. 16 sec
C. 14 sec
D. 67 sec
E. 13 sec

multiply(multiply(multiply(const_0_2778, subtract(60, 40)), 75), inverse(multiply(const_0_2778, add(60, 40))))

Explanation: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 75 d = 75 * 100 / 18 = 1250 / 3 rs = 60 + 50 = 100 * 5 / 18 t = 1250 / 3 * 18 / 500 = 15 sec answer : a"


Question: if 40 % of a certain number is 160 , then what is 90 % of that number ?

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

<gadget id="calculator">160 / (2/5)</gadget>
<output>400</output>

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

<gadget id="calculator">400 * (9/10)</gadget>
<output>360</output>
<result>360</result>

Choices:
A. 270
B. 380
C. 260
D. 360
E. 290

multiply(divide(160, divide(40, const_100)), divide(90, const_100))

Explanation: "explanation : 40 % = 40 * 4 = 160 90 % = 90 * 4 = 360 answer : option d"


Question: subtracting 30 from a number , the remainder is one fourth of the number . find the number ?

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

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

<gadget id="calculator">30 / (3/4)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 29
B. 88
C. 40
D. 28
E. 27

divide(30, subtract(const_1, divide(const_1, const_4)))

Explanation: explanation : 3 / 4 x = 30 = > x = 40 answer : c


Question: anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?

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

<gadget id="calculator">18 + 8</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 25
B. 26
C. 39
D. 21
E. 11

Explanation: "add the numbers of doughnuts . 12 + 6 + 8 = 26 . answer is b ."


Question: in what time will a train 100 m long cross an electric pole , it its speed be 90 km / hr ?

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

<gadget id="calculator">90 * (5/18)</gadget>
<output>25</output>

<gadget id="calculator">100 / 25</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 2.5
B. 2.9
C. 4 sec
D. 2.8
E. 2.1

Explanation: "speed = 90 * 5 / 18 = 25 m / sec time taken = 100 / 25 = 4 sec . answer : c"


Question: if the number is divided by 3 , it reduced by 34 . the number is

<gadget id="calculator">34 * 3</gadget>
<output>102</output>

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

<gadget id="calculator">102 / 2</gadget>
<output>51</output>
<result>51</result>

Choices:
A. 51
B. 50
C. 45
D. 40
E. 36

divide(multiply(34, 3), subtract(3, const_1))

Explanation: explanation : let the number be x . then , x - ( x / 3 ) = 34 = > 2 x / 3 = 34 = > x = 51 answer : option a


Question: if a train runs at 40 kmph , it reach its destination late by 11 minutes but if it runs at 50 kmph it is late by 5 minutes only . the correct time for a train to complete its journey is ? let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min

<gadget id="calculator">60 * 40</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 * 11</gadget>
<output>26_400</output>

<gadget id="calculator">60 * 50</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 * 5</gadget>
<output>15_000</output>

<gadget id="calculator">26_400 - 15_000</gadget>
<output>11_400</output>

<gadget id="calculator">3_000 - 2_400</gadget>
<output>600</output>

<gadget id="calculator">11_400 / 600</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 19 min
B. 19 hrs
C. 52 min
D. 126 min
E. 52 min

divide(subtract(multiply(multiply(60, 40), 11), multiply(multiply(60, 50), 5)), subtract(multiply(60, 50), multiply(60, 40)))

Explanation: let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min answer ( a )


Question: share rs . 5400 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?

<gadget id="calculator">5_400 / 2</gadget>
<output>2_700</output>

<gadget id="calculator">5_400 / 6</gadget>
<output>900</output>

<gadget id="calculator">2_700 - 900</gadget>
<output>1_800</output>
<result>1_800</result>

Choices:
A. 1800
B. 980
C. 1200
D. 1240
E. 1400

subtract(divide(5400, 2), divide(5400, 6))

Explanation: "amount received by sanjay . 4 / 12 x 5400 = 1800 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1800 . a"


Question: a room is a square of side 50 feet . a second room is of area 100 square yards . a third room is of area 200 square feet . which of these can seat maximum people ? ( hint : 1 yard = 3 feet )

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

Choices:
A. 200 sq feet
B. 300 sq feet
C. 400 sq feet
D. 500 sq feet
E. 600 sq feet

Explanation: first room because area 50 * 50 = 2500 sq feet second room area 100 sq yard in feet 300 sq feet third room area 200 sq feet answer : a


Question: alex and brian start a business with rs . 7000 each , and after 8 months , brian withdraws half of his capital . how should they share the profits at the end of the 18 months ?

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

<gadget id="calculator">18 / 13</gadget>
<output>18/13 = around 1.384615</output>
<result>18/13 = around 1.384615</result>

Choices:
A. 5 : 4
B. 4 : 3
C. 18 : 11
D. 3 : 2
E. 18 : 13

Explanation: alex invests rs . 7000 for 18 months , but brian invests rs . 7000 for the first 8 months and then withdraws rs . 3500 . so , the investment of brian for remaining 10 months is rs . 3500 only . alex : brian 7000 * 18 : ( 7000 * 8 ) + ( 3500 * 10 ) 126000 : 91000 alex : brian = 18 : 13 answer : e


Question: of the people who responded to a market survey , 240 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 6 to 1 , how many people responded to the survey ?

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

<gadget id="calculator">40 + 240</gadget>
<output>280</output>
<result>280</result>

Choices:
A. 80
B. 160
C. 280
D. 360
E. 480

Explanation: "ratio = 6 : 1 = > 6 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 240 = > 6 x = 240 = > x = 40 hence total no . of respondents = 240 + 40 = 280 hence c is the answer ."


Question: two trains 119 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?

<gadget id="calculator">119 + 165</gadget>
<output>284</output>

<gadget id="calculator">80 + 65</gadget>
<output>145</output>

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

<gadget id="calculator">145 * (5/18)</gadget>
<output>725/18 = around 40.277778</output>

<gadget id="calculator">284 / (725/18)</gadget>
<output>5_112/725 = around 7.051034</output>
<result>5_112/725 = around 7.051034</result>

Choices:
A. 7.19
B. 7.17
C. 7.2
D. 7.15
E. 7.05

Explanation: "t = ( 119 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.05 answer : e"


Question: if an integer e is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that e ( e + 1 ) ( e + 2 ) will be divisible by 8 ?

<gadget id="calculator">96 / 8</gadget>
<output>12</output>

<gadget id="calculator">12 / 8</gadget>
<output>3/2 = around 1.5</output>

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

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

<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<result>5/8 = around 0.625</result>

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

divide(add(multiply(divide(divide(96, 8), 8), 2), 2), 8)

Explanation: for e total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d


Question: if 20 men can build a wall 66 metres long in 10 days , what length of a similar can be built by 86 men in 8 days ?

<gadget id="calculator">86 * 8</gadget>
<output>688</output>

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

<gadget id="calculator">688 / 200</gadget>
<output>86/25 = around 3.44</output>

<gadget id="calculator">66 * (86/25)</gadget>
<output>5_676/25 = around 227.04</output>
<result>5_676/25 = around 227.04</result>

Choices:
A. 227.04 mtrs
B. 378.4 mtrs
C. 478.4 mtrs
D. 488.4 mtrs
E. 578.4 mtrs

multiply(66, divide(multiply(86, 8), multiply(20, 10)))

Explanation: "if 20 men can build a wall 66 metres long in 10 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 10 * 20 ) = 227.04 mtrs answer : a"


Question: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 9 ) , what is the value of x ?

<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 9
B. 11
C. 13
D. 15
E. 17

Explanation: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 9 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 9 hence x = 11 . answer is b"


Question: by travelling at 60 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?

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

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

<gadget id="calculator">360 / 3</gadget>
<output>120</output>

<gadget id="calculator">180 - 120</gadget>
<output>60</output>

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

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

Choices:
A. 30 kmph
B. 28 kmph
C. 26 kmph
D. 24 kmph
E. 22 kmph

divide(subtract(multiply(60, const_3), divide(multiply(multiply(60, const_3), const_2), const_3)), subtract(const_3, const_1))

Explanation: "let the time taken to reach the destination be 3 x hours . total distance = 60 * 3 x = 180 x km he covered 2 / 3 * 180 x = 120 x km in 1 / 3 * 3 x = x hours so , the remaining 60 x km , he has to cover in 2 x hours . required speed = 60 x / 2 x = 30 kmph . answer : a"


Question: a candidate got 35 % of the votes polled and he lost to his rival by 2430 votes . how many votes were cast ?

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">1 - (7/20)</gadget>
<output>13/20 = around 0.65</output>

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

<gadget id="calculator">2_430 / (3/10)</gadget>
<output>8_100</output>
<result>8_100</result>

Choices:
A. 7500
B. 3388
C. 8100
D. 2888
E. 2661

divide(2430, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100)))

Explanation: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2430 100 % - - - - - - - - - ? = > 8100 answer : c"


Question: if the average of 5 positive integers is 65 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?

<gadget id="calculator">65 * 5</gadget>
<output>325</output>

<gadget id="calculator">325 - 10</gadget>
<output>315</output>

<gadget id="calculator">315 / 5</gadget>
<output>63</output>

<gadget id="calculator">63 + 10</gadget>
<output>73</output>
<result>73</result>

Choices:
A. 50
B. 52
C. 59
D. 68
E. 73

add(divide(subtract(multiply(65, 5), 10), 5), 10)

Explanation: "sum of 5 integer ( a , b , c , d , e ) = 5 * 65 = 325 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 325 i . e . 5 a = 315 i . e . a = 63 i . e . largest e = 63 + 10 = 73 answer : option e"


Question: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 20 days to complete the same work . then q alone can do it in

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

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

<gadget id="calculator">(1/10) + (1/20)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">(3/20) / 2</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">(3/40) - (1/20)</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">1 / (1/40)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 20
B. 22
C. 25
D. 27
E. 40

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

Explanation: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 20 work done by p , q and r in 1 day = 1 / 10 + 1 / 20 = 3 / 20 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 3 / 20 = > work done by p in 1 day = 3 / 40 = > work done by q and r in 1 day = 3 / 40 hence work done by q in 1 day = 3 / 40 â € “ 1 / 20 = 1 / 40 so q alone can do the work in 40 days answer is e ."


Question: sale of rs 6835 , rs . 9927 , 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 , 6500 ?

<gadget id="calculator">6_835 + 9_927</gadget>
<output>16_762</output>

<gadget id="calculator">16_762 + 6_855</gadget>
<output>23_617</output>

<gadget id="calculator">23_617 + 7_230</gadget>
<output>30_847</output>

<gadget id="calculator">30_847 + 6_562</gadget>
<output>37_409</output>

<gadget id="calculator">37_409 / 5</gadget>
<output>37_409/5 = around 7_481.8</output>

<gadget id="calculator">(37_409/5) - 6_500</gadget>
<output>4_909/5 = around 981.8</output>

<gadget id="calculator">(4_909/5) * 5</gadget>
<output>4_909</output>
<result>4_909</result>

Choices:
A. 4966
B. 2477
C. 2877
D. 2676
E. 1881

Explanation: total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 34009 ) = rs . 4966 answer : a


Question: find the area of a parallelogram with base 15 cm and height 40 cm ?

<gadget id="calculator">15 * 40</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 200 cm 2
B. 100 cm 2
C. 42 cm 2
D. 600 cm 2
E. 230 cm 2

Explanation: "area of a parallelogram = base * height = 15 * 40 = 600 cm 2 answer : d"


Question: a sum of money is distributed among a , b , c , d in the proportion of 1 : 3 : 4 : 2 . if c gets $ 500 more than d , what is the b ' s share ?

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

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

<gadget id="calculator">2_000 / 4</gadget>
<output>500</output>

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

<gadget id="calculator">1_500 / 2</gadget>
<output>750</output>
<result>750</result>

Choices:
A. $ 450
B. $ 500
C. $ 750
D. $ 800
E. $ 840

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

Explanation: let the shares of a , b , c , d are x , 3 x , 4 x , 2 x 4 x - 2 x = 500 x = 250 b ' s share = 3 x = $ 750 answer is c


Question: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 507 sq m , then what is the breadth of the rectangular plot ?

<gadget id="calculator">507 / 3</gadget>
<output>169</output>

<gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 16
B. 17
C. 13
D. 19
E. 14

Explanation: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 507 3 b 2 = 507 b 2 = 169 b = 13 m . answer : option c"


Question: the number 341 is equal to the sum of the cubes of two integers . what is the product of those integers ?

<gadget id="calculator">341 / 2</gadget>
<output>341/2 = around 170.5</output>

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

<gadget id="calculator">(341/2) ** (1/3)</gadget>
<output>2**(2/3)*341**(1/3)/2 = around 5.545084</output>

<gadget id="calculator">floor(2**(2/3)*341**(1/3)/2)</gadget>
<output>5</output>

<gadget id="calculator">5 ** 3</gadget>
<output>125</output>

<gadget id="calculator">341 - 125</gadget>
<output>216</output>

<gadget id="calculator">216 ** (1/3)</gadget>
<output>6</output>

<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 8
B. 15
C. 21
D. 30
E. 39

multiply(floor(power(divide(341, const_2), divide(const_1, const_3))), power(subtract(341, power(floor(power(divide(341, const_2), divide(const_1, const_3))), const_3)), divide(const_1, const_3)))

Explanation: 5 ^ 3 + 6 ^ 3 = 341 number is 5 * 6 = 30 d


Question: 45 x ? = 25 % of 900

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

<gadget id="calculator">(1/4) * 900</gadget>
<output>225</output>

<gadget id="calculator">225 / 45</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 16.2
B. 4
C. 5
D. 500
E. none

divide(multiply(divide(25, const_100), 900), 45)

Explanation: "answer let 45 x a = ( 25 x 900 ) / 100 ∴ a = ( 25 x 9 ) / 45 = 5 correct option : c"


Question: | x + 3 | – | 4 - x | = | 7 + x | how many solutions will this equation have ?

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

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

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

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

Explanation: you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , s ố x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , s ố í t becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 c


Question: a man is 24 years older than his son . in three years , his age will be twice the age of his son . the present age of the son is

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

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

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

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

<gadget id="calculator">22 / 1</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 14 years
B. 18 years
C. 20 years
D. 21 years
E. none

divide(subtract(24, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))

Explanation: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 3 = 2 ( x + 3 ) â € ¹ = â € º x + 27 = 2 x + 6 x = 21 . answer d"


Question: a man covers a certain distance q in a train . if the train moved 4 km / hr faster , it would take 30 min less . if it moved 2 km / hr slower , it would take 20 mins more . find the distance ?

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

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

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

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

Choices:
A. 200 km
B. 50 km
C. 20 km
D. 60 km
E. 80 km

multiply(divide(subtract(multiply(4, 2), 4), const_2), 30)

Explanation: not really . when you solve the 2 equation above , you get , 6 t - 4 / 3 = 5 r / 6 from simplifying equation 1 4 t - 2 = r / 2 from simplifying equation 2 you can now multiply equation 2 by 5 to get 5 ( 4 t - 2 = r / 2 ) = 20 t - 10 = 5 r / 2 and then subtract this new equation from equation 1 to get t = 3 , followed by r = 20 to give you distance q = r * t = 20 * 3 = 60 km . d


Question: if the a radio is sold for rs 490 and sold for rs 465.50 . find loss % .

<gadget id="calculator">490 - 465.5</gadget>
<output>24.5</output>

<gadget id="calculator">24.5 / 490</gadget>
<output>0.05</output>

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

Choices:
A. 4 %
B. 5 %
C. 6 %
D. 3 %
E. 5.5 %

multiply(divide(subtract(490, 465.50), 490), const_100)

Explanation: "sol . cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . loss % = [ ( 24.50 / 490 ) * 100 ] % = 5 % answer is b ."


Question: a cycle is bought for rs . 900 and sold for rs . 1160 , find the gain percent ?

<gadget id="calculator">1_160 - 900</gadget>
<output>260</output>

<gadget id="calculator">260 / 900</gadget>
<output>13/45 = around 0.288889</output>

<gadget id="calculator">(13/45) * 100</gadget>
<output>260/9 = around 28.888889</output>
<result>260/9 = around 28.888889</result>

Choices:
A. 11
B. 29
C. 99
D. 77
E. 18

multiply(divide(subtract(1160, 900), 900), const_100)

Explanation: "900 - - - - 260 100 - - - - ? = > 29 % answer : b"


Question: the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ?

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

Choices:
A. 8
B. 1
C. 3
D. 4
E. 6

Explanation: perimeter of rectangular yard = 2 ( l + b ) = 12 - - > l + b = 6 area = l * b = 9 b = 6 - l l ( 6 - l ) = 9 6 l - l ^ 2 = 9 l ^ 2 - 6 l + 9 = 0 upon simplifying we get l = 3 . answer : b


Question: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 7 will be equal to :

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

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

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

<gadget id="calculator">9 / 49</gadget>
<output>9/49 = around 0.183673</output>
<result>9/49 = around 0.183673</result>

Choices:
A. 3
B. 6
C. 1 / 9
D. 1 / 3
E. 9 / 49

divide(multiply(1, power(3, const_2)), power(7, const_2))

Explanation: explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 7 ^ 2 = 9 / 49 answer : e


Question: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 50 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?

<gadget id="calculator">50 * 3</gadget>
<output>150</output>

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

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

<gadget id="calculator">50 + 225</gadget>
<output>275</output>
<result>275</result>

Choices:
A. 160
B. 275
C. 360
D. 440
E. 560

add(50, multiply(divide(multiply(50, 3), const_2), 3))

Explanation: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 50 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 50 = 225 . total area = 50 + 225 = 275 . answer : b ."


Question: a clothing store purchased a pair of pants for $ 90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?

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

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

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

<gadget id="calculator">80 * 120</gadget>
<output>9_600</output>

<gadget id="calculator">9_600 / 100</gadget>
<output>96</output>

<gadget id="calculator">96 - 90</gadget>
<output>6</output>
<result>6</result>

Choices:
A. $ 14
B. $ 5
C. $ 10
D. $ 6
E. $ 8

subtract(divide(multiply(subtract(const_100, 20), add(divide(90, const_3), 90)), const_100), 90)

Explanation: sale price ( sp ) = 90 + markup ( mp ) - - > mp = sp - 90 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 90 3 sp / 4 = 90 sp = 120 now a discount of 20 % is given so new sp is . 8 * 120 = 96 profit = 96 - 90 = 6.0 $ answer is d


Question: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 6 per metre approximately

Choices:
A. 4457
B. 4567
C. 4235
D. 4547
E. 8915

multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 6)

Explanation: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 6 ) = rs . 8915 . answer : option e"


Question: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q 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. q = 20
B. q = 25
C. q = 30
D. q = 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: a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in .

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

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

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

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

Choices:
A. 24 days
B. 12 days
C. 29 days
D. 25 days
E. 27 days

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

Explanation: "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : a"


Question: how many unique positive odd integers less than 70 are equal to the product of a positive multiple of 5 and an odd number ?

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

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

Choices:
A. 4
B. 7
C. 11
D. 12
E. 15

Explanation: "the question basically asks how many positive odd integers less than 70 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 and 65 = 7 ans b"


Question: find the value of 201834 x 99999 = m ?

Choices:
A. 20183198166
B. 20194181766
C. 20175292556
D. 20132191166
E. 20153198166

Explanation: "201834 x 99999 = 201834 x ( 100000 - 1 ) = 201834 x 100000 - 201834 x 1 = 20183400000 - 201834 = 20183198166 a"


Question: if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 70 , how much more remains to be paid ?

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

<gadget id="calculator">70 * 20</gadget>
<output>1_400</output>

<gadget id="calculator">1_400 - 70</gadget>
<output>1_330</output>
<result>1_330</result>

Choices:
A. $ 1120
B. $ 1190
C. $ 1260
D. $ 1330
E. $ 1400

subtract(multiply(70, divide(const_100, 5)), 70)

Explanation: "95 % remains to be paid so the remaining amount is 19 * 70 = $ 1330 . the answer is d ."


Question: for all even integers n , h ( n ) is defined to be the sum of the even integers between 4 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?

<gadget id="calculator">18 + 4</gadget>
<output>22</output>

<gadget id="calculator">18 - 4</gadget>
<output>14</output>

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

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

<gadget id="calculator">22 * 8</gadget>
<output>176</output>

<gadget id="calculator">176 / 2</gadget>
<output>88</output>

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

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

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

<gadget id="calculator">4 + 10</gadget>
<output>14</output>

<gadget id="calculator">4 * 14</gadget>
<output>56</output>

<gadget id="calculator">56 / 2</gadget>
<output>28</output>

<gadget id="calculator">88 / 28</gadget>
<output>22/7 = around 3.142857</output>
<result>22/7 = around 3.142857</result>

Choices:
A. 3
B. 1.8
C. 6
D. 18
E. 60

divide(divide(multiply(add(18, 4), add(divide(subtract(18, 4), const_2), const_1)), const_2), divide(multiply(add(divide(subtract(10, 4), const_2), const_1), add(4, 10)), const_2))

Explanation: concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 4 + 18 ) / 2 ] * 8 = 88 h ( 10 ) = ( 4 + 10 ) / 2 ] * 4 = 28 h ( 18 ) / h ( 10 ) = ( 88 ) / ( 28 ) ~ 3 answer : a


Question: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1.5 % more . she would get how much ?

<gadget id="calculator">1.5 / 100</gadget>
<output>0.015</output>

<gadget id="calculator">9_200 - 8_000</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 / 3</gadget>
<output>400</output>

<gadget id="calculator">400 / 8_000</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">0.015 + (1/20)</gadget>
<output>0.065</output>

<gadget id="calculator">0.065 * 8_000</gadget>
<output>520</output>

<gadget id="calculator">520 * 3</gadget>
<output>1_560</output>

<gadget id="calculator">1_560 + 8_000</gadget>
<output>9_560</output>
<result>9_560</result>

Choices:
A. 9560
B. 96288
C. 26667
D. 1662
E. 2882

add(multiply(multiply(add(divide(1.5, const_100), divide(divide(subtract(9200, 8000), 3), 8000)), 8000), 3), 8000)

Explanation: ( 8000 * 3 * 1.5 ) / 100 = 360 9200 - - - - - - - - 9560 answer : a


Question: a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long . over how much area of the field can it graze ?

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

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

<gadget id="calculator">(144*pi) / 4</gadget>
<output>36*pi = around 113.097336</output>
<result>36*pi = around 113.097336</result>

Choices:
A. 154 cm 2
B. 113 m 2
C. 123 m 2
D. 115 m 2
E. none of these

divide(multiply(power(12, const_2), const_pi), const_4)

Explanation: "area of the shaded portion = 1 ⁄ 4 × π × ( 12 ) 2 = 113 m 2 answer b"


Question: there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .

<gadget id="calculator">151 * 7</gadget>
<output>1_057</output>

<gadget id="calculator">6 * 170</gadget>
<output>1_020</output>

<gadget id="calculator">1_057 - 1_020</gadget>
<output>37</output>
<result>37</result>

Choices:
A. 37
B. 168
C. 189
D. 190
E. 200

subtract(multiply(151, 7), multiply(6, 170))

Explanation: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 170 ) = 1057 - 1020 = 37 . answer a"


Question: the mean of 50 observations is 100 . but later he found that there is decrements of 13 from each observations . what is the the updated mean is ?

<gadget id="calculator">100 - 13</gadget>
<output>87</output>
<result>87</result>

Choices:
A. 87
B. 97
C. 67
D. 57
E. 46

Explanation: "87 answer is a"


Question: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?

<gadget id="calculator">83 - 63</gadget>
<output>20</output>

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

Choices:
A. 13
B. 18
C. 40
D. 82
E. 43

Explanation: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 answer : c"


Question: a trader sells 23 meters of cloth for rs . 529 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ?

<gadget id="calculator">529 / 23</gadget>
<output>23</output>

<gadget id="calculator">23 - 5</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 26
B. 88
C. 90
D. 42
E. 18

Explanation: "sp of 1 m of cloth = 529 / 23 = rs . 23 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 23 - rs . 5 = rs . 18 answer : e"


Question: if an article is sold at 18 % profit instead of 9 % profit , then the profit would be $ 54 more . what is the cost price ?

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

<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<result>600</result>

Choices:
A. $ 500
B. $ 600
C. $ 700
D. $ 800
E. $ 900

Explanation: 9 % * cost price = $ 54 1 % * cost price = $ 54 / 9 = $ 6 the cost price is $ 600 . the answer is b .


Question: if 8 cats can kill 8 rats in 8 minutes , how long will it take 100 cats to kill 100 rats ?

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

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

Explanation: it will take 8 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 8 minutes , so 100 cats can kill 100 rats in 8 minutes answer c


Question: peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 600 at the end of another 2 years . what was the rate of interest in which he invested his sum ?

<gadget id="calculator">600 - 400</gadget>
<output>200</output>

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

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

<gadget id="calculator">400 - 300</gadget>
<output>100</output>

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

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

Choices:
A. 100 %
B. 12.5 %
C. 67 %
D. 25 %
E. 33 %

multiply(divide(divide(subtract(600, 400), 2), subtract(400, multiply(divide(subtract(600, 400), 2), 3))), const_100)

Explanation: "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 3 years the principal p amounts to $ 400 and after a time of 5 years ( question says after another 5 years so 3 + 2 ) p becomes $ 600 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 400 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 5 r / 100 ) = 600 dividing a 2 by a 1 we get ( 1 + 5 r / 100 ) / ( 1 + 3 r / 100 ) = 6 / 8 after cross multiplication we are left with r = 100 option : a"


Question: 3 / 4 of 1 / 2 of 2 / 5 of 5080 = ?

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

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

<gadget id="calculator">(3/4) * (1/2)</gadget>
<output>3/8 = around 0.375</output>

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

<gadget id="calculator">(3/8) * (2/5)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">(3/20) * 5_080</gadget>
<output>762</output>
<result>762</result>

Choices:
A. 392
B. 229
C. 753
D. 493
E. 762

multiply(multiply(multiply(divide(3, 4), divide(1, 2)), divide(2, 5)), 5080)

Explanation: "e 762 ? = 5080 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 762"


Question: √ 4 percent of 4 √ 4 =

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

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

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

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

Choices:
A. 0.16
B. 0.17
C. 0.18
D. 0.2
E. 0.19

divide(multiply(multiply(sqrt(4), sqrt(4)), 4), const_100)

Explanation: √ 4 = 2 so , √ 4 percent of 4 √ 4 = 2 percent of ( 4 ) ( 2 ) = ( 2 / 100 ) ( 8 ) = 16 / 100 = 0.16 answer : a


Question: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 12 hours a day , the number of men required ?

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

<gadget id="calculator">120 * 8</gadget>
<output>960</output>

<gadget id="calculator">8 * 12</gadget>
<output>96</output>

<gadget id="calculator">960 / 96</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 11 days
B. 12 days
C. 9 days
D. 8 days
E. 10 days

divide(multiply(multiply(12, 10), 8), multiply(8, 12))

Explanation: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 12 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 12 × 8 = 8 days e )"


Question: 8 people decided to split the restaurant bill evenly . if the bill was $ 214.15 dollars , how much money did they 1 cent is the smallest unit ?

<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>

<gadget id="calculator">214.15 + (3/100)</gadget>
<output>214.18</output>
<result>214.18</result>

Choices:
A. $ 214.16
B. $ 214.17
C. $ 214.18
D. $ 214.19
E. $ 214.20

Explanation: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 415 not divisible by a hence , we need to add 1 to this number for it to be divisible by 8 correct option : a"


Question: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what y percent of the list price is the lowest possible sale price ?

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

Choices:
A. 20
B. 25
C. 30
D. 40
E. 50

Explanation: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which y is 40 % of 80 hence , d is the answer"


Question: each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .

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

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) ** 4</gadget>
<output>625/256 = around 2.441406</output>

<gadget id="calculator">12_500 / (625/256)</gadget>
<output>5_120</output>
<result>5_120</result>

Choices:
A. 5113
B. 5117
C. 5120
D. 8119
E. 10115

Explanation: "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , d , e the answer to be c again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 5120 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 5120 = 12500 hence , correct answer = c"


Question: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000.00001 more . at the end of the year , their profits amounted to rs . 714 find the share of a .

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>

<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>

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

<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>

<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>

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

<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>

<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>

<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>

<gadget id="calculator">714 / 84_000</gadget>
<output>17/2_000 = around 0.0085</output>

<gadget id="calculator">(17/2_000) * 32_000</gadget>
<output>272</output>
<result>272</result>

Choices:
A. 240
B. 272
C. 379
D. 277
E. 122

multiply(divide(714, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

Explanation: explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 714 = 272 answer : b


Question: a train 120 m long running at 60 kmph crosses a platform in 35 sec . what is the length of the platform ?

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

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

<gadget id="calculator">35 * (50/3)</gadget>
<output>1_750/3 = around 583.333333</output>

<gadget id="calculator">(1_750/3) - 120</gadget>
<output>1_390/3 = around 463.333333</output>
<result>1_390/3 = around 463.333333</result>

Choices:
A. 338
B. 277
C. 463
D. 456
E. 271

subtract(multiply(35, multiply(60, const_0_2778)), 120)

Explanation: "d = 60 * 5 / 18 = 35 = 583 – 120 = 463 answer : c"


Question: jar a has 6 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?

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

<gadget id="calculator">6 + 100</gadget>
<output>106</output>

<gadget id="calculator">3 / 106</gadget>
<output>3/106 = around 0.028302</output>

<gadget id="calculator">(3/106) * 100</gadget>
<output>150/53 = around 2.830189</output>
<result>150/53 = around 2.830189</result>

Choices:
A. 2.8 %
B. 3.0 %
C. 3.2 %
D. 3.4 %
E. 3.6 %

multiply(divide(divide(6, const_2), add(6, const_100)), const_100)

Explanation: "an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 106 marbles . now , for both jars to have equal marbles we should move 3 marbles from a to b , which is 3 / 106 = ~ 2.8 % of a . answer : a ."


Question: what number has a 5 : 1 ratio to the number 10 ?

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

Choices:
A. 74
B. 50
C. 94
D. 59
E. 48

Explanation: "answer : option b explanation : 5 : 1 = x : 10 x = 50 answer : option b"


Question: a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they take to finish the work , if all the three work together ?

<gadget id="calculator">1 / 28</gadget>
<output>1/28 = around 0.035714</output>

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">1 / 14</gadget>
<output>1/14 = around 0.071429</output>

<gadget id="calculator">(1/7) + (1/14)</gadget>
<output>3/14 = around 0.214286</output>

<gadget id="calculator">(1/28) + (3/14)</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 4
B. 9
C. 2
D. 11
E. none

Explanation: "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 all three can finish the work in 4 days answer : a"


Question: in the youth summer village there are 200 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?

<gadget id="calculator">100 + 75</gadget>
<output>175</output>

<gadget id="calculator">175 + 125</gadget>
<output>300</output>

<gadget id="calculator">300 - 200</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 125
B. 150
C. 100
D. 130
E. 140

Explanation: total = 200 not working = 100 having family = 75 like to sing in shower = 125 working = 200 - 100 = 100 not having family = 200 - 75 = 125 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 c


Question: nitin ranks 18 th in a class of 49 students . what is rank from the last ?

<gadget id="calculator">49 - 18</gadget>
<output>31</output>
<result>31</result>

Choices:
A. 33
B. 38
C. 32
D. 28
E. 19

Explanation: "explanation : number students behind the nitin in rank = ( 49 - 18 ) = 31 nitin is 32 nd from the last answer : c ) 32"


Question: lamp a flashes every 6 seconds , lamp b flashes every 8 seconds , lamp c flashes every 10 seconds . at a certain instant of time all 3 lamps flash simultaneously . during the period of 6 minutes after that how many times will exactly two lamps flash ? ( please include any flash of exactly two lights which occurs at the 6 minute mark . )

<gadget id="calculator">6 * 60</gadget>
<output>360</output>

<gadget id="calculator">lcm(6, 8)</gadget>
<output>24</output>

<gadget id="calculator">360 / 24</gadget>
<output>15</output>

<gadget id="calculator">lcm(6, 10)</gadget>
<output>30</output>

<gadget id="calculator">360 / 30</gadget>
<output>12</output>

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

<gadget id="calculator">lcm(8, 10)</gadget>
<output>40</output>

<gadget id="calculator">360 / 40</gadget>
<output>9</output>

<gadget id="calculator">27 + 9</gadget>
<output>36</output>

<gadget id="calculator">lcm(24, 10)</gadget>
<output>120</output>

<gadget id="calculator">360 / 120</gadget>
<output>3</output>

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

<gadget id="calculator">36 - 9</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 24
B. 25
C. 26
D. 27
E. 28

subtract(add(add(divide(multiply(6, const_60), lcm(6, 8)), divide(multiply(6, const_60), lcm(6, 10))), divide(multiply(6, const_60), lcm(8, 10))), multiply(divide(multiply(6, const_60), lcm(lcm(6, 8), 10)), 3))

Explanation: 6 minutes is 360 seconds . lamp a and lamp b will flash together every 24 seconds . 360 / 24 = 15 . in the time period , lamp a and lamp b will flash together 15 times . lamp a and lamp c will flash together every 30 seconds . 360 / 30 = 12 . in the time period , lamp a and lamp c will flash together 12 times . lamp b and lamp c will flash together every 40 seconds . 360 / 40 = 9 . in the time period , lamp b and lamp c will flash together 9 times . all three lights will flash together every 2 * 2 * 2 * 3 * 5 = 120 seconds . 360 / 120 = 3 . we have counted these triple flashes three times , so we need to subtract three times the number of times that all three lights flash together . the number of times that exactly two lights flash together is 15 + 12 + 9 - 9 = 27 times . the answer is d .


Question: a man walking at a rate of 10 km / hr crosses a bridge in 12 minutes . the length of the bridge is ?

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

<gadget id="calculator">10_000 / 60</gadget>
<output>500/3 = around 166.666667</output>

<gadget id="calculator">(500/3) * 12</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 2000
B. 1492
C. 1667
D. 1254
E. 1112

multiply(divide(multiply(10, const_1000), const_60), 12)

Explanation: speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 12 * 60 = 2000 m answer is a


Question: there are 1000 students in a school and among them 30 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?

<gadget id="calculator">30 * 1_000</gadget>
<output>30_000</output>

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

<gadget id="calculator">300 * 10</gadget>
<output>3_000</output>

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

Choices:
A. 1
B. 10
C. 100
D. 30
E. 20

divide(multiply(divide(multiply(30, 1000), const_100), 10), const_100)

Explanation: 30 % of 1000 gives 300 . so 300 attends chess and 10 % of 300 gives 30 . so 30 enrolled for swimming answer : d


Question: exactly 15 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?

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

<gadget id="calculator">15 / 75</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) * 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 20 %
B. 42 %
C. 44 %
D. 80 %
E. 84 %

multiply(subtract(const_1, divide(15, subtract(const_100, 25))), const_100)

Explanation: "let ' s assume there are 100 reporters - - > 15 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 15 ( # of reporters who cover local politics ) : 0.75 x = 15 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."


Question: of 70 players on a football team , 43 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?

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

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

<gadget id="calculator">70 - 43</gadget>
<output>27</output>

<gadget id="calculator">(2/3) * 27</gadget>
<output>18</output>

<gadget id="calculator">18 + 43</gadget>
<output>61</output>
<result>61</result>

Choices:
A. 54
B. 59
C. 61
D. 71
E. 92

add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 43)), 43)

Explanation: "total = 70 thrower = 43 rest = 70 - 43 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 43 + 18 = 61 so c . 61 is the right answer"


Question: in how many seconds will a train 100 meters long pass an oak tree , if the speed of the train is 36 km / hr ?

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

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

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

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

Explanation: "speed = 36 * 5 / 18 = 10 m / s time = 100 / 10 = 10 seconds the answer is c ."


Question: the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ?

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

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

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

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

<gadget id="calculator">1_512 / 12</gadget>
<output>126</output>
<result>126</result>

Choices:
A. rs . 126
B. rs . 132
C. rs . 120
D. rs . 114
E. none of these

divide(1512, add(multiply(divide(6, const_2), divide(4, const_3)), 8))

Explanation: let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a


Question: a goods bullet train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 seconds . what is the length of the goods bullet train ?

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

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

<gadget id="calculator">20 * 26</gadget>
<output>520</output>

<gadget id="calculator">520 - 250</gadget>
<output>270</output>
<result>270</result>

Choices:
A. 220 m
B. 250 m
C. 280 m
D. 210 m
E. 270 m

subtract(multiply(multiply(72, const_0_2778), 26), 250)

Explanation: e 270 m


Question: a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

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

<gadget id="calculator">140 * (1/10)</gadget>
<output>14</output>

<gadget id="calculator">140 - 14</gadget>
<output>126</output>

<gadget id="calculator">126 - 100</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 26 %
B. 20 %
C. 17 %
D. 18 %
E. none of these

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

Explanation: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 10 % of 140 = rs . 140 - 14 = rs . 126 . gain = rs . 126 â € “ rs . 100 = rs . 26 therefore , gain / profit percent = 26 % . answer : option a"


Question: evaluate : | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?

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

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

<gadget id="calculator">6 - (-72)</gadget>
<output>78</output>

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

<gadget id="calculator">-(-6)</gadget>
<output>6</output>

<gadget id="calculator">78 - 6</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 40
B. 50
C. 72
D. 70
E. 80

subtract(subtract(6, multiply(8, subtract(3, 12))), negate(subtract(5, 11)))

Explanation: "according to order of operations , inner brackets first . hence | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 6 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 6 + 72 | - | 5 - 11 | = | 78 | - | - 6 | = 78 - 6 = 72 correct answer c ) 72"


Question: on a trip , a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles . if the cyclist returned immediately via the same route and took a total of 9 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?

<gadget id="calculator">22 + 20</gadget>
<output>42</output>

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

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

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

<gadget id="calculator">9 - 4</gadget>
<output>5</output>

<gadget id="calculator">42 / 5</gadget>
<output>42/5 = around 8.4</output>
<result>42/5 = around 8.4</result>

Choices:
A. 7.6
B. 7.8
C. 8
D. 8.2
E. 8.4

divide(add(22, 20), subtract(9, add(divide(22, 11), divide(20, 10))))

Explanation: the time to go 42 miles was 22 / 11 + 20 / 10 = 2 + 2 = 4 hours . the average speed for the return trip was 42 miles / 5 hours = 8.4 mph . the answer is e .


Question: on increasing the number of lines in a page by 100 , they become 240 . what is the % of increase in the no . of lines in the page ?

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

<gadget id="calculator">240 / 140</gadget>
<output>12/7 = around 1.714286</output>

<gadget id="calculator">(12/7) * 100</gadget>
<output>1_200/7 = around 171.428571</output>

<gadget id="calculator">(1_200/7) - 100</gadget>
<output>500/7 = around 71.428571</output>
<result>500/7 = around 71.428571</result>

Choices:
A. 20 %
B. 305
C. 50 %
D. 71.4 %
E. 60 %

subtract(multiply(divide(240, subtract(240, 100)), const_100), const_100)

Explanation: "explanation : number of pages increased = 100 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 100 = 140 % increase in the number of pages in the book = 100 / 140 x 100 % = 71.4 % d"


Question: find the sum 3 / 10 + 5 / 100 + 8 / 1000 in decimal form ?

<gadget id="calculator">8 / 1_000</gadget>
<output>1/125 = around 0.008</output>

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

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

<gadget id="calculator">(3/10) + (1/20)</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">(1/125) + (7/20)</gadget>
<output>179/500 = around 0.358</output>
<result>179/500 = around 0.358</result>

Choices:
A. 0.853
B. 0.358
C. 3.58
D. 8.35
E. none

Explanation: answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b


Question: 3 distinct single digit no a , b , c are in g . p . if abs ( x ) for real x is the absolute value of x ( x if x is positive or zero , and x if x is negative ) , then the no . of different possible values of abs ( a + b - c ) is

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

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

Explanation: if a = 1 , r = 2 then a = 1 , b = 2 , c = 4 then abs ( a + b - c ) = 1 if a = 1 , r = 3 then a = 1 , a = 3 , a = 9 then abs ( 1 + 3 - 9 ) = 5 if a = 2 , r = 2 , then a = 2 , b = 4 , c = 8 then abs ( 2 + 4 - 8 ) = 2 if a = 1 , r = - 2 then a = 1 , b = - 2 , c = 4 the abs ( 1 - 2 - 4 ) = 5 if a = 1 , r = - 3 then a = 1 , b = - 3 , c = 9 then abs ( 1 - 3 - 9 ) = 11 if a = 2 , r = - 2 then a = 2 , b = - 4 , c = - 8 then abs ( 2 - 4 - 8 ) = 10 so total 5 abs ( ) values answer : d


Question: sum of 19 odd numbers is ?

<gadget id="calculator">19 * 2</gadget>
<output>38</output>

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

<gadget id="calculator">38 * (19/2)</gadget>
<output>361</output>
<result>361</result>

Choices:
A. 341
B. 351
C. 361
D. 371
E. 381

multiply(multiply(19, const_2), divide(19, const_2))

Explanation: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 19 odd numbers = 19 ^ 2 = 361 answer : c"


Question: an engine moves at the speed of 90 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 78 kmph . what will be the speed of train when 25 coaches are attached .

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

<gadget id="calculator">90 - 78</gadget>
<output>12</output>

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

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

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

<gadget id="calculator">90 - 20</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 90
B. 85
C. 80
D. 60
E. 70

subtract(90, multiply(sqrt(25), divide(subtract(90, 78), sqrt(9))))

Explanation: "1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 90 - 20 = 70 e"


Question: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds . the length of the train ( in metres ) is :

<gadget id="calculator">20 - 8</gadget>
<output>12</output>

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

<gadget id="calculator">22 * 8</gadget>
<output>176</output>
<result>176</result>

Choices:
A. 188
B. 176
C. 175
D. 96
E. none of these

multiply(divide(264, subtract(20, 8)), 8)

Explanation: "explanation : let the length of train be l m . acc . to question ( 264 + l ) / 20 = l / 8 2112 + 8 l = 20 l l = 2112 / 12 = 176 m answer b"


Question: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 10 miles per gallon , and from town b to town c , the car averaged 12 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?

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

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

<gadget id="calculator">120 + 60</gadget>
<output>180</output>

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

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

<gadget id="calculator">12 + 5</gadget>
<output>17</output>

<gadget id="calculator">180 / 17</gadget>
<output>180/17 = around 10.588235</output>
<result>180/17 = around 10.588235</result>

Choices:
A. 11.5
B. 9.5
C. 13.5
D. 10.6
E. 14.5

divide(add(multiply(12, const_10), divide(multiply(12, const_10), const_2)), add(divide(multiply(12, const_10), 10), divide(divide(multiply(12, const_10), const_2), 12)))

Explanation: "step 1 ) took lcm of 10 and 12 . . came as 30 . just multiplied by 10 . . . ( to make easy calculation ) step 2 ) 300 distance between b to c . . . do 300 / 12 hence 25 gallons used step 3 ) twice distance . . hence 300 * 2 = 600 . . . do as above . . 600 / 10 = 60 gallons used step 4 ) total gallons . . 25 + 60 = 85 gallons step ) total miles = 300 + 600 = 900 miles hence . . average of whole journey = 900 / 85 which comes to 10.6 answer : d"


Question: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 16 miles on saturday and sunday , how many miles did bill run on sunday ?

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

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

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

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

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

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

add(divide(subtract(16, add(4, multiply(const_2, 4))), 4), 4)

Explanation: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 16 . . 4 x + 12 = 16 . . x = 1 . . ans = x + 4 = 1 + 4 = 5 answer a"


Question: a train 450 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?

<gadget id="calculator">68 - 8</gadget>
<output>60</output>

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

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

<gadget id="calculator">450 / (50/3)</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 5 sec
B. 39 sec
C. 27 sec
D. 15 sec
E. 18 sec

divide(450, multiply(subtract(68, 8), const_0_2778))

Explanation: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 450 m at 50 / 3 m / sec = 450 * 3 / 50 sec = 27 sec answer : c ."


Question: during a thanksgiving weekend , a car rental company rented 6 - tenths of their vehicles , including two - fifths of the 4 wds that it had . if 40 % of the vehicles are 4 wds , then what percent of the vehicles that were not rented were not 4 wds ?

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

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

<gadget id="calculator">80 / 5</gadget>
<output>16</output>

<gadget id="calculator">16 / 40</gadget>
<output>2/5 = around 0.4</output>

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

Choices:
A. 20 %
B. 30 %
C. 40 %
D. 50 %
E. 60 %

multiply(divide(divide(multiply(const_2, 40), add(const_3, const_2)), 40), const_100)

Explanation: 4 / 10 of all the vehicles were not rented . ( 3 / 5 ) ( 2 / 5 ) = 6 / 25 of all the vehicles are 4 wds that were not rented . ( 6 / 25 ) / ( 4 / 10 ) = 3 / 5 is the fraction of non - rented vehicles that were 4 wds 1 - 3 / 5 = 40 % of non - rented vehicles were not 4 wds . the answer is c .


Question: if x < y < z and y - x > 7 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?

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

<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<result>11</result>

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

Explanation: "we have : 1 ) x < y < z 2 ) y - x > 5 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 7 the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 11 ( y - 2 = 9 , y = 11 ) 2 < 11 < z , since z is odd , the least possible value for z is 13 z - x = 13 - 2 = 11 answer c"


Question: jim drove 1096 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?

<gadget id="calculator">1_200 - 1_096</gadget>
<output>104</output>
<result>104</result>

Choices:
A. 104 miles
B. 432 miles
C. 456 miles
D. 887 miles
E. 767 miles

Explanation: "the number of miles to drive to finish his journey is given by 1200 - 1096 = 104 miles correct answer a"


Question: ram , who is half as efficient as krish , will take 18 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>

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

<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>

<gadget id="calculator">(1/18) + (1/9)</gadget>
<output>1/6 = around 0.166667</output>

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

Choices:
A. 16 days
B. 12 days
C. 8 days
D. 6 days
E. 18 days

inverse(add(divide(const_1, 18), divide(const_1, divide(18, const_2))))

Explanation: "number of days taken by ram to complete task = 18 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 18 days is 18 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 18 w / 3 w = 6 days answer d"


Question: a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm ^ 3 , then the weight of the pipe is :

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

<gadget id="calculator">pi * (4 ** 2) * 21</gadget>
<output>336*pi = around 1_055.575132</output>

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

<gadget id="calculator">pi * (3 ** 2) * 21</gadget>
<output>189*pi = around 593.761012</output>

<gadget id="calculator">(336*pi) - (189*pi)</gadget>
<output>147*pi = around 461.81412</output>

<gadget id="calculator">(147*pi) * 8</gadget>
<output>1176*pi = around 3_694.512961</output>

<gadget id="calculator">(1176*pi) / 1_000</gadget>
<output>147*pi/125 = around 3.694513</output>
<result>147*pi/125 = around 3.694513</result>

Choices:
A. 3.6 kg
B. 3.696 kg
C. 36 kg
D. 36.9 kg
E. 3.06 kg

divide(multiply(subtract(volume_cylinder(divide(8, const_2), 21), volume_cylinder(subtract(divide(8, const_2), 1), 21)), 8), const_1000)

Explanation: "external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"


Question: the average weight of 7 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?

<gadget id="calculator">7 * 1.5</gadget>
<output>10.5</output>

<gadget id="calculator">65 + 10.5</gadget>
<output>75.5</output>
<result>75.5</result>

Choices:
A. 76 kg
B. 77 kg
C. 75.5 kg
D. data inadequate
E. none of these

Explanation: "total weight increases = 7 × 1.5 = 10.5 kg so the weight of new person = 65 + 10.5 = 75.5 kg answer c"


Question: mr . jones gave 40 % of the money he had to his wife . he also gave 20 % of the remaining amount to his 3 sons . and half of the amount now left was spent on miscellaneous items and the remaining amount of rs . 12000 was deposited in the bank . how much money did mr . jones have initially ?

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

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

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

<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>

<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">(3/5) * (4/5)</gadget>
<output>12/25 = around 0.48</output>

<gadget id="calculator">(1/2) * (12/25)</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">12_000 / (6/25)</gadget>
<output>50_000</output>
<result>50_000</result>

Choices:
A. 40000
B. 45000
C. 50000
D. 62000
E. none of these

divide(12000, multiply(divide(divide(const_100, const_2), const_100), multiply(subtract(const_1, divide(40, const_100)), subtract(const_1, divide(20, const_100)))))

Explanation: explanation : let the initial amount be x , amount given to his wife = ( 40 / 100 ) x = 2 x / 5 balance = ( x - ( 2 x / 5 ) ) = 3 x / 5 amount given to his wife = ( 20 / 100 ) * ( 3 x / 5 ) = 3 x / 25 balance = 3 x / 5 - 3 x / 25 = 12 x / 25 amountt spent on miscellaneous items = ( 1 / 2 ) * ( 12 x / 25 ) = 6 x / 25 which is equal to 12000 hence , = > 6 x / 25 = 12000 = > x = 50000 answer : c


Question: he total marks obtained by a student in physics , chemistry and mathematics is 170 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?

<gadget id="calculator">170 / 2</gadget>
<output>85</output>
<result>85</result>

Choices:
A. 55
B. 65
C. 75
D. 85
E. 95

Explanation: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 170 + p c + m = 170 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 170 / 2 = 85 . answer : d"


Question: 25 onions on a scale weigh 5.12 kg . when 3 onions are removed from the scale , the average weight of the 22 onions is 200 grams . what is the average weight ( in grams ) of the 3 onions which were removed ?

<gadget id="calculator">5.12 * 1_000</gadget>
<output>5_120</output>

<gadget id="calculator">22 * 200</gadget>
<output>4_400</output>

<gadget id="calculator">5_120 - 4_400</gadget>
<output>720</output>

<gadget id="calculator">720 / 3</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 200
B. 220
C. 240
D. 260
E. 280

divide(subtract(multiply(5.12, const_1000), multiply(22, 200)), 3)

Explanation: 22 * 200 = 4400 . the other 3 onions weigh a total of 720 grams . the average weight is 720 / 3 = 240 grams . the answer is c .


Question: a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?

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

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

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

<gadget id="calculator">600 / (5/6)</gadget>
<output>720</output>

<gadget id="calculator">720 / 2</gadget>
<output>360</output>

<gadget id="calculator">720 / 3</gadget>
<output>240</output>

<gadget id="calculator">360 - 240</gadget>
<output>120</output>
<result>120</result>

Choices:
A. s . 220
B. s . 120
C. s . 320
D. s . 50
E. s . 90

subtract(divide(divide(600, add(divide(1, 2), divide(1, 3))), 2), divide(divide(600, add(divide(1, 2), divide(1, 3))), 3))

Explanation: "a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 360 and 240 . difference in profit share = 360 - 240 = 120 answer : b"


Question: 3 candidates contested an election and received 1000 , 2000 and 4000 votes respectively . what percentage of the total votes did the winning candidate got ?

<gadget id="calculator">1_000 + 2_000</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 + 4_000</gadget>
<output>7_000</output>

<gadget id="calculator">4_000 / 7_000</gadget>
<output>4/7 = around 0.571429</output>

<gadget id="calculator">(4/7) * 100</gadget>
<output>400/7 = around 57.142857</output>
<result>400/7 = around 57.142857</result>

Choices:
A. 30 %
B. 50 %
C. 57 %
D. 62 %
E. 75 %

Explanation: total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c


Question: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers . how many coins did the old man have ?

<gadget id="calculator">floor(64)</gadget>
<output>64</output>
<result>64</result>

Choices:
A. 24
B. 26
C. 30
D. 64
E. 40

Explanation: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 64 ( x - y ) - - > x + y = 64 . answer : d ."


Question: 20 litres of mixture contains 40 % alcohol and the rest water . if 8 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?

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

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

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

<gadget id="calculator">(3/5) * 20</gadget>
<output>12</output>

<gadget id="calculator">12 + 8</gadget>
<output>20</output>

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

<gadget id="calculator">8 / 28</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>

Choices:
A. 26.32 %
B. 35.14 %
C. 28.57 %
D. 25 %
E. 31.14 %

multiply(divide(subtract(add(20, 8), add(multiply(divide(subtract(const_100, 40), const_100), 20), 8)), add(20, 8)), const_100)

Explanation: "alcohol in the 20 litres of mix . = 40 % of 20 litres = ( 40 * 20 / 100 ) = 8 litres water in it = 20 - 8 = 12 litres new quantity of mix . = 20 + 8 = 28 litres quantity of alcohol in it = 8 litres percentage of alcohol in new mix . = 8 * 100 / 28 = 50 / 3 = 28.57 % answer is c"


Question: 12.036 divided by 0.04 gives :

<gadget id="calculator">12.036 / 0.04</gadget>
<output>300.9</output>
<result>300.9</result>

Choices:
A. 30.09
B. 300.9
C. 30.06
D. 100.9
E. 300.6

Explanation: "= 12.036 / 0.04 = 1203.6 / 4 = 300.9 answer is b ."


Question: if 20 liters of chemical x are added to 80 liters of a mixture that is 5 % chemical x and 95 % chemical y , then what percentage of the resulting mixture is chemical x ?

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

<gadget id="calculator">(1/20) * 80</gadget>
<output>4</output>

<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 24 %
B. 26 %
C. 28 %
D. 30 %
E. 32 %

add(20, multiply(divide(5, const_100), 80))

Explanation: "the amount of chemical x in the solution is 20 + 0.05 ( 80 ) = 24 liters . 24 liters / 100 liters = 24 % the answer is a ."


Question: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score r for the exam ?

<gadget id="calculator">58 * 3</gadget>
<output>174</output>

<gadget id="calculator">98 * 2</gadget>
<output>196</output>

<gadget id="calculator">174 + 196</gadget>
<output>370</output>

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

<gadget id="calculator">370 / 5</gadget>
<output>74</output>
<result>74</result>

Choices:
A. 74
B. 76
C. 78
D. 80
E. 82

divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))

Explanation: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a ."


Question: a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 240 meter length ?

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

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

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

<gadget id="calculator">600 / (25/2)</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 65 seconds
B. 46 seconds
C. 40 seconds
D. 97 seconds
E. 48 seconds

divide(add(360, 240), divide(multiply(45, const_1000), const_3600))

Explanation: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 240 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : e"


Question: in one year , the population , of a village increased by 10 % and in the next year , it decreased by 10 % . if at the end of 2 nd year , the population was 7920 , what was it in the beginning ?

<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">7_920 / (9/10)</gadget>
<output>8_800</output>

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

<gadget id="calculator">8_800 / (11/10)</gadget>
<output>8_000</output>
<result>8_000</result>

Choices:
A. 8008
B. 8000
C. 8022
D. 8021
E. 8022

divide(divide(7920, subtract(const_1, divide(10, const_100))), add(const_1, divide(10, const_100)))

Explanation: "x * 110 / 100 * 90 / 100 = 7920 x * 0.99 = 7920 x = 7920 / 0.99 = > 8000 answer : b"


Question: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 35 % profit ?

<gadget id="calculator">832 + 448</gadget>
<output>1_280</output>

<gadget id="calculator">1_280 / 2</gadget>
<output>640</output>

<gadget id="calculator">640 * 35</gadget>
<output>22_400</output>

<gadget id="calculator">22_400 / 100</gadget>
<output>224</output>

<gadget id="calculator">224 + 640</gadget>
<output>864</output>
<result>864</result>

Choices:
A. $ 480
B. $ 450
C. $ 960
D. $ 864
E. $ 660

add(divide(multiply(divide(add(832, 448), const_2), 35), const_100), divide(add(832, 448), const_2))

Explanation: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 135 % of $ 640 = $ 864 d"


Question: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3720 , r will receive

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

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

<gadget id="calculator">15 + 10</gadget>
<output>25</output>

<gadget id="calculator">25 + 6</gadget>
<output>31</output>

<gadget id="calculator">6 / 31</gadget>
<output>6/31 = around 0.193548</output>

<gadget id="calculator">3_720 * (6/31)</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 720
B. 700
C. 800
D. 900
E. none of these

multiply(3720, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

Explanation: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3720 * ( 6 / 31 ) = 120 * 6 = 720 . answer : option a"