Question: the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 86436 cu . m . its width is

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

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

<gadget id="calculator">86_436 / 252</gadget>
<output>343</output>

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

<gadget id="calculator">343 ** (1/3)</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 4 m
B. 5 m
C. 6 m
D. 7 m
E. 8 m

power(divide(86436, multiply(multiply(6, 7), 6)), divide(const_1, const_3))

Explanation: "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 86436 x = 7 answer : d"


Question: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2000 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?

<gadget id="calculator">112 / 8</gadget>
<output>14</output>

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

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

<gadget id="calculator">2_000 * 9</gadget>
<output>18_000</output>
<result>18_000</result>

Choices:
A. $ 3,750
B. $ 5,600
C. $ 8,100
D. $ 18,000
E. $ 22,500

multiply(2000, power(const_3, divide(28, divide(112, 8))))

Explanation: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2000 triples to $ 6000 , in 28 years , it will again triple to $ 6000 * 3 = $ 18,000 answer d"


Question: a man buys rs . 44 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :

<gadget id="calculator">100 / 12</gadget>
<output>25/3 = around 8.333333</output>

<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>

<gadget id="calculator">(9/100) * 44</gadget>
<output>99/25 = around 3.96</output>

<gadget id="calculator">(25/3) * (99/25)</gadget>
<output>33</output>
<result>33</result>

Choices:
A. s . 12
B. s . 15
C. s . 18
D. s . 21
E. s . 33

multiply(divide(const_100, 12), multiply(divide(9, const_100), 44))

Explanation: "dividend on rs . 44 = rs . 9 / 100 x 44 = rs . 3.96 . rs . 12 is an income on rs . 100 . rs . 3.96 is an income on rs . 100 / 12 x 3.96 = rs . 33 . answer : option e"


Question: the duplicate ratio of 4 : 5 is ?

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

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

<gadget id="calculator">16 / 25</gadget>
<output>16/25 = around 0.64</output>
<result>16/25 = around 0.64</result>

Choices:
A. 1 : 2
B. 1 : 4
C. 1 : 8
D. 1 : 18
E. 16 : 25

divide(power(4, const_2), power(5, const_2))

Explanation: 4 ^ 2 : 5 ^ 2 = 16 : 25 answer : e


Question: how many different ways can 2 students be seated in a row of 5 desks , so that there is always at least one empty desk between the students ?

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

<gadget id="calculator">factorial(4) / factorial(4 - 2)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 2
B. 3
C. 4
D. 6
E. 12

Explanation: "6 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 6 x 2 = 12 e"


Question: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?

<gadget id="calculator">2.5 * 8</gadget>
<output>20</output>

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

Choices:
A. 90 kg
B. 55 kg
C. 45 kg
D. 85 kg
E. 25 kg

Explanation: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 70 + 20 ) kg = 90 kg . answer : a"


Question: if the function q is defined by the formula q = 5 w / ( 4 h ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , h is doubled , and z is tripled ?

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

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

<gadget id="calculator">4 / 18</gadget>
<output>2/9 = around 0.222222</output>
<result>2/9 = around 0.222222</result>

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

divide(4, multiply(2, power(const_3, 2)))

Explanation: "we just need to find the factor thats all , w - > quadrupled - > 4 w h - > doubled - > 2 h z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and h * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b"


Question: the radius of a wheel is 20.4 cm . what is the distance covered by the wheel in making 400 resolutions ?

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

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

<gadget id="calculator">21 + 1</gadget>
<output>22</output>

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

<gadget id="calculator">(22/7) * 20.4</gadget>
<output>64.114286</output>

<gadget id="calculator">64.114286 * 2</gadget>
<output>128.228572</output>

<gadget id="calculator">128.228572 * 400</gadget>
<output>51_291.4288</output>

<gadget id="calculator">51_291.4288 / 100</gadget>
<output>512.914288</output>
<result>512.914288</result>

Choices:
A. 512.448 m
B. 704 m
C. 510.448 m
D. 706 m
E. 204 m

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 20.4), const_2), 400), const_100)

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 400 resolutions . = 400 * 2 * 22 / 7 * 20.4 = 51244.8 cm = 512.448 m answer : a"


Question: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 20 % . what was its profit on the items sold in february ?

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

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

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

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

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

<gadget id="calculator">120 * (5/4)</gadget>
<output>150</output>

<gadget id="calculator">(4/5) * 150</gadget>
<output>120</output>

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

Choices:
A. 20 %
B. 30 %
C. 35 %
D. 37.5 %
E. 40 %

subtract(multiply(divide(subtract(const_100, 20), const_100), multiply(add(const_100, 20), divide(add(const_100, 25), const_100))), const_100)

Explanation: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.8 * 150 x = 120 x hence total profit = 20 % option a"


Question: if the cost price of 50 articles is equal to the selling price of 20 articles , then the gain or loss percent is ?

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

<gadget id="calculator">2_000 / 50</gadget>
<output>40</output>

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

<gadget id="calculator">60 / 40</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">100 * (3/2)</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 16
B. 127
C. 12
D. 18
E. 150

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

Explanation: "percentage of profit = 30 / 20 * 100 = 150 % answer : e"


Question: what is rate of interest if principal . amount be 400 , simple interest 160 and time 2 year .

<gadget id="calculator">400 * 2</gadget>
<output>800</output>

<gadget id="calculator">160 / 800</gadget>
<output>1/5 = around 0.2</output>

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

Choices:
A. 10
B. 12.5
C. 20
D. 12
E. 14.5

multiply(divide(160, multiply(400, 2)), const_100)

Explanation: s . i = ( p * r * t ) / 100 160 = 800 r / 100 r = 160 / 8 = 20 % answer c


Question: the radius of a sphere is increased by 50 % . the increase in surface area of the sphere is :

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

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

<gadget id="calculator">4 * pi * ((3/2) ** 2)</gadget>
<output>9*pi = around 28.274334</output>

<gadget id="calculator">4 * pi * (1 ** 2)</gadget>
<output>4*pi = around 12.566371</output>

<gadget id="calculator">(9*pi) - (4*pi)</gadget>
<output>5*pi = around 15.707963</output>

<gadget id="calculator">(5*pi) / (4*pi)</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 100</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 168
B. 125
C. 186
D. 197
E. 191

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

Explanation: "explanation : take radius 100 . then surface area is 4 × π π × 100 × 100 . after increase radius by 50 % the radius becomes 100 + 50 % of 100 = 150 then new surface area is 4 × π π × 150 × 150 then put the values into formula of percentage = 4 π 1502 − 4 π 10024 π 1002 × 1004 π 1502 − 4 π 10024 π 1002 × 100 = 125 % answer : b"


Question: a man can row 4 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

<gadget id="calculator">4 + 1.2</gadget>
<output>5.2</output>

<gadget id="calculator">4 - 1.2</gadget>
<output>2.8</output>

<gadget id="calculator">5.2 * 2.8</gadget>
<output>14.56</output>

<gadget id="calculator">5.2 + 2.8</gadget>
<output>8</output>

<gadget id="calculator">14.56 / 8</gadget>
<output>1.82</output>

<gadget id="calculator">1.82 * 2</gadget>
<output>3.64</output>
<result>3.64</result>

Choices:
A. 5.98
B. 3.98
C. 3.54
D. 3.87
E. 3.82

multiply(divide(multiply(add(4, 1.2), subtract(4, 1.2)), add(add(4, 1.2), subtract(4, 1.2))), const_2)

Explanation: "m = 4 s = 1.2 ds = 4.8 us = 2.8 x / 4.8 + x / 2.8 = 1 x = 1.77 d = 1.77 * 2 = 3.54 answer : c"


Question: in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive difference w between n and m ?

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

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

Explanation: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result w will be 8 - 5 = 3 and answer b"


Question: h is a positive integer and 225 and 216 are both divisors of h . if h = ( 2 ^ a ) * ( 3 ^ b ) * ( 5 ^ c ) , where a , b and c are positive integers , what is the least possible value of a + b + c ?

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

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

Choices:
A. 4
B. 8
C. 6
D. 7
E. 5

Explanation: lets make factorization of 225 and 216 . . 225 = 5 x 5 x 3 x 3 x 3 216 = 2 x 2 x 2 x 3 x 3 x 3 h would have to have 3 two ' s , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once . . . 225 has 2 fives . . . so we had them together and we get 3 + 3 + 2 = 8 ( b ) ( answer ) . . .


Question: if p and q are both odd prime numbers andp < q , then how many different positive integer factors does 2 pqhave ?

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

Choices:
A. 3
B. 4
C. 6
D. 8
E. 12

Explanation: p and q are both odd prime numbers - it means either p or q is not 2 and since prime numbers have only two factors - 1 and the number itself p and q each will have ( 1 + 1 ) = 2 factors hence 2 pq will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer


Question: ? x 12 = 173 x 240

<gadget id="calculator">173 * 240</gadget>
<output>41_520</output>

<gadget id="calculator">41_520 / 12</gadget>
<output>3_460</output>
<result>3_460</result>

Choices:
A. 3460
B. 685
C. 865
D. 495
E. 534

Explanation: "let y x 12 = 173 x 240 then y = ( 173 x 240 ) / 12 = 3460 answer : a"


Question: a man goes to shopkeeper and says that if u give me as much as i have , i will spend rs . 10 / - on ur shop . shopkeeper agrees and man moves to another shopkeeper ans asked same . at 3 rd shop after all the transaction , he was left with no money . find the initial amount with the man

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

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

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

<gadget id="calculator">(15/2) + 10</gadget>
<output>35/2 = around 17.5</output>

<gadget id="calculator">(35/2) / 2</gadget>
<output>35/4 = around 8.75</output>
<result>35/4 = around 8.75</result>

Choices:
A. 5.75
B. 6.75
C. 7.75
D. 8.75
E. 9.75

divide(add(divide(add(divide(10, const_2), 10), const_2), 10), const_2)

Explanation: man has rs . x he leaves - 1 st shop wid rs . ( 2 x - 10 ) 2 nd shop wid rs . [ 2 ( 2 x - 10 ) - 10 ] 3 rd shop wid rs . { 2 [ 2 ( 2 x - 10 ) - 10 ] - 10 } = 0 ( since he has no money left ) so solving the eqn x = 8.75 answer : d


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

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

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

<gadget id="calculator">126_000 / 2</gadget>
<output>63_000</output>

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

<gadget id="calculator">63_000 / 7</gadget>
<output>9_000</output>
<result>9_000</result>

Choices:
A. 7000
B. 9000
C. 8000
D. 9900
E. 7900

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

Explanation: ratio in which profit is divided = 2 : 3 assume that b ' s contribution to the capital = b 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 × 3 = 2 × b × 7 ⇒ b = 3500 × 12 × 3 / 2 × 7 = 500 × 6 × 3 = 9000 answer : b


Question: two trains of length 180 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?

<gadget id="calculator">180 + 280</gadget>
<output>460</output>

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

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

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

<gadget id="calculator">460 / 20</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 22 sec
B. 23 sec
C. 76 sec
D. 20 sec
E. 66 sec

Explanation: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 180 + 280 = 400 m . the time required = d / s = 460 / 20 = 23 sec . answer : b"


Question: a train running at the speed of 60 km / hr crosses a pole in 7 sec . what is the length of the train ?

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

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

<gadget id="calculator">(50/3) * 7</gadget>
<output>350/3 = around 116.666667</output>
<result>350/3 = around 116.666667</result>

Choices:
A. 112.21
B. 27.21
C. 117.66
D. 277
E. 116.66

multiply(divide(multiply(60, const_1000), const_3600), 7)

Explanation: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 7 = 116.66 answer : e"


Question: sand is poured into a box so that the box is being filled at the rate of 4 cubic feet per hour . if the empty rectangular box is 7 feet long , 6 feet wide , and 2 feet deep , approximately how many hours does it take to fill the box ?

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

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

<gadget id="calculator">84 / 4</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 20
B. 21
C. 22
D. 23
E. 24

Explanation: the volume the box is : length * width * depth = 7 * 6 * 2 = 84 cubic feet . 84 cubic feet / 4 cubic feet per hour = 21 hours . it will take 21 hours to fill the box . the answer is b .


Question: two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 40 km and the other at the rate of 50 kmph . in what time will they be completely clear of each other from the moment they meet ?

<gadget id="calculator">111 + 165</gadget>
<output>276</output>

<gadget id="calculator">40 + 50</gadget>
<output>90</output>

<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">276 / 25</gadget>
<output>276/25 = around 11.04</output>
<result>276/25 = around 11.04</result>

Choices:
A. 11.04
B. 10.0
C. 6.85
D. 5.85
E. 6.15

Explanation: "t = ( 111 + 165 ) / ( 40 + 50 ) * 18 / 5 t = 11.04 answer : a"


Question: a and b walk around a circular track . they start at 8 a . m from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 9 a . m

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

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

Explanation: explanation : relative speed = ( 2 + 3 ) = 5 rounds per hour so , they cross each other 5 times in an hour hence , they cross 5 times before 9 a . m answer : option a


Question: 10 men and 15 women together can complete a work in 6 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?

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

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

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

<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">15 * 6</gadget>
<output>90</output>

<gadget id="calculator">(5/2) * 90</gadget>
<output>225</output>
<result>225</result>

Choices:
A. 127 days
B. 667 days
C. 177 days
D. 187 days
E. 225 days

multiply(divide(multiply(const_1, 100), subtract(multiply(const_1, 100), multiply(10, 6))), multiply(15, 6))

Explanation: 1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 6 15 women ' s 1 day work = ( 1 / 6 - 10 / 100 ) = 1 / 15 1 woman ' s 1 day work = 1 / 225 1 woman alone can complete the work in 225 days . answer : e


Question: in a basket of apples , 12 % of them are rotten and 66 are in good condition . find the total number of apples in the basket .

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

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

<gadget id="calculator">66 / (22/25)</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 33
B. 75
C. 23
D. 20
E. 287

divide(66, subtract(const_1, divide(12, const_100)))

Explanation: let the total number of apples in the basket be m 12 % of the apples are rotten , and apples in good condition are 66 therefore , according to the question , 88 % of m = 66 88 / 100 × m = 66 m = ( 66 × 100 ) / 88 m = 3 × 25 m = 75 therefore , total number of apples in the basket is 75 . answer : b


Question: a piece of cloth cost rs 35 . if the length of the piece would have been 4 m longer and each meter cost re 1 less , the cost would have remained unchanged . how long is the piece ?

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

<gadget id="calculator">16 * 35</gadget>
<output>560</output>

<gadget id="calculator">560 + 16</gadget>
<output>576</output>

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

<gadget id="calculator">4 + 24</gadget>
<output>28</output>

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

<gadget id="calculator">28 / 8</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">35 / (7/2)</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 5 mtrs
B. 10 mtrs
C. 12 mtrs
D. 15 mtrs
E. 18 mtrs

divide(35, divide(add(4, sqrt(add(multiply(multiply(4, 4), 35), multiply(4, 4)))), multiply(const_2, 4)))

Explanation: if length of piece is x and cost per mtr is c , then x * c = 35 or c = 35 / x ( x + 4 ) * ( c - 1 ) = 35 or x * c + 4 c - x - 4 = 35 or 35 + 4 c - x - 4 = 35 4 c - x = 4 4 * ( 35 / x ) - x = 4 x = 10 mtrs answer : b


Question: what is the average of 4 tenths and 5 thousandths ?

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

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

<gadget id="calculator">5 / 1_000</gadget>
<output>1/200 = around 0.005</output>

<gadget id="calculator">(2/5) + (1/200)</gadget>
<output>81/200 = around 0.405</output>

<gadget id="calculator">(81/200) / 2</gadget>
<output>81/400 = around 0.2025</output>
<result>81/400 = around 0.2025</result>

Choices:
A. 0.2022
B. 0.2012
C. 0.2025
D. 0.2021
E. 0.2029

divide(add(divide(4, const_10), divide(5, multiply(const_10, const_100))), const_2)

Explanation: four tenths = 0.4 five thousandths = 0.005 the average is ( 0.4 + 0.005 ) / 2 = 0.2025 answer : c


Question: the average weight of a , b and c is 43 kg . if the average weight of a and b be 48 kg and that of b and c be 42 kg , then the weight of b is :

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

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

<gadget id="calculator">96 + 84</gadget>
<output>180</output>

<gadget id="calculator">43 * 3</gadget>
<output>129</output>

<gadget id="calculator">180 - 129</gadget>
<output>51</output>
<result>51</result>

Choices:
A. 55 kg
B. 53 kg
C. 49 kg
D. 52 kg
E. 51 kg

subtract(add(multiply(48, const_2), multiply(42, const_2)), multiply(43, const_3))

Explanation: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 43 x 3 ) = 129 â € ¦ . ( i ) a + b = ( 48 x 2 ) = 96 â € ¦ . ( ii ) b + c = ( 42 x 2 ) = 84 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 180 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 51 . b â € ™ s weight = 51 kg . answer e"


Question: pipe p can fill a tank in 3 hours , pipe q in 9 hours and pipe r in 18 hours . if all the pipes are open , in how many hours will the tank be filled ?

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

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

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

<gadget id="calculator">(1/3) + (1/9)</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">(1/18) + (4/9)</gadget>
<output>1/2 = around 0.5</output>

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

Choices:
A. 2 hours
B. 2.4 hours
C. 3 hours
D. 3.5 hours
E. 4.5 hours

inverse(add(divide(const_1, 18), add(divide(const_1, 3), divide(const_1, 9))))

Explanation: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 3 + 1 / 9 + 1 / 18 ) = 1 / 2 all the three pipes together will fill the tank = 2 / 1 = 2 hours answer a"


Question: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 25 minutes ?

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

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

Choices:
A. 80
B. 100
C. 150
D. 240
E. 300

Explanation: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 25 minutes the population increases by 25 x 4 = 100 people . answer . b ."


Question: a monkey ascends a greased pole 10 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?

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

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

<gadget id="calculator">16 + 1</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 10 th minute
B. 21 st minute
C. 17 th minute
D. 22 nd minute
E. 13 th minute

add(multiply(multiply(const_4, const_2), 2), 1)

Explanation: the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 10 meters . i mean this will continue for first 8 * 2 = 16 mins . he would have reached 8 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 16 + 1 = 17 mins . so , asnwer will be c


Question: the number 35 is equal to the sum of the cubes of two integers . what is the product of those integers ?

<gadget id="calculator">35 / 2</gadget>
<output>35/2 = around 17.5</output>

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

<gadget id="calculator">(35/2) ** (1/3)</gadget>
<output>2**(2/3)*35**(1/3)/2 = around 2.596247</output>

<gadget id="calculator">floor(2**(2/3)*35**(1/3)/2)</gadget>
<output>2</output>

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

<gadget id="calculator">35 - 8</gadget>
<output>27</output>

<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>

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

Choices:
A. 6
B. 15
C. 21
D. 27
E. 39

multiply(floor(power(divide(35, const_2), divide(const_1, const_3))), power(subtract(35, power(floor(power(divide(35, const_2), divide(const_1, const_3))), const_3)), divide(const_1, const_3)))

Explanation: "2 ^ 3 + 3 ^ 3 = 35 therefore product is 2 * 3 = 6 a"


Question: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?

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

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

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

<gadget id="calculator">9 - (198/25)</gadget>
<output>27/25 = around 1.08</output>

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

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

<gadget id="calculator">(27/25) / 9</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(11/50) - (3/25)</gadget>
<output>1/10 = around 0.1</output>

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

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

multiply(subtract(divide(22, const_100), divide(subtract(9, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100)

Explanation: "let x be the percentage decrease in fox jeans pony jeans = 22 - x ( 15 * x / 100 ) * 3 + ( 18 ( 22 - x ) / 100 ) * 2 = 9 . . . . . . . . . . . given 45 x / 100 + 792 - 36 x / 100 = 9 9 x + 792 / 100 = 9 9 x + 792 = 900 9 x = 108 x = 12 = fox jeans hence pony jeans = 22 - 12 = 10 answer : b"


Question: if i walk at 4 km / h , i miss the bus by 10 minutes . if i walk at 5 km / h , i reach 5 minutes before the arrival of the bus . how far i walk to reach the bus stand ?

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

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

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

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

<gadget id="calculator">15 / 60</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 5 km
B. 4.5 km
C. 5 1 ⁄ 4 km / h
D. can not be determined
E. none of these

multiply(divide(multiply(4, 5), subtract(5, 4)), divide(add(10, 5), const_60))

Explanation: "d = product of speed difference of time / difference of speed d = 4 × 5 / 60 [ 10 − ( − 5 ) / 5 − 4 ] [ here , – ve sign indicates before the schedule time ] ⇒ d = 5 km answer a"


Question: a jogger running at 9 kmph along side a railway track is 260 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?

<gadget id="calculator">260 + 120</gadget>
<output>380</output>

<gadget id="calculator">380 / 1_000</gadget>
<output>19/50 = around 0.38</output>

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

<gadget id="calculator">(19/50) / 36</gadget>
<output>19/1_800 = around 0.010556</output>

<gadget id="calculator">(19/1_800) * 60</gadget>
<output>19/30 = around 0.633333</output>

<gadget id="calculator">(19/30) * 60</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 3.6 sec
B. 38 sec
C. 36 sec
D. 72 sec
E. none of these

multiply(multiply(divide(divide(add(260, 120), const_1000), subtract(45, 9)), const_60), const_60)

Explanation: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 260 + 120 ) m = 380 m . ∴ time taken = ( 380 ⁄ 10 ) sec = 38 sec . answer b"


Question: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 2 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?

<gadget id="calculator">100 / 3</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">(100/3) / 6</gadget>
<output>50/9 = around 5.555556</output>

<gadget id="calculator">(50/9) / 100</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">(1/18) * 100</gadget>
<output>50/9 = around 5.555556</output>
<result>50/9 = around 5.555556</result>

Choices:
A. 20 %
B. 17 %
C. 5.5 %
D. 3.3 %
E. 2.8 %

multiply(divide(divide(divide(const_100, const_3), 6), const_100), const_100)

Explanation: 33.33 / 6 = 5.5 answer : c


Question: find the quotient when total no . of divisors of 16 ! is divided by right most non - zero digit of 15 !

<gadget id="calculator">16 * 15</gadget>
<output>240</output>

<gadget id="calculator">240 * 3</gadget>
<output>720</output>

<gadget id="calculator">720 - 100</gadget>
<output>620</output>

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

<gadget id="calculator">620 + 40</gadget>
<output>660</output>
<result>660</result>

Choices:
A. 672
B. 682
C. 692
D. 745
E. 845

add(subtract(multiply(multiply(16, 15), const_3), const_100), multiply(const_10, const_4))

Explanation: first find the factors of 16 ! and then divide with non zero digit of 15 ! factors of 16 ! prime no below 16 are 2 3 5 7 11 13 now highest power of 2 in 16 ! is 15 3 is 65 is 37 is 211 , is 113 is 1 so no of factors is 16 * 7 * 4 * 3 * 2 * 2 = 5376 now last digit in 15 ! it can be written as 2 ^ 11 * 3 ^ 6 * 5 ^ 3 * 7 ^ 2 * 11 ^ 1 * 13 * 1 5 ^ 3 * 2 ^ 3 gives 0 so remaining is 2 ^ 3 = 8 therefore 5376 / 8 = 672 answer : a


Question: if the wheel is 14 cm then the number of revolutions to cover a distance of 1408 cm is ?

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

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

<gadget id="calculator">300 + 10</gadget>
<output>310</output>

<gadget id="calculator">310 + 4</gadget>
<output>314</output>

<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>

<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>

<gadget id="calculator">(157/25) * 14</gadget>
<output>2_198/25 = around 87.92</output>

<gadget id="calculator">1_408 / (2_198/25)</gadget>
<output>17_600/1_099 = around 16.014559</output>
<result>17_600/1_099 = around 16.014559</result>

Choices:
A. 16
B. 10
C. 14
D. 12
E. 11

divide(1408, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14))

Explanation: "2 * 22 / 7 * 14 * x = 1408 = > x = 16 answer : a"


Question: calculate the area of a triangle , if the sides of are 65 cm , 60 cm and 25 cm , what is its area ?

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

<gadget id="calculator">30 * 25</gadget>
<output>750</output>
<result>750</result>

Choices:
A. 850 cm 2
B. 750 cm 2
C. 450 cm 2
D. 550 cm 2
E. 650 cm 2

Explanation: "the triangle with sides 65 cm , 60 cm and 25 cm is right angled , where the hypotenuse is 65 cm . area of the triangle = 1 / 2 * 60 * 25 = 750 cm 2 answer : b"


Question: the admission charge in a water park is $ 1 by adult and $ 0.75 by child accompanying an adult . how much was there of child with an adult who paid in quite $ 3.25 to have access to the water park ?

<gadget id="calculator">3.25 * 1</gadget>
<output>3.25</output>

<gadget id="calculator">3.25 * 2</gadget>
<output>6.5</output>

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

<gadget id="calculator">6.5 - (1/4)</gadget>
<output>6.25</output>

<gadget id="calculator">6.25 - (1/4)</gadget>
<output>6</output>

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

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

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

subtract(add(subtract(subtract(multiply(multiply(3.25, 1), const_2), const_0_25), const_0_25), 1), const_4)

Explanation: a = # of adults price for on adult = $ 1.00 e = # of kids price for on kid ( accompanying an adult ) = $ 0.75 t = total ( $ ) $ 3.25 t = price for an adult * a + price for on kid * e 3.25 = $ 1 * a + $ 0.75 * e 3.25 = a + $ 0.75 * e because the kids have to be accompanying by an adult , a = 1 $ 3.25 = 1 + $ 0.75 * e $ 3.25 - 1 = 1 - 1 + $ 0.75 * e $ 2.25 = $ 0.75 * e $ 2.25 / $ 0.75 = ( $ 0.75 * e ) / $ 0.75 3 = e = number of kids accompanying an adult . correct option : c ) 3 kids


Question: the area of a square is 4225 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .

<gadget id="calculator">4_225 ** (1/2)</gadget>
<output>65</output>

<gadget id="calculator">65 - 24</gadget>
<output>41</output>

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

<gadget id="calculator">41 / 130</gadget>
<output>41/130 = around 0.315385</output>
<result>41/130 = around 0.315385</result>

Choices:
A. 5 : 28
B. 5 : 19
C. 5 : 12
D. 5 : 13
E. 41 : 130

divide(subtract(sqrt(4225), 24), multiply(sqrt(4225), const_2))

Explanation: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4225 a = 65 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 41 : 130 answer : e"


Question: jisha walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?

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

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

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

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

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

<gadget id="calculator">18 + 20</gadget>
<output>38</output>

<gadget id="calculator">24 + 38</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 24
B. 44
C. 58
D. 60
E. 62

add(multiply(speed(18, 3), add(const_1, 3)), add(18, multiply(subtract(speed(18, 3), const_1), add(const_1, 3))))

Explanation: jisha walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e


Question: the spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls . the diameters of two of these are 1 1 / 2 cm and 2 cm respectively . the diameter of third ball is ?

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

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

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

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

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

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

<gadget id="calculator">27 - 8</gadget>
<output>19</output>

<gadget id="calculator">19 - 1</gadget>
<output>18</output>

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

<gadget id="calculator">18 ** (1/3)</gadget>
<output>18**(1/3) = around 2.620741</output>

<gadget id="calculator">(18**(1/3)) * 1</gadget>
<output>18**(1/3) = around 2.620741</output>
<result>18**(1/3) = around 2.620741</result>

Choices:
A. 2.8
B. 2.5
C. 2.2
D. 2.0
E. 2.1

multiply(power(subtract(subtract(power(divide(3, 1), 3), power(divide(add(1, divide(1, 1)), 1), 3)), 1), inverse(3)), 1)

Explanation: "4 / 3 π * 3 * 3 * 3 = 4 / 3 π [ ( 3 / 2 ) 3 + 23 + r 3 ] r = 1.25 d = 2.5 answer : b"


Question: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent . overall he make a .

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

<gadget id="calculator">1 - (1/50)</gadget>
<output>49/50 = around 0.98</output>

<gadget id="calculator">15_000 * (49/50)</gadget>
<output>14_700</output>

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

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

<gadget id="calculator">8_000 * (11/10)</gadget>
<output>8_800</output>

<gadget id="calculator">14_700 + 8_800</gadget>
<output>23_500</output>

<gadget id="calculator">15_000 + 8_000</gadget>
<output>23_000</output>

<gadget id="calculator">23_500 - 23_000</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 228
B. 288
C. 500
D. 200
E. 881

subtract(add(multiply(15000, subtract(const_1, divide(2, const_100))), multiply(8000, add(const_1, divide(10, const_100)))), add(15000, 8000))

Explanation: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 500 was made . answer : c"


Question: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 28 inch from the base of the mountain . how many km is he from the base of the mountain ?

<gadget id="calculator">28 * 136</gadget>
<output>3_808</output>

<gadget id="calculator">3_808 / 312</gadget>
<output>476/39 = around 12.205128</output>
<result>476/39 = around 12.205128</result>

Choices:
A. 14.83
B. 12.2
C. 14.8
D. 14.82
E. 14.12

Explanation: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 28 inch = ( 136 ã — 28 ) / 312 = 12.2 km answer : b"


Question: positive integer y is 50 percent of 25 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?

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

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

<gadget id="calculator">(1/2) * (1/4)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 1_000</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 50
B. 125
C. 200
D. 1,000
E. 2,000

multiply(multiply(divide(50, 100), divide(25, const_100)), const_1000)

Explanation: y = 50 % of 25 % 0 f x = x / 8 and y / 100 of x = 100 y / 100 * 8 y = 100 y = 125 answer - b


Question: in simple interest what sum amounts of rs . 1120 / - in 4 years and rs . 1200 / - in 5 years ?

<gadget id="calculator">1_200 - 1_120</gadget>
<output>80</output>

<gadget id="calculator">4 * 80</gadget>
<output>320</output>

<gadget id="calculator">1_120 - 320</gadget>
<output>800</output>
<result>800</result>

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

subtract(1120, multiply(4, subtract(1200, 1120)))

Explanation: for 1 year interest = 1200 - 1120 = 80 for 4 year 320 then sum = 1120 - 320 = 800 answer : c


Question: the current of a stream runs at the rate of 4 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?

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

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

Choices:
A. 5
B. 6
C. 8
D. 4
E. 1

Explanation: s = 4 m = x ds = x + 4 us = x - 4 6 / ( x + 4 ) + 6 / ( x - 4 ) = 2 x = 8 answer : c


Question: cathy and jim begin running at the same time and they start at the same place on a straight path . cathy runs at 10 miles per hour , and jim runs at 6 miles per hour . after 18 minutes , cathy stops to stretch . if it takes cathy 27 minutes to stretch and jim continues to run during this time , how many minutes will it take cathy to catch up to jim ?

<gadget id="calculator">18 + 27</gadget>
<output>45</output>

<gadget id="calculator">45 / 60</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">6 * (3/4)</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>

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

<gadget id="calculator">(9/2) - 3</gadget>
<output>3/2 = around 1.5</output>

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

<gadget id="calculator">4 / 60</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(3/2) / (1/15)</gadget>
<output>45/2 = around 22.5</output>
<result>45/2 = around 22.5</result>

Choices:
A. 20.5
B. 21.5
C. 22.5
D. 23.5
E. 24.5

divide(subtract(multiply(6, divide(add(18, 27), const_60)), multiply(10, divide(18, const_60))), divide(subtract(10, 6), const_60))

Explanation: in 18 minutes , cathy runs 3 miles . in 45 minutes , jim runs 4.5 miles . cathy can catch jim at a rate of 4 miles per hour . since jim is ahead by 1.5 miles , it will take cathy 1.5 / 4 hours = 22.5 minutes to catch jim . the answer is c .


Question: the speed of a car is 65 km in the first hour and 45 km in the second hour . what is the average speed of the car ?

<gadget id="calculator">65 + 45</gadget>
<output>110</output>

<gadget id="calculator">110 / 2</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 72 kmph
B. 55 kmph
C. 50 kmph
D. 80 kmph
E. 82 kmph

Explanation: "s = ( 65 + 45 ) / 2 = 55 kmph answer : b"


Question: set x consists of all two - digit primes and set y consists of all positive multiples of 4 less than 100 . if the two sets are combined into one , what will be the range of the new set ?

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

<gadget id="calculator">97 - 4</gadget>
<output>93</output>
<result>93</result>

Choices:
A. 84
B. 93
C. 90
D. 92
E. 95

Explanation: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 4 , 8 , 12 , . . . . . . . . . . . . . . . , 88 , 92 , 96 } combining two sets , say set z set z = { 4,8 , 11 , 12,13 , 17 , . . . . . . . . . . . . . . . . . . . , 83 , 88 , 89 , 92 , 96 , 97 } range = max value - min value range ( z ) = 97 - 4 = 93 oa b is the answer ."


Question: car z travels 50 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?

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

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

<gadget id="calculator">(4/5) * 50</gadget>
<output>40</output>

<gadget id="calculator">40 * 10</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 320
B. 375.2
C. 400
D. 408.3
E. 440

multiply(multiply(subtract(const_1, divide(20, const_100)), 50), 10)

Explanation: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 50 miles / hour , the car will run 40 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40 miles / gallon * 10 gallons = 400 miles . answer c ."


Question: 30 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?

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

<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 25
B. 30
C. 50
D. 55
E. 75

Explanation: "i came up with ( e ) 75 think of 100 people total : from the first fact , 30 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 30 equals the number of fair haired men , which is 45 men with fair hair . add this 45 to the 30 women and get 75 fair haired men and women out of 100 total men and women . 75 % e"


Question: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 255 , then the mean profit for the last 15 days would be

<gadget id="calculator">30 * 350</gadget>
<output>10_500</output>

<gadget id="calculator">15 * 255</gadget>
<output>3_825</output>

<gadget id="calculator">10_500 - 3_825</gadget>
<output>6_675</output>

<gadget id="calculator">6_675 / 15</gadget>
<output>445</output>
<result>445</result>

Choices:
A. rs . 200
B. rs . 445
C. rs . 275
D. rs . 425
E. none of these

divide(subtract(multiply(30, 350), multiply(15, 255)), 15)

Explanation: "average would be : 350 = ( 255 + x ) / 2 on solving , x = 445 . answer : b"


Question: a rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares . through how many of the squares does a diagonal of the rectangle pass ?

<gadget id="calculator">8 + 6</gadget>
<output>14</output>

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

Choices:
A. 6
B. 8
C. 10
D. 12
E. 16

Explanation: 1 ) if the two sides are co - prime , sum of sides - 1 . . 2 ) and if not co - prime , sum of sides - hcf of sides . . the difference is related to the diagonal passing through a vertex of squares at some place . . here 6 and 8 are not co - primes , so ans = 6 + 8 − hcf ( 6,8 ) = 14 − 2 = 12 answer : d


Question: if x + y = 3 and x 2 y 3 + y 2 x 3 = 27 , what is the value of xy ?

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

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

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

Explanation: "xy = 3 as x + y = 3 x 2 y 3 + y 2 x 3 = 27 x 2 y 2 ( y + x ) = 27 substituting x + y x 2 y 2 = 9 xy = 3 answer : c"


Question: a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 7.2 kilometer long bridge , at the same speed ?

<gadget id="calculator">7.2 * 1_000</gadget>
<output>7_200</output>

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

<gadget id="calculator">7_200 / 15</gadget>
<output>480</output>

<gadget id="calculator">480 / 60</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 4 min
B. 2 min
C. 8 min
D. 9 min
E. 3 min

divide(divide(multiply(7.2, const_1000), speed(600, 40)), const_60)

Explanation: "s = 600 / 40 = 15 mps s = 7200 / 15 = 480 sec = 8 min . answer : c"


Question: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 100 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?

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

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

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

<gadget id="calculator">38 / 3_600</gadget>
<output>19/1_800 = around 0.010556</output>

<gadget id="calculator">1 / (19/1_800)</gadget>
<output>1_800/19 = around 94.736842</output>
<result>1_800/19 = around 94.736842</result>

Choices:
A. 71.5
B. 72
C. 72.5
D. 73
E. 94.7

divide(1, divide(add(multiply(const_3600, divide(1, 100)), 2), const_3600))

Explanation: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 100 kilometers per hour is 1 / 100 hours = 3,600 / 100 seconds = 36 seconds ; time to cover this distance at regular speed is 36 + 2 = 38 seconds = 38 / 3,600 hours = 4 / 379 hours ; so , we get that to cover 1 kilometer 1 / ( 4 / 379 ) hours is needed - - > regular speed 94.7 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e ."


Question: a can do a piece of work in 5 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?

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

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

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

<gadget id="calculator">(1/2) - (1/5)</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(1/3) - (3/10)</gadget>
<output>1/30 = around 0.033333</output>

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

Choices:
A. 30
B. 20
C. 10
D. 6
E. 5

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

Explanation: "a ' s 1 hour ' s work = 1 / 5 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 5 + 1 / 3 ) = 8 / 15 . b ' s 1 hour ' s work = ( 8 / 15 - 1 / 2 ) = 1 / 30 . therefore a alone will take 30 hours to do the work . a"


Question: lally ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning lally makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?

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

<gadget id="calculator">7 * 0.5</gadget>
<output>3.5</output>

<gadget id="calculator">3.5 * 10</gadget>
<output>35</output>

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

Choices:
A. 15
B. 24
C. 25
D. 26
E. 13

subtract(multiply(12, 5), multiply(multiply(7, 0.5), const_10))

Explanation: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now lally can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional payments i . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c


Question: a retailer bought a machine at a wholesale price of $ 108 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?

<gadget id="calculator">108 * 20</gadget>
<output>2_160</output>

<gadget id="calculator">2_160 / 100</gadget>
<output>108/5 = around 21.6</output>

<gadget id="calculator">108 + (108/5)</gadget>
<output>648/5 = around 129.6</output>

<gadget id="calculator">(648/5) * 100</gadget>
<output>12_960</output>

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

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

<gadget id="calculator">12_960 / 90</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 81
B. 100
C. 120
D. 135
E. 144

divide(multiply(add(108, divide(multiply(108, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10))

Explanation: "my solution : wholesale price = 108 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 108 + 1 / 5 ( 108 ) x = 144 ; answer : e"


Question: in one day , juan sends keith 8 times as many messages as he sends laurence , and laurence sends missy 4.5 times as many messages as he receives from juan . if missy received 18 messages from laurence , how many messages does keith receive from juan ?

<gadget id="calculator">18 / 4.5</gadget>
<output>4</output>

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

Choices:
A. 13
B. 26
C. 32
D. 48
E. 56

Explanation: juan - - > laurence = x messages ; juan - - > keith = 8 x messages ( juan sends keith eight times as many messages as he sends laurence ) ; laurence - - > missy = 4.5 x = 18 ( laurence sends missy 4.5 times as many messages as he receives from juan ) . 4.5 x = 18 - - > x = 4 - - > 8 x = 32 . answer : c .


Question: edward earns $ 7.00 per hour for the first 40 hours he works per week , and twice this rate for overtime . if michael earned $ 210 last week , how many hours did he work ?

<gadget id="calculator">7 * 40</gadget>
<output>280</output>

<gadget id="calculator">280 - 210</gadget>
<output>70</output>

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

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

<gadget id="calculator">5 + 40</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 43
B. 44
C. 45
D. 46
E. 47

add(divide(subtract(multiply(7, 40), 210), multiply(7, const_2)), 40)

Explanation: $ 7 * 40 + $ 12 * x = $ 210 - - > x = 5 hours . total working hours = 40 + 5 = 45 answer : c .


Question: i bought two books ; for rs . 470 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?

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

<gadget id="calculator">470 * 119</gadget>
<output>55_930</output>

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

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

<gadget id="calculator">55_930 / 204</gadget>
<output>1_645/6 = around 274.166667</output>
<result>1_645/6 = around 274.166667</result>

Choices:
A. 274.17
B. 280.17
C. 299.17
D. 266.17
E. 279.17

divide(multiply(470, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19)))

Explanation: "x * ( 85 / 100 ) = ( 470 - x ) 119 / 100 x = 274.17 answer : a"


Question: 18 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?

<gadget id="calculator">18 * 7</gadget>
<output>126</output>

<gadget id="calculator">5 / 126</gadget>
<output>5/126 = around 0.039683</output>

<gadget id="calculator">18 * 14</gadget>
<output>252</output>

<gadget id="calculator">18 / 252</gadget>
<output>1/14 = around 0.071429</output>

<gadget id="calculator">(5/126) + (1/14)</gadget>
<output>1/9 = around 0.111111</output>

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

Choices:
A. 8 days
B. 6 days
C. 7 days
D. 9 days
E. 1 days

inverse(add(divide(5, multiply(18, 7)), divide(18, multiply(18, 14))))

Explanation: "1 women ' s 1 day work = 1 / 126 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 126 + 10 / 140 ) = 1 / 9 5 women and 10 children will complete the work in 9 days . answer : d"


Question: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.45 , what is the value of y ?

<gadget id="calculator">floor(96.45)</gadget>
<output>96</output>

<gadget id="calculator">96.45 - 96</gadget>
<output>0.45</output>

<gadget id="calculator">9 / 0.45</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 96
B. 75
C. 48
D. 20
E. 12

Explanation: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.45 and remainder is 9 so . 45 x y = 9 hence y = 20 ans d"


Question: an employee ’ s annual salary was increased $ 5000 . if her new annual salary now equals $ 25000 what was the percent increase ?

<gadget id="calculator">25_000 - 5_000</gadget>
<output>20_000</output>

<gadget id="calculator">20_000 / 25_000</gadget>
<output>4/5 = around 0.8</output>

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

Choices:
A. 15 %
B. 80 %
C. 20 %
D. 22 %
E. 24 %

multiply(divide(subtract(25000, 5000), 25000), const_100)

Explanation: new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5000 . = $ 20000 % increase = ( $ 15000 / $ 75000 ) * 100 = 80 % hence b .


Question: of the 200 employees in a certain company , 30 percent will be relocated to city x and the remaining 70 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?

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

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

Choices:
A. 115
B. 120
C. 140
D. 152
E. 165

Explanation: 120 prefer x ( group 1 ) ; 80 prefer y ( group 2 ) . city y needs 140 people : letall 80 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 60 people : 120 - 60 = 60 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 80 + 60 = 140 . answer : c .


Question: the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.7 , respectively . what value is exactly 2 standard deviations less than the mean ?

<gadget id="calculator">2 * 1.7</gadget>
<output>3.4</output>

<gadget id="calculator">14.5 - 3.4</gadget>
<output>11.1</output>
<result>11.1</result>

Choices:
A. 10.5
B. 11
C. 11.1
D. 12
E. 12.5

Explanation: "mean = 14.5 two standard deviations is 1.7 + 1.7 = 3.4 there could be two calues for this . mean + two standard deviations = 17.9 mean - two standard deviations = 11.1 answer choice has 11.1 and so c is the answer ."


Question: what is the x - intercept of a line that passes through the point ( 3 , 4 ) and has a slope of 2 ?

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

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

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

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

Explanation: first , plot the point ( 3 , 4 ) on a graph . a slope of 2 means “ up 2 , over 1 , ” so plot this point on a graph , too . here ’ s the resulting graph : y over 1 up 2 ( 1 , 0 ) ( 2 , 2 ) ( 3 , 4 ) ( 4 , 6 ) x the line passes through the x - axis at 1 , making the correct answer d ) 1


Question: raja spends 35 % of his monthly income on household items , 20 % of his monthly income on buying cloths , 5 % of his monthly income on medicines and saves the remaining amount which is rs . 15000 . find his monthly income .

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

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

<gadget id="calculator">(7/20) + (1/5)</gadget>
<output>11/20 = around 0.55</output>

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

<gadget id="calculator">(11/20) + (1/20)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">15_000 / (2/5)</gadget>
<output>37_500</output>
<result>37_500</result>

Choices:
A. rs . 40000
B. rs . 36000
C. rs . 37500
D. rs . 45000
E. none of these

divide(15000, subtract(const_1, add(add(divide(35, const_100), divide(20, const_100)), divide(5, const_100))))

Explanation: savings 40 % - 15000 expenditure 60 % - 22500 total - 37500 answer : c


Question: what least number should be subtracted from 13600 such that the remainder is divisible by 87 ?

<gadget id="calculator">13_600 % 87</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 27
B. 29
C. 28
D. 30
E. 31

Explanation: "13600 ÷ 87 = 156 , remainder = 28 hence 28 is the least number which can be subtracted from 13600 such that the remainder is divisible by 87 answer is c"


Question: list k consists of 12 consecutive integers . if - 5 is the least integer in list k , what is the range of the positive integers in list k ?

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

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

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

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

subtract(subtract(subtract(12, 5), const_1), const_1)

Explanation: "answer = a = 5 if least = - 5 , then largest = 6 range = 6 - 1 = 5"


Question: a dishonest dealer professes to sell goods at the cost price but uses a weight of 920 grams per kg , what is his percent ?

<gadget id="calculator">100 / 920</gadget>
<output>5/46 = around 0.108696</output>

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

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

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

<gadget id="calculator">(5/46) * 1_000</gadget>
<output>2_500/23 = around 108.695652</output>

<gadget id="calculator">(2_500/23) - 100</gadget>
<output>200/23 = around 8.695652</output>
<result>200/23 = around 8.695652</result>

Choices:
A. 22 %
B. 25 %
C. 77 %
D. 99 %
E. 8.7 %

subtract(multiply(divide(const_100, 920), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

Explanation: "920 - - - 80 100 - - - ? = > 8.7 % answer : e"


Question: a case contains c cartons . each carton contains b boxes , and each box contains 600 paper clips . how many paper clips are contained in 2 cases ?

<gadget id="calculator">2 * 600</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. 600 bc
B. 600 b / c
C. 1200 bc
D. 1200 b / c
E. 1200 / bc

Explanation: 2 cases * c cartons / case * b boxes / carton * 600 clips / box = 1200 bc paper clips the answer is c .


Question: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 10000 people who applied for the army and 350 were finally selected , what was the value of n ?

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

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

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

Choices:
A. 4
B. 5
C. 6
D. 9
E. 8

add(add(const_2, add(const_1, const_4)), const_2)

Explanation: "fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 last step of accepting 70 % of 500 = 350 ( our target ) total 8 steps required . ans d"


Question: a ladder 30 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 10 feet from the base of the wall . if the top of the ladder slips down 5 feet , how many feet will the bottom of the ladder slip ?

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

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

<gadget id="calculator">900 - 100</gadget>
<output>800</output>

<gadget id="calculator">800 ** (1/2)</gadget>
<output>20*sqrt(2) = around 28.284271</output>

<gadget id="calculator">(20*sqrt(2)) - 5</gadget>
<output>-5 + 20*sqrt(2) = around 23.284271</output>

<gadget id="calculator">(-5 + 20*sqrt(2)) ** 2</gadget>
<output>(-5 + 20*sqrt(2))**2 = around 542.157288</output>

<gadget id="calculator">900 - ((-5 + 20*sqrt(2))**2)</gadget>
<output>900 - (-5 + 20*sqrt(2))**2 = around 357.842712</output>

<gadget id="calculator">(900 - (-5 + 20*sqrt(2))**2) ** (1/2)</gadget>
<output>sqrt(900 - (-5 + 20*sqrt(2))**2) = around 18.916731</output>
<result>sqrt(900 - (-5 + 20*sqrt(2))**2) = around 18.916731</result>

Choices:
A. 14
B. 15
C. 18.92
D. 19
E. 25

sqrt(subtract(power(30, const_2), power(subtract(sqrt(subtract(power(30, const_2), power(10, const_2))), 5), const_2)))

Explanation: 30 ^ 2 - 10 ^ 2 = 800 it means that the height is equal to 28.28 . since the top of the ladder slips down 5 feet , then the height of the wall = 28.28 - 5 = 23.28 the bottom = sqrt ( 30 ^ 2 - 23.28 ^ 2 ) = sqrt ( 900 - 541.95 ) = 18.92 ans is c


Question: if 3 workers collect 48 kg of cotton in 4 days , how many kg of cotton will 9 workers collect in 2 days ?

<gadget id="calculator">48 / 3</gadget>
<output>16</output>

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

<gadget id="calculator">4 * 9</gadget>
<output>36</output>

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

Choices:
A. 88 kg
B. 65 kg
C. 72 kg
D. 44 kg
E. 55 kg

multiply(multiply(divide(divide(48, 3), 4), 9), 2)

Explanation: ( 3 * 4 ) / 48 = ( 9 * 2 ) / x x = 72 kg answer : c


Question: evaluate : | 8 - 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">8 - (-72)</gadget>
<output>80</output>

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

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

<gadget id="calculator">80 - 6</gadget>
<output>74</output>
<result>74</result>

Choices:
A. 40
B. 74
C. 60
D. 70
E. 80

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

Explanation: "according to order of operations , inner brackets first . hence | 8 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 8 - 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 = | 8 + 72 | - | 5 - 11 | = | 80 | - | - 6 | = 80 - 6 = 74 correct answer b ) 74"


Question: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 25 litres of tomato juice ?

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

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

<gadget id="calculator">(1/10) * 25</gadget>
<output>5/2 = around 2.5</output>

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

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

<gadget id="calculator">(5/2) / (4/5)</gadget>
<output>25/8 = around 3.125</output>
<result>25/8 = around 3.125</result>

Choices:
A. 2.8 liters .
B. 3.125 liters .
C. 8.5 liters .
D. 2.6 liters .
E. 2.1 liters .

divide(multiply(divide(subtract(const_100, 90), const_100), 25), divide(subtract(const_100, 20), const_100))

Explanation: answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 25 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 3.125 liters . answer : b


Question: triathlete dan runs along a 4 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ?

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

<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 60</gadget>
<output>40</output>

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

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

<gadget id="calculator">40 + 24</gadget>
<output>64</output>

<gadget id="calculator">8 / 64</gadget>
<output>1/8 = around 0.125</output>
<result>1/8 = around 0.125</result>

Choices:
A. 1 / 8
B. 2 / 15
C. 3 / 15
D. 1 / 4
E. 3 / 8

divide(add(4, 4), add(multiply(divide(4, 6), const_60), multiply(divide(4, 10), const_60)))

Explanation: "dan travels 8 miles round trip . running part : ( 4 / 10 * 60 = 24 minutes ) swimming part : ( 4 / 6 * 60 = 40 minutes ) 8 miles in ( 24 + 40 ) minutes 8 / 64 = 1 / 8 mile per minute answer : 1 / 8 mile per minute"


Question: at a small company , 58 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?

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

<gadget id="calculator">58 / 100</gadget>
<output>29/50 = around 0.58</output>

<gadget id="calculator">1 - (29/50)</gadget>
<output>21/50 = around 0.42</output>

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

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

<gadget id="calculator">(21/50) * (1/3)</gadget>
<output>7/50 = around 0.14</output>

<gadget id="calculator">(3/5) - (7/50)</gadget>
<output>23/50 = around 0.46</output>

<gadget id="calculator">(23/50) / (29/50)</gadget>
<output>23/29 = around 0.793103</output>
<result>23/29 = around 0.793103</result>

Choices:
A. 5 / 16
B. 1 / 3
C. 23 / 29
D. 7 / 10
E. 5 / 7

divide(subtract(divide(60, const_100), multiply(subtract(const_1, divide(58, const_100)), subtract(const_1, divide(2, 3)))), divide(58, const_100))

Explanation: lets take total employees are 100 . given that , total women = 58 and total married = 60 . total men = 100 - 58 = 42 and single men = 2 / 3 * 42 = 28 . married men = total men - single men = 42 - 28 = 14 . married women = total married - married men = 60 - 14 = 46 . fraction of women are married = married women / total women = 46 / 58 = 23 / 29 . ans c


Question: if 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?

<gadget id="calculator">36 * 30</gadget>
<output>1_080</output>

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

<gadget id="calculator">240 / 80</gadget>
<output>3</output>

<gadget id="calculator">1_080 / 3</gadget>
<output>360</output>
<result>360</result>

Choices:
A. 127
B. 237
C. 360
D. 450
E. 281

divide(multiply(36, 30), divide(multiply(10, 24), 80))

Explanation: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 10 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 10 * 30 / 24 * 80 x = 360 answer : c"


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 10 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">10 - 4</gadget>
<output>6</output>
<result>6</result>

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

Explanation: "explanation : he covered 5 km in 1 hour , so he might cover 20 km in 4 hours . but he took 10 hours . he would have saved 10 – 4 = 6 hours . answer : d"


Question: a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 15 % . their gross income from sales for one month increases by what percent ?

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

<gadget id="calculator">15 / 10</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">5 - (3/2)</gadget>
<output>7/2 = around 3.5</output>
<result>7/2 = around 3.5</result>

Choices:
A. 1.5 %
B. 2.5 %
C. 3.5 %
D. 4.5 %
E. 5.5 %

subtract(subtract(15, 10), divide(15, 10))

Explanation: "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.15 x = 1.035 * ( p * x ) , an increase of 3.5 % . the answer is c ."


Question: if a man lost 8 % by selling oranges at the rate of 25 a rupee at how many a rupee must he sell them to gain 25 % ?

<gadget id="calculator">100 - 8</gadget>
<output>92</output>

<gadget id="calculator">92 * 25</gadget>
<output>2_300</output>

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

<gadget id="calculator">2_300 / 125</gadget>
<output>92/5 = around 18.4</output>
<result>92/5 = around 18.4</result>

Choices:
A. 20
B. 15
C. 18.4
D. 20
E. 12.8

divide(multiply(subtract(const_100, 8), 25), add(const_100, 25))

Explanation: "92 % - - - - 25 125 % - - - - ? 92 / 125 * 25 = 18.4 answer : c"


Question: express a speed of 90 kmph in meters per second ?

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

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

Choices:
A. 10 mps
B. 76 mps
C. 26 mps
D. 97 mps
E. 25 mps

Explanation: "90 * 5 / 18 = 25 mps answer : e"


Question: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many w hours would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?

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

<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">(1/4) + (1/11)</gadget>
<output>15/44 = around 0.340909</output>

<gadget id="calculator">(15/44) / 15</gadget>
<output>1/44 = around 0.022727</output>

<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 22 hours
B. 30 hours
C. 44 hours
D. 60 hours
E. it can not be determined from the information above .

divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))

Explanation: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job w in 44 hours . answer : c ."


Question: a man traveled from the village to the post - office at the rate of 25 kmph and walked back at the rate of 4 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village ?

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

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

<gadget id="calculator">25 + 4</gadget>
<output>29</output>

<gadget id="calculator">200 / 29</gadget>
<output>200/29 = around 6.896552</output>

<gadget id="calculator">29 / 5</gadget>
<output>29/5 = around 5.8</output>

<gadget id="calculator">(200/29) * (29/5)</gadget>
<output>40</output>

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

Choices:
A. 70 m
B. 80 km
C. 20 km
D. 10 km
E. 73 km

divide(multiply(divide(multiply(multiply(const_2, 25), 4), add(25, 4)), divide(add(25, 4), 5)), const_2)

Explanation: explanation : average speed = , here a = 25 b = 4 = 2 x 25 x 4 / ( 25 + 4 ) = 200 / 29 km / hr . distance covered in 5 hours 48 minutes = speed x time = ( 200 / 29 ) x ( 29 / 5 ) distance covered in 5 hours 48 minutes = 40 kms . distance of the post office from the village = ( 40 / 2 ) = 20 km . answer : c


Question: a bag contains 21 toys numbered 1 to 21 . a toy is drawn and then another toy is drawn without replacement . find the probability that both toys will show even numbers .

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

<gadget id="calculator">floor(21/2)</gadget>
<output>10</output>

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

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

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

<gadget id="calculator">10 / 21</gadget>
<output>10/21 = around 0.47619</output>

<gadget id="calculator">(9/20) * (10/21)</gadget>
<output>3/14 = around 0.214286</output>
<result>3/14 = around 0.214286</result>

Choices:
A. 5 / 21
B. 9 / 42
C. 6 / 22
D. 4 / 21
E. 3 / 21

multiply(divide(subtract(floor(divide(21, const_2)), const_1), subtract(21, const_1)), divide(floor(divide(21, const_2)), 21))

Explanation: since there are 10 even numbers in the given range , the probability that the first toy shows an even number = 10 / 21 since the toy is not replaced , there are now 9 even numbered toys and total 20 toys left . hence , probability that the second toy shows an even number = 9 / 20 . required probability = 10 / 21 x 9 / 20 = 9 / 42 . answer : b


Question: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 4 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 4 ) . what is its perimeter ?

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

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

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

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

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

<gadget id="calculator">23 + 11</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 34
B. 36
C. 38
D. 40
E. 42

Explanation: "this one may look challenging initially , but all kinds of simplifying tricks . first of all , j & k have the same x - coordinate , so that ’ s a vertical segment , and the length is jk = 1 – ( – 4 ) = 5 . l & m also have the same x - coordinate , so that ’ s also a vertical segment , and the length is lm = 7 – ( – 4 ) = 11 . j & m have the same y - coordinate , so that ’ s also a horizontal segment , and the length is jm = 6 – ( – 2 ) = 8 . right there , we have the lengths of three of the four sides . the last side to find is kl . from k = ( – 2 , 1 ) , we have to go over 8 and up 6 to get to l = ( 6 , 7 ) , so 6 and 8 the legs of the right triangle , and kl is the hypotenuse . we recognize another common pythagorean triplet — ( 6 , 8 , 10 ) , which is a multiple of the ( 3 , 4 , 5 ) triplet . thus , without further calculations , we immediately know kl = 10 . perimeter = jk + kl + lm + jm = 5 + 10 + 11 + 8 = 34 answer = a"


Question: a tradesman by means of his false balance defrauds to the extent of 20 % ? in buying goods as well as by selling the goods . what percent does he gain on his outlay ? a . 20 % b . 45 %

<gadget id="calculator">20 + 20</gadget>
<output>40</output>

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

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

<gadget id="calculator">40 + 4</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 77
B. 66
C. 44
D. 99
E. 11

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

Explanation: g % = 20 + 20 + ( 20 * 20 ) / 100 = 44 % answer : c


Question: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability e that all 3 jellybeans removed from the bag are blue ?

<gadget id="calculator">binomial(10, 3)</gadget>
<output>120</output>

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

<gadget id="calculator">binomial(20, 3)</gadget>
<output>1_140</output>

<gadget id="calculator">120 / 1_140</gadget>
<output>2/19 = around 0.105263</output>
<result>2/19 = around 0.105263</result>

Choices:
A. 9 / 100
B. 2 / 19
C. 1 / 8
D. 3 / 20
E. 3 / 10

divide(choose(10, 3), choose(add(10, 10), 3))

Explanation: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability e = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"


Question: a train 50 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?

<gadget id="calculator">50 / 6</gadget>
<output>25/3 = around 8.333333</output>

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

<gadget id="calculator">(25/3) / (5/18)</gadget>
<output>30</output>

<gadget id="calculator">30 - 5</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 15 kmph
B. 25 kmph
C. 35 kmph
D. 45 kmph
E. 55 kmph

subtract(divide(divide(50, 6), const_0_2778), 5)

Explanation: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 50 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 900 x = 25 kmph answer is b"


Question: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with 5 times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.80 per glass on the first day , what was the price per glass on the second day ?

<gadget id="calculator">0.8 / 3</gadget>
<output>0.266667</output>
<result>0.266667</result>

Choices:
A. $ 015
B. $ 0.27
C. $ 0.30
D. $ 0.40
E. $ 0.45

Explanation: on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 5 units of water was used to make 6 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 6 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 6 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 6 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.8 = 6 * x - - > x = $ 0.27 . answer : b .


Question: the average of 11 10 prime numbers which are odd is ?

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

<gadget id="calculator">11 / (1/3)</gadget>
<output>33</output>

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

<gadget id="calculator">(33/2) + 1</gadget>
<output>35/2 = around 17.5</output>
<result>35/2 = around 17.5</result>

Choices:
A. 17.72
B. 18.52
C. 19.63
D. 16.53
E. 15.63

add(divide(divide(11, const_0_33), const_2), const_1)

Explanation: explanation : sum of first 11 prime no . which are odd = 195 average = 195 / 11 = 17.72 answer : a


Question: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 25 ?

<gadget id="calculator">25 / 6</gadget>
<output>25/6 = around 4.166667</output>

<gadget id="calculator">(25/6) * 12</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 45
B. 49
C. 53
D. 57
E. 61

Explanation: "$ 25 = 4 * $ 6 + $ 1 the number of doughnuts is 4 * 12 + 1 = 49 the answer is b ."


Question: during the first two weeks of january , the total rainfall in springdale was 25 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?

<gadget id="calculator">1 + 1.5</gadget>
<output>2.5</output>

<gadget id="calculator">1.5 / 2.5</gadget>
<output>0.6</output>

<gadget id="calculator">25 * 0.6</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 5 inches
B. 6 inches
C. 9 inches
D. 10 inches
E. 15 inches

multiply(25, divide(1.5, add(const_1, 1.5)))

Explanation: "total rainfall in 2 weeks = 25 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 25 inches x = 10 and 1.5 x = 15 rainfall during second week = 9 inches option e"


Question: a train crosses a bridge of length 200 m in 10 seconds and a lamp post on the bridge in 5 seconds . what is the length of the train in metres ?

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

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

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

Choices:
A. 375 m
B. 750 m
C. 200 m
D. 800 m
E. 300 m

multiply(divide(200, subtract(10, 5)), 5)

Explanation: "let length of train = l case - 1 : distance = 200 + l ( while crossing the bridge ) time = 10 seconds i . e . speed = distance / time = ( 200 + l ) / 10 case - 2 : distance = l ( while passing the lamp post ) time = 5 seconds i . e . speed = distance / time = ( l ) / 5 but since speed has to be same in both cases so ( 200 + l ) / 10 = ( l ) / 5 i . e . 2 l = l + 200 i . e . l = 200 answer : option c"


Question: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 385 the other is

<gadget id="calculator">30 * 2_310</gadget>
<output>69_300</output>

<gadget id="calculator">69_300 / 385</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 180
B. 300
C. 270
D. 250
E. 350

Explanation: the other number = l . c . m * h . c . f / given number = 2310 * 30 / 385 = 180 answer is a .


Question: mary and mike enter into a partnership by investing $ 550 and $ 450 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1000 more than mike did , what was the profit made by their business in that year ?

<gadget id="calculator">550 / 1_000</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">450 / 1_000</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(11/20) - (9/20)</gadget>
<output>1/10 = around 0.1</output>

<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">(1/10) * (2/3)</gadget>
<output>1/15 = around 0.066667</output>

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

Choices:
A. $ 8000
B. $ 10000
C. $ 15000
D. $ 12000
E. $ 12500

divide(1000, multiply(subtract(divide(550, const_1000), divide(450, const_1000)), subtract(const_1, divide(const_1, const_3))))

Explanation: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 5.5 : 4.5 i . e . , 55 % of 2 x would go to mary and 45 % of 2 x would go to mike . hence , mary would get ( 55 - 45 ) % of 2 x more than mike or 10 % of 2 x = $ 1000 i . e . , ( 60 / 100 ) * 2 x = 1000 or 2 x = 10000 . hence , the profit made by the company during the year $ 3 x = $ 15000 . answer : c"


Question: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 24 seconds . what is the length of the goods train ?

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

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

<gadget id="calculator">250 / 20</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">24 - (25/2)</gadget>
<output>23/2 = around 11.5</output>

<gadget id="calculator">(23/2) * 20</gadget>
<output>230</output>
<result>230</result>

Choices:
A. 230 m
B. 240 m
C. 260 m
D. 270 m
E. none of these

multiply(subtract(24, divide(250, multiply(const_0_2778, 72))), multiply(const_0_2778, 72))

Explanation: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 24 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 24 ] = 20 = > x + 250 = 480 = > x = 230 . answer : a"


Question: 20 men can dig a tunnel in 30 days . if after 10 days , 20 more men are deployed to dig the tunnel , how many more days it will take to dig the whole tunnel ?

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

<gadget id="calculator">(1/30) * 10</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">(1/30) * 2</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(2/3) / (1/15)</gadget>
<output>10</output>
<result>10</result>

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

divide(subtract(const_1, multiply(divide(const_1, 30), 10)), multiply(divide(const_1, 30), const_2))

Explanation: a remaining work can be completed by 20 men in 30 - 10 = 20 days . if 20 men can do x work in 20 days , and let us say 40 men take n days to do the same work . now , more men , less number of days ( inversely proportion ) 20 : 40 : : n : 20 n = 20 x 20 / 40 = 10 days .


Question: if the product of 10 integers is negative , at most how many of the integers can be negative ?

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

Choices:
A. 2
B. 3
C. 4
D. 9
E. 6

Explanation: "the product of 10 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 9 correct option : d"


Question: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 72 . find the principal ?

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

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

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

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

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

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

<gadget id="calculator">72 / (1/25)</gadget>
<output>1_800</output>
<result>1_800</result>

Choices:
A. 2277
B. 2667
C. 3600
D. 2766
E. 1800

divide(72, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1)))

Explanation: "p = 72 ( 100 / 5 ) ^ 2 = > p = 1800 answer : e"


Question: in a division , a student took 63 as divisor instead of 36 . his answer was 24 . the correct answer is -

<gadget id="calculator">63 * 24</gadget>
<output>1_512</output>

<gadget id="calculator">1_512 / 36</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 42
B. 32
C. 48
D. 28
E. 38

Explanation: "x / 63 = 24 . x = 24 * 63 . so correct answer would be , ( 24 * 63 ) / 36 = 42 . answer : a"


Question: the sum of the numbers is 550 . if the first number be twice the second and third number be one - third of the first , then the second number is :

<gadget id="calculator">550 * 3</gadget>
<output>1_650</output>

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

<gadget id="calculator">1_650 / 11</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 48
B. 150
C. 72
D. 84
E. 27

divide(multiply(550, const_3), add(const_10, const_1))

Explanation: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 550 11 x / 3 = 550 x = 150 answer : b"


Question: if ( 1 – 1.25 ) n = 4 , then n =

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

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

Choices:
A. − 400
B. − 16
C. − 4
D. 4
E. 400

Explanation: "( 1 – 1.25 ) n = 4 simplify to get : - 0.25 n = 4 rewrite as ( - 1 / 4 ) n = 4 multiply both sides by - 4 to get : n = - 16 answer : b"


Question: a team p of 20 engineers can complete work or task in 32 days . another team q of 16 engineers can complete same task in 30 days . then the ratio of working capacity of 1 member of p to the 1 member of q is a . 3 : 2

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

<gadget id="calculator">30 + 4</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 22
B. 34
C. 77
D. 29
E. 21

Explanation: explanation : let the capacity of an engineer in p = x units , and in q = y units . working capacity of p = x × 32 × 20 working capacity of q = y × 16 × 30 as the total work is same , we equate the above equations . ⇒ x × 32 × 20 = y × 16 × 30 ⇒ xy = 16 × 3032 × 20 = 34 answer : b


Question: a certain kind of necklace is made from 9 green , 6 white , and 3 orange beads . what is the maximum number of these necklaces that can be made from 45 beads of each color ?

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

Choices:
A. 7
B. 8
C. 5
D. 6
E. 2

Explanation: atleast 9 green breads are needed to make a necklace , so irrespective of the combinations of white and orange beads , the number of necklaces that can be formed will be 45 / 9 = 5 answer : - c


Question: the average of 45 results is 25 and the average of other 25 results is 45 . what is the average of all the results ?

<gadget id="calculator">45 * 25</gadget>
<output>1_125</output>

<gadget id="calculator">25 * 45</gadget>
<output>1_125</output>

<gadget id="calculator">1_125 + 1_125</gadget>
<output>2_250</output>

<gadget id="calculator">45 + 25</gadget>
<output>70</output>

<gadget id="calculator">2_250 / 70</gadget>
<output>225/7 = around 32.142857</output>
<result>225/7 = around 32.142857</result>

Choices:
A. 24
B. 32
C. 48
D. 50
E. none

divide(add(multiply(45, 25), multiply(25, 45)), add(45, 25))

Explanation: "answer sum of 70 result = sum of 45 result + sum of 25 result . = 45 x 25 + 25 x 45 = 2250 / 70 correct option : b"


Question: 10 friends meet for movie 20 for picnic and 5 for games 4 for movie & picnic 2 for movie & games , 0 for picnic & games , 2 for all , how many are students are there in all ?

<gadget id="calculator">10 + 20</gadget>
<output>30</output>

<gadget id="calculator">30 - 4</gadget>
<output>26</output>

<gadget id="calculator">26 + 5</gadget>
<output>31</output>

<gadget id="calculator">31 - 2</gadget>
<output>29</output>

<gadget id="calculator">29 + 2</gadget>
<output>31</output>
<result>31</result>

Choices:
A. 30
B. 31
C. 32
D. 33
E. 34

add(subtract(add(subtract(add(10, 20), 4), 5), 2), 2)

Explanation: n ( a u b u c ) = n ( a ) + n ( b ) + n ( c ) - n ( a intersection b ) - n ( a intersection c ) - n ( c intersection b ) + n ( a intersection b - intersection c ) hence , total no . of students = 10 + 20 + 5 - 4 - 0 - 2 + 2 = 31 . answer : b