Question: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction q of the sum of the 21 numbers in the list ?

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

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

<gadget id="calculator">5 + 21</gadget>
<output>26</output>

<gadget id="calculator">26 / 4</gadget>
<output>13/2 = around 6.5</output>

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

<gadget id="calculator">13 - 4</gadget>
<output>9</output>

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

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

Choices:
A. 1 / 20
B. 1 / 6
C. 1 / 5
D. 4 / 21
E. 5 / 21

divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))

Explanation: this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction q of n to the total would be 4 a / 24 a or 1 / 6 answer b


Question: if 12 men can reap 120 acres of land in 16 days , how many acres of land can 36 men reap in 32 days ?

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

<gadget id="calculator">32 / 16</gadget>
<output>2</output>

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

<gadget id="calculator">120 * 6</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 269
B. 512
C. 369
D. 720
E. 450

multiply(120, multiply(divide(36, 12), divide(32, 16)))

Explanation: 12 men 120 acres 16 days 36 men ? 32 days 120 * 36 / 12 * 32 / 16 120 * 3 * 2 120 * 6 = 720 answer : d


Question: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 4 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?

<gadget id="calculator">4 / 50</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">50 / (2/25)</gadget>
<output>625</output>
<result>625</result>

Choices:
A. 200
B. 325
C. 565
D. 625
E. 700

Explanation: "total fish = x percentage of second catch = ( 4 / 50 ) * 100 = 8 % so , x * 8 % = 50 x = 625 ans d ."


Question: an inspector rejects 0.04 % of the meters as defective . how many will he examine to reject 2 ?

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

<gadget id="calculator">200 / 0.04</gadget>
<output>5_000</output>
<result>5_000</result>

Choices:
A. 1500
B. 2000
C. 2500
D. 5000
E. 3100

Explanation: "let the number of meters to be examined be x then , 0.04 % of x = 2 ( 4 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 5000 answer is d"


Question: john makes $ 50 a week from his job . he earns a raise andnow makes $ 90 a week . what is the % increase ?

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

<gadget id="calculator">40 / 50</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. 16.66 %
C. 17.8 %
D. 80 %
E. 21 %

multiply(divide(subtract(90, 50), 50), const_100)

Explanation: "increase = ( 40 / 50 ) * 100 = ( 4 / 5 ) * 100 = 80 % . d"


Question: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 48 now , the son age 5 years back was

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

<gadget id="calculator">24 - 5</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 14
B. 17
C. 11
D. 19
E. 99

Explanation: "let the son ' s present age be x years . then , ( 48 - x ) = x x = 24 . son ' s age 5 years back = ( 24 - 5 ) = 19 years answer : d"


Question: a man can row upstream at 25 kmph and downstream at 43 kmph , and then find the speed of the man in still water ?

<gadget id="calculator">25 + 43</gadget>
<output>68</output>

<gadget id="calculator">68 / 2</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 86
B. 34
C. 30
D. 15
E. 17

Explanation: "us = 25 ds = 43 m = ( 43 + 25 ) / 2 = 34 answer : b"


Question: if | x - 20 | = 40 what is the sum of all the values of x .

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

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

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

Choices:
A. 0
B. 60
C. - 80
D. 40
E. 80

Explanation: "there will be two cases x - 20 = 40 and x - 20 = - 40 solve for x = > x = 40 + 20 = > x = 60 or x = - 40 + 20 = > x = - 20 the sum of both values will be 60 + - 20 = 40 answer is d"


Question: the length and breadth of a rectangular courtyard is 75 m and 32 m . find the cost of leveling it at the rate of $ 3 per m 2 . also , find the distance covered by a boy to take 4 rounds of the courtyard .

<gadget id="calculator">75 * 32</gadget>
<output>2_400</output>

<gadget id="calculator">3 * 2_400</gadget>
<output>7_200</output>
<result>7_200</result>

Choices:
A. 3573
B. 3455
C. 8600
D. 7000
E. 7200

Explanation: length of the courtyard = 75 m breadth of the courtyard = 32 m perimeter of the courtyard = 2 ( 75 + 32 ) m = 2 × 107 m = 214 m distance covered by the boy in taking 4 rounds = 4 × perimeter of courtyard = 4 × 214 = 856 m we know that area of the courtyard = length × breadth = 75 × 32 m 2 = 2400 m 2 for 1 m 2 , the cost of levelling = $ 3 for 2400 m 2 , the cost of levelling = $ 3 × 2400 = $ 7200 answer : e


Question: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 40 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?

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

<gadget id="calculator">6 / 40</gadget>
<output>3/20 = around 0.15</output>
<result>3/20 = around 0.15</result>

Choices:
A. 5 : 00
B. 5 : 30
C. 6 : 40
D. 6 : 30
E. 7 : 00

Explanation: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 4 : 40 pm + 2 hrs = 6 : 40 pm answer : c . 6 : 40"


Question: a corporation that had $ 2 billion in profits for the year paid out $ 100 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )

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

<gadget id="calculator">10 ** 6</gadget>
<output>1_000_000</output>

<gadget id="calculator">100 * 1_000_000</gadget>
<output>100_000_000</output>

<gadget id="calculator">10 ** 9</gadget>
<output>1_000_000_000</output>

<gadget id="calculator">2 * 1_000_000_000</gadget>
<output>2_000_000_000</output>

<gadget id="calculator">100_000_000 / 2_000_000_000</gadget>
<output>1/20 = around 0.05</output>

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

Choices:
A. 50 %
B. 20 %
C. 5 %
D. 2 %
E. 0.2 %

multiply(divide(multiply(100, power(10, add(const_3, const_3))), multiply(2, power(10, 9))), const_100)

Explanation: "required answer = [ employee benefit / profit ] * 100 = [ ( 100 million ) / ( 2 billion ) ] * 100 = [ ( 100 * 10 ^ 6 ) / ( 2 * 10 ^ 9 ) ] * 100 = ( 50 / 1000 ) * 100 = 5 % so answer is ( c )"


Question: a man and a boy complete a work together in 24 days . if for the last 6 days man alone does the work then it is completed in 26 days . how long the boy will take to complete the work alone ?

<gadget id="calculator">26 - 6</gadget>
<output>20</output>

<gadget id="calculator">26 * 2</gadget>
<output>52</output>

<gadget id="calculator">20 + 52</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 72 days
B. 20 days
C. 24 days
D. 36 days
E. 34 days

add(subtract(26, 6), multiply(26, const_2))

Explanation: explanation : ( man + boy ) ’ s 1 day ’ s work = 1 / 24 their 20 day ’ s work = 1 / 24 × 20 = 5 / 6 the remaining 1 / 6 work is done by the man in 6 days therefore , the man alone will finish the work in 6 × 6 days = 36 days man ’ s 1 day ’ s work = 1 / 36 therefore , boy ’ s 1 day ’ s work = 1 / 24 – 1 / 36 = 3 – 2 / 72 = 1 / 72 therefore , the boy alone will finish the work in 72 days . answer : option a


Question: mathew is planning a vacation trip to london next year from today for 5 days , he has calculated he would need about $ 3000 for expenses , including a round - trip plane ticket from l . a to london . he nets around $ 1500 monthly in gross income , after all bills are paid , he is left with about $ 350 each month free for whatever he desires . how much money would mathew need to evenly save from his $ 350 to have $ 3000 in his bank within 12 months ?

<gadget id="calculator">3_000 / 12</gadget>
<output>250</output>
<result>250</result>

Choices:
A. $ 240
B. $ 350
C. $ 217
D. $ 250
E. $ 340

Explanation: answer is ( d ) . if mathew is left with about $ 350 after all expenses each month , he would need to divide the total expense budget to london ( $ 3000 ) by 12 months to determine how much he would need to put away every single month to hit his target . $ 3000 / 12 = $ 250 .


Question: the present worth of rs . 1014 due in 2 years at 4 % per annum compound interest is

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

<gadget id="calculator">(1/25) + 1</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>

<gadget id="calculator">1_014 / (676/625)</gadget>
<output>1_875/2 = around 937.5</output>
<result>1_875/2 = around 937.5</result>

Choices:
A. rs . 150.50
B. rs . 937.5
C. rs . 156.25
D. rs . 158
E. none

divide(1014, power(add(divide(4, const_100), const_1), 2))

Explanation: "solution present worth = rs . [ 1014 / ( 1 + 4 / 100 ) ² ] = rs . ( 1014 x 25 / 26 x 25 / 26 ) = rs . 937.5 answer b"


Question: if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 281 pounds . what is jake ’ s present weight , in pounds ?

<gadget id="calculator">281 - 8</gadget>
<output>273</output>

<gadget id="calculator">273 / 3</gadget>
<output>91</output>

<gadget id="calculator">91 * 2</gadget>
<output>182</output>

<gadget id="calculator">182 + 8</gadget>
<output>190</output>
<result>190</result>

Choices:
A. 125
B. 135
C. 140
D. 165
E. 190

add(multiply(divide(subtract(281, 8), const_3), const_2), 8)

Explanation: "j + k = 281 and so k = 281 - j j - 8 = 2 k j - 8 = 2 ( 281 - j ) 3 j = 570 j = 190 the answer is e ."


Question: the total cost of 100 paper plates and 200 paper cups is $ 8.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?

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

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

Choices:
A. $ . 90
B. $ 1.00
C. $ 1.20
D. $ 1.50
E. $ 1.60

Explanation: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 8.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.60 therefore oa is e"


Question: 2 cow ’ s and 5 goats are brought for rs . 1050 . if the average price of a goat be rs . 90 . what is the average price of a cow .

<gadget id="calculator">5 * 90</gadget>
<output>450</output>

<gadget id="calculator">1_050 - 450</gadget>
<output>600</output>

<gadget id="calculator">600 / 2</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 300
B. 320
C. 330
D. 350
E. 375

divide(subtract(1050, multiply(5, 90)), 2)

Explanation: "explanation : average price of a goat = rs . 90 total price of 5 goats = 5 * 90 = rs . 450 but total price of 2 cows and 5 goats = rs . 1050 total price of 2 cows is = 1050 - 450 = 600 average price of a cow = 600 / 2 = rs . 300 answer : a"


Question: 24 oz of juice p and 25 oz of juice v are mixed to make smothies x and y . the ratio of p to v in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?

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

Choices:
A. 5
B. 10
C. 15
D. 20
E. 25

Explanation: let us now solve for x : ( 4 / 5 ) x + ( 1 / 6 ) ( 49 - x ) = 24 24 x + 5 ( 49 - x ) = ( 24 ) ( 30 ) 24 x + 245 - 5 x = ( 24 ) ( 30 ) 19 x = 720 - 245 19 x = 475 x = 25 answer : e


Question: a certain industrial loom weaves 0.13 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?

<gadget id="calculator">15 / 0.13</gadget>
<output>115.384615</output>
<result>115.384615</result>

Choices:
A. 114
B. 115
C. 116
D. 117
E. 118

Explanation: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.13 : 15 : : 1 : x = > 0.13 * x = 15 = > x = 15 / 0.13 = > x = 115 answer : b"


Question: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 8 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight

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

<gadget id="calculator">1 - (1/8)</gadget>
<output>7/8 = around 0.875</output>

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

<gadget id="calculator">(7/8) * (1/2)</gadget>
<output>7/16 = around 0.4375</output>
<result>7/16 = around 0.4375</result>

Choices:
A. 1 / 7
B. 1 / 8
C. 1 / 4
D. 3 / 4
E. 4 / 9

multiply(subtract(1, divide(1, 8)), divide(1, 2))

Explanation: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 8 of the garden is green , so , since all the flowers must be either green or yellow , we know that 7 / 8 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 7 / 8 * 1 / 2 = 4 / 9 , or e ."


Question: how many 3 digit positive integers with distinct digits are there , which are not multiples of 10 ?

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

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

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

<gadget id="calculator">72 * 8</gadget>
<output>576</output>
<result>576</result>

Choices:
A. 576
B. 520
C. 504
D. 432
E. 348

multiply(multiply(multiply(3, 3), subtract(multiply(3, 3), const_1)), subtract(multiply(3, 3), const_1))

Explanation: a number not to be a multiple of 10 should not have the units digit of 0 . xxx 9 options for the first digit ( from 1 to 9 inclusive ) . 8 options for the third digit ( from 1 to 9 inclusive minus the one we used for the first digit ) . 8 options for the second digit ( from 0 to 9 inclusive minus 2 digits we used for the first and the third digits ) 9 * 8 * 8 = 576 . answer : a .


Question: 3 pounds of 05 grass seed contain 1 percent herbicide . a different type of grass seed , 20 , which contains 20 percent herbicide , will be mixed with 3 pounds of 05 grass seed . how much grass seed of type 20 should be added to the 3 pounds of 05 grass seed so that the mixture contains 15 percent herbicide ?

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

<gadget id="calculator">45 - 3</gadget>
<output>42</output>

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

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

Choices:
A. 3
B. 3.75
C. 4.5
D. 8.4
E. 9

divide(subtract(multiply(15, 3), 3), subtract(20, 15))

Explanation: 05 grass seed contains 5 % herbicide and its amount is 3 pound 20 grass seed contains 20 % herbicide and its amount is x when these two types of grass seeds are mixed , their average becomes 15 % thus we have 3 ( 1 ) + x ( 20 ) / ( x + 3 ) = 15 3 + 20 x = 15 x + 45 5 x = 42 or x = 8.4 d


Question: if f ( f ( n ) ) + f ( n ) = 2 n + 3 and f ( 0 ) = 1 , what is the value of f ( 2012 ) ?

<gadget id="calculator">1 + 2_012</gadget>
<output>2_013</output>
<result>2_013</result>

Choices:
A. 222
B. 2787
C. 2013
D. 2778
E. 10222

Explanation: "put n = 0 then f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) + 1 = 3 ⇒ ⇒ f ( 1 ) = 2 put n = 1 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) + 2 = 5 ⇒ ⇒ f ( 2 ) = 3 put n = 2 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) + 3 = 7 ⇒ ⇒ f ( 3 ) = 4 . . . . . . f ( 2012 ) = 2013 answer : c"


Question: a certain barrel , which is a right circular cylinder , is filled to capacity with 60 gallons of oil . the first barrel is poured into a second barrel , also a right circular cylinder , which is empty . the second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel . if all of the oil in the first barrel is poured into the second barrel , how much empty capacity , in gallons , is left in the second barrel ?

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

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

<gadget id="calculator">480 - 60</gadget>
<output>420</output>
<result>420</result>

Choices:
A. there is no empty capacity
B. 100 gallons
C. 300 gallons
D. 420 gallons
E. 840 gallons

subtract(multiply(60, power(const_2, const_3)), 60)

Explanation: radius of first cylinder = r , diameter = 2 r , height = h radius of second cylinder = 2 r , diamter = 2 d and height = 2 h volume of first cylinder = pie ( r ^ 2 ) * h = 60 volume of second cylinder = pie ( 2 r ^ 2 ) 2 h put the value of pie ( r ^ 2 ) * h = 60 in the second cylinder , volume = pie ( r ^ 2 ) * 4 * 2 = 60 * 8 = 480 gallons empty capacity = 420 gallons answer d


Question: concentrated apples juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches . the tubes are packed into wooden boxes , each with dimensions of 11 inches by 10 inches by 31 inches . how many tubes of concentrated apples juice , at the most , can fit into 3 wooden boxes ?

<gadget id="calculator">11 * 10</gadget>
<output>110</output>

<gadget id="calculator">110 * 31</gadget>
<output>3_410</output>

<gadget id="calculator">3_410 * 3</gadget>
<output>10_230</output>

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

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

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

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

<gadget id="calculator">2.5 ** 2</gadget>
<output>6.25</output>

<gadget id="calculator">(22/7) * 6.25</gadget>
<output>19.642857</output>

<gadget id="calculator">19.642857 * 15</gadget>
<output>294.642855</output>

<gadget id="calculator">10_230 / 294.642855</gadget>
<output>34.72</output>

<gadget id="calculator">34.72 - 10</gadget>
<output>24.72</output>
<result>24.72</result>

Choices:
A. 24 .
B. 28 .
C. 36 .
D. 42 .
E. 48 .

subtract(divide(multiply(multiply(multiply(11, 10), 31), 3), multiply(multiply(divide(multiply(add(const_10, const_1), const_2), add(const_3, const_4)), power(2.5, const_2)), 15)), 10)

Explanation: concentrated apples juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way now , diameter of each tube = 5 inches therefore , 4 * 2 can be put in each wooden box in 3 boxes 3 * 4 * 2 can be accommodated = 24 = a


Question: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 51.84 , the number of the member is the group is :

<gadget id="calculator">51.84 * 100</gadget>
<output>5_184</output>

<gadget id="calculator">5_184 ** (1/2)</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 57
B. 67
C. 72
D. 87
E. 97

Explanation: "explanation : money collected = ( 51.84 x 100 ) paise = 5184 paise . ∴ number of members = √ ( 5184 ) = 72 . answer : c"


Question: a cube has a volume of 125 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?

<gadget id="calculator">125 ** (1/3)</gadget>
<output>5</output>

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

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

Choices:
A. 24
B. 48
C. 64
D. 80
E. 1000

Explanation: "volume = 125 = side ^ 3 i . e . side of cube = 5 new cube has dimensions 10 , 10 , and 10 as all sides are twice of teh side of first cube volume = 10 * 10 * 10 = 1000 square feet answer : option e"


Question: in an election , candidate a got 65 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?

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

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

<gadget id="calculator">560_000 * (17/20)</gadget>
<output>476_000</output>

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

<gadget id="calculator">476_000 * (13/20)</gadget>
<output>309_400</output>
<result>309_400</result>

Choices:
A. 355600
B. 355800
C. 356500
D. 309400
E. 357000

multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(65, const_100))

Explanation: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 65 % therefore , the number of valid votes polled in favour of candidate a = 65 % of 476000 = 65 / 100 × 476000 = 30940000 / 100 = 309400 d )"


Question: in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 6 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?

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

<gadget id="calculator">432 * 4</gadget>
<output>1_728</output>

<gadget id="calculator">1_728 / 72</gadget>
<output>24</output>

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

Choices:
A. 4
B. 6
C. 8
D. 9
E. 12

divide(divide(multiply(multiply(36, 12), const_4), 72), 6)

Explanation: the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 6 = 4 ans a


Question: how many 3 digit number formed by using 23 , 45 , 67 once such that number is divisible by 15 .

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

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

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

Choices:
A. 8
B. 13
C. 12
D. 20
E. 22

Explanation: 4 * 2 * 1 = 8 at one ' s place only 5 will come and at ten ' s place 4 and 7 can be placed , and at 100 th place rest of the 4 digits can come . . . so the answer is 8 answer : a


Question: how many 3 digit positive integers t exist that when divided by 7 leave a remainder of 5 ?

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

<gadget id="calculator">1_000 - 1</gadget>
<output>999</output>

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

<gadget id="calculator">14 * 7</gadget>
<output>98</output>

<gadget id="calculator">98 + 5</gadget>
<output>103</output>

<gadget id="calculator">999 - 103</gadget>
<output>896</output>

<gadget id="calculator">896 / 7</gadget>
<output>128</output>
<result>128</result>

Choices:
A. 128
B. 142
C. 143
D. 141
E. 129

divide(subtract(subtract(multiply(const_100, const_10), const_1), add(multiply(add(const_10, const_4), 7), 5)), 7)

Explanation: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."


Question: the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?

<gadget id="calculator">36 - 26</gadget>
<output>10</output>

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

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

Choices:
A. 17
B. 18
C. 19
D. 22
E. 24

Explanation: "explanation : 10 * 16 + 36 – 26 = 170 = > 170 / 10 = 17 a )"


Question: 48 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?

<gadget id="calculator">48 * 12</gadget>
<output>576</output>

<gadget id="calculator">576 * 5</gadget>
<output>2_880</output>

<gadget id="calculator">30 * 6</gadget>
<output>180</output>

<gadget id="calculator">2_880 / 180</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 10
B. 16
C. 13
D. 18
E. 19

divide(multiply(multiply(48, 12), 5), multiply(30, 6))

Explanation: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 48 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 48 x 5 x 12 x = ( 48 x 5 x 12 ) / ( 30 x 6 ) x = 16 answer b"


Question: the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 20 = 190 , what is the value of x ?

<gadget id="calculator">20 - 1</gadget>
<output>19</output>

<gadget id="calculator">190 / 19</gadget>
<output>10</output>

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

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

Explanation: "ab = ( a - 1 ) ( b - 1 ) x 20 = ( x - 1 ) ( 20 - 1 ) = 190 - - > x - 1 = 10 - - > x = 11 answer : c"


Question: how many 5 digit nos are there if the 2 leftmost digits are odd and the digit 4 ca n ' t appear more than once in the number ? could someone please provide a solution using a approach other than ( 1 - x ( none ) ) approach ?

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

<gadget id="calculator">20 - 1</gadget>
<output>19</output>

<gadget id="calculator">19 * 5</gadget>
<output>95</output>

<gadget id="calculator">95 * 5</gadget>
<output>475</output>

<gadget id="calculator">475 * 5</gadget>
<output>2_375</output>

<gadget id="calculator">2_375 * 10</gadget>
<output>23_750</output>
<result>23_750</result>

Choices:
A. 24300
B. 25700
C. 26500
D. 24400
E. 26300

multiply(multiply(multiply(multiply(subtract(multiply(4, 5), 1), 5), 5), 5), const_10)

Explanation: a . 4 is used once : oo * * 4 - - > ( 5 * 5 * 9 * 9 ) * 3 : 5 choices for the first digit as there are 5 odd numbers , 5 choices for the second digit for the same reason , 9 choices for one of the two * ( not - 4 digit ) , 9 choices for another * ( not - 4 digit ) , multiplied by 3 as 4 can take the place of any of the three last digits ( oo * * 4 , oo * 4 * , oo 4 * * ) ; b . 4 is not used : oo * * * - - > 5 * 5 * 9 * 9 * 9 : the same logic as above . 5 * 5 * 9 * 9 * 3 + 5 * 5 * 9 * 9 * 9 = 24300 . answer : a


Question: a cat leaps 6 leaps for every 5 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?

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

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

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

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

Explanation: "given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 6 / 3 * 5 = 4 : 5 ' ' answer : 4 : 5 ;"


Question: a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 18 m long . over how much area of the field can it graze ?

<gadget id="calculator">18 ** 2</gadget>
<output>324</output>

<gadget id="calculator">324 * pi</gadget>
<output>324*pi = around 1_017.87602</output>

<gadget id="calculator">(324*pi) / 4</gadget>
<output>81*pi = around 254.469005</output>
<result>81*pi = around 254.469005</result>

Choices:
A. 154 cm 2
B. 308 m 2
C. 254 m 2
D. 260 m 2
E. none of these

divide(multiply(power(18, const_2), const_pi), const_4)

Explanation: "area of the shaded portion = 1 ⁄ 4 × π × ( 18 ) 2 = 254 m 2 answer c"


Question: if the arithmetic mean of seventy 5 numbers is calculated , it is 35 . if each number is increased by 5 , then mean of new number is ?

<gadget id="calculator">35 + 5</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 87
B. 40
C. 37
D. 28
E. 26

Explanation: a . m . of 75 numbers = 35 sum of 75 numbers = 75 * 35 = 2625 total increase = 75 * 5 = 375 increased sum = 2625 + 375 = 3000 increased average = 3000 / 75 = 40 . answer : b


Question: 8873 + x = 13200 , then x is ?

<gadget id="calculator">13_200 - 8_873</gadget>
<output>4_327</output>
<result>4_327</result>

Choices:
A. 3327
B. 4327
C. 3337
D. 2337
E. none of these

Explanation: answer x = 13200 - 8873 = 4327 option : b


Question: a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?

<gadget id="calculator">16 - 1</gadget>
<output>15</output>

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

Choices:
A. 1 / 190
B. 1 / 20
C. 1 / 19
D. 1 / 10
E. 1 / 15

Explanation: "the problem with your solution is that we do n ' t choose 1 shoe from 16 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 15 ( as after taking one at random there are 15 shoes left and only one is the pair of the first one ) = 1 / 15 answer : e ."


Question: sales price is $ 60 , gross profit is 140 % of cost , what is the value of gross profit ?

<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">1 + (7/5)</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">60 / (12/5)</gadget>
<output>25</output>

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

Choices:
A. 32
B. 33
C. 39
D. 35
E. 42

subtract(60, divide(60, add(const_1, divide(140, const_100))))

Explanation: "cost + profit = sales cost + ( 140 / 100 ) cost = 60 cost = 25 profit = 60 - 25 = 35 answer ( d )"


Question: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts 6 hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?

<gadget id="calculator">30 * 6</gadget>
<output>180</output>

<gadget id="calculator">40 - 30</gadget>
<output>10</output>

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

<gadget id="calculator">6 + 18</gadget>
<output>24</output>

<gadget id="calculator">30 * 24</gadget>
<output>720</output>

<gadget id="calculator">720 / 60</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 3
B. 4.5
C. 4
D. 12
E. 5

divide(multiply(30, add(6, divide(multiply(30, 6), subtract(40, 30)))), 60)

Explanation: the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )


Question: in an exam 80 % of the boys and 40 % of the girls passed . the number of girls who passed is 120 , which is 2 / 3 rd of the number of boys who failed . what is the total number of students who appeared for the exam ?

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

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

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

<gadget id="calculator">(1/5) * (2/3)</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">120 / (2/15)</gadget>
<output>900</output>

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

<gadget id="calculator">120 / (2/5)</gadget>
<output>300</output>

<gadget id="calculator">900 + 300</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. 1200
B. 380
C. 3800
D. 2180
E. 3180

add(divide(120, multiply(divide(subtract(const_100, 80), const_100), divide(2, 3))), divide(120, divide(40, const_100)))

Explanation: let the number of boys = x , number of girls = y 40 y / 100 = 120 y = 300 120 = 2 / 3 * 20 x / 100 = 2 x / 15 x = 900 total = x + y = 300 + 900 = 1200 answer : a


Question: pipe a fills a tank in 42 minutes . pipe b can fill the same tank 6 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?

<gadget id="calculator">1 / 42</gadget>
<output>1/42 = around 0.02381</output>

<gadget id="calculator">6 / 42</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">(1/42) + (1/7)</gadget>
<output>1/6 = around 0.166667</output>

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

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

inverse(add(divide(const_1, 42), divide(6, 42)))

Explanation: "a ' s rate is 1 / 42 and b ' s rate is 1 / 7 . the combined rate is 1 / 42 + 1 / 7 = 1 / 6 the pipes will fill the tank in 6 minutes . the answer is d ."


Question: by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?

<gadget id="calculator">6.5 * 800</gadget>
<output>5_200</output>

<gadget id="calculator">5_200 / 100</gadget>
<output>52</output>

<gadget id="calculator">1 + 52</gadget>
<output>53</output>

<gadget id="calculator">53 / 1_000</gadget>
<output>53/1_000 = around 0.053</output>

<gadget id="calculator">(53/1_000) * 100</gadget>
<output>53/10 = around 5.3</output>
<result>53/10 = around 5.3</result>

Choices:
A. 4.5 %
B. 5.0 %
C. 5.5 %
D. 5.8 %
E. 6.0 %

multiply(divide(add(const_1, divide(multiply(6.5, 800), const_100)), const_1000), const_100)

Explanation: "the number of grams of liquid x is 1.5 ( 200 ) / 100 + 6.5 ( 800 ) / 100 = 3 + 52 = 55 grams . 55 / 1000 = 5.5 % the answer is c ."


Question: 900 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?

<gadget id="calculator">15 * 900</gadget>
<output>13_500</output>

<gadget id="calculator">900 + 200</gadget>
<output>1_100</output>

<gadget id="calculator">13_500 / 1_100</gadget>
<output>135/11 = around 12.272727</output>
<result>135/11 = around 12.272727</result>

Choices:
A. 12.88
B. 12.6
C. 12.55
D. 12.21
E. 12.27

Explanation: "900 * 15 = 1100 * x x = 12.27 . answer : e"


Question: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 2 ?

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

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

Explanation: points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is b


Question: a snail , climbing a 24 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?

<gadget id="calculator">24 - 4</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 12
B. 16
C. 17
D. 20
E. 21

Explanation: total transaction in two days = 4 - 2 = 2 feet in 20 days it will climb 20 feet on the 21 st day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 21 e


Question: a ’ s speed is 25 / 18 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?

<gadget id="calculator">25 - 18</gadget>
<output>7</output>

<gadget id="calculator">7 / 25</gadget>
<output>7/25 = around 0.28</output>
<result>7/25 = around 0.28</result>

Choices:
A. 1 / 18
B. 7 / 18
C. 7 / 25
D. 3 / 25
E. 1 / 25

Explanation: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 25 meters , b covers 18 meters in that time . so if the race is 25 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 25 meters ) would be the same as the time required by b ( to cover 18 meters ) to reach the finish line . so b should get a head start of 7 / 25 th of the race . answer ( c )"


Question: the marked price of a book is 20 % more than the cost price . after the book is sold , the vendor realizes that he had wrongly raised the cost price by a margin of 25 % . if the marked price of the book is rs . 30 , what is the original cost price of the book ?

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

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

<gadget id="calculator">30 / (6/5)</gadget>
<output>25</output>

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

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

<gadget id="calculator">25 / (5/4)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. rs . 30
B. rs . 25
C. rs . 45
D. rs . 20
E. rs . 10

divide(divide(30, add(const_1, divide(20, const_100))), add(const_1, divide(25, const_100)))

Explanation: let the incorrect cost price be c 1 and let the original cost price be c 2 . marked price of book is rs . 30 . it is 20 % more than c 1 . therefore , ( 120 / 100 ) x c 1 = 30 or c 1 = 25 . c 1 is more than c 2 margin of 25 % . or c 1 = ( 125 / 100 ) c 2 therefore , c 2 = ( 100 / 125 ) x 25 = rs 20 answer : d


Question: the h . c . f . of two numbers is 18 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :

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

Choices:
A. 270
B. 300
C. 299
D. 322
E. 345

Explanation: "the numbers are ( 18 x 11 ) and ( 18 x 15 ) . larger number = ( 18 x 15 ) = 270 . answer : a"


Question: the ratio of buses to cars on river road is 1 to 3 . if there are 20 fewer buses than cars on river road , how many cars are on river road ?

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

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

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

Choices:
A. 100
B. 120
C. 140
D. 30
E. 150

Explanation: "b / c = 1 / 3 c - b = 20 . . . . . . . . . > b = c - 20 ( c - 20 ) / c = 1 / 3 testing answers . clearly eliminate abce put c = 30 . . . . . . . . . > ( 30 - 20 ) / 30 = 10 / 30 = 1 / 3 answer : d"


Question: the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is

<gadget id="calculator">324 * 25</gadget>
<output>8_100</output>

<gadget id="calculator">71 * 100</gadget>
<output>7_100</output>

<gadget id="calculator">8_100 - 7_100</gadget>
<output>1_000</output>

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

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

Choices:
A. 238
B. 277
C. 278
D. 200
E. 288

divide(subtract(multiply(324, 25), multiply(71, const_100)), subtract(25, 20))

Explanation: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 * ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . . answer : d ) 200"


Question: if annual decrease in the population of a town is 5 % and the present number of people is 40000 what will the population be in 2 years ?

<gadget id="calculator">100 - 5</gadget>
<output>95</output>

<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>

<gadget id="calculator">(19/20) ** 2</gadget>
<output>361/400 = around 0.9025</output>

<gadget id="calculator">(361/400) * 40_000</gadget>
<output>36_100</output>
<result>36_100</result>

Choices:
A. 24560
B. 26450
C. 36100
D. 38920
E. 45200

multiply(power(divide(subtract(const_100, 5), const_100), 2), 40000)

Explanation: population in 2 years = 40000 ( 1 - 5 / 100 ) ^ 2 = 40000 * 19 * 19 / 20 * 20 = 36100 answer is c


Question: the price of lunch for 15 people was $ 206.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?

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

<gadget id="calculator">206 / 115</gadget>
<output>206/115 = around 1.791304</output>

<gadget id="calculator">(206/115) * 100</gadget>
<output>4_120/23 = around 179.130435</output>

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

<gadget id="calculator">(4_120/23) * (1/15)</gadget>
<output>824/69 = around 11.942029</output>
<result>824/69 = around 11.942029</result>

Choices:
A. $ 11.73
B. $ 12.48
C. $ 13.80
D. $ 14.00
E. $ 15.87

multiply(multiply(divide(206, add(const_100, 15)), const_100), divide(const_1, 15))

Explanation: take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 206 is for 115 then we have to calculate for 100 for 115 206 for 100 x so by cross multiplication we get 115 x = 100 * 206 = > x = 100 * 206 / 110 by simplifying we get x as 187.27 which is the price of lunch before gratuity so the gratuity is 18.73 so as the question ask the average price person excluding gratuity is 187.27 / 15 = 12.48 so our answer is b )


Question: joe drives 600 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?

<gadget id="calculator">600 + 120</gadget>
<output>720</output>

<gadget id="calculator">600 / 60</gadget>
<output>10</output>

<gadget id="calculator">120 / 40</gadget>
<output>3</output>

<gadget id="calculator">10 + 3</gadget>
<output>13</output>

<gadget id="calculator">720 / 13</gadget>
<output>720/13 = around 55.384615</output>
<result>720/13 = around 55.384615</result>

Choices:
A. 42
B. 55
C. 50
D. 54
E. 56

Explanation: "t 1 = 600 / 60 = 10 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 13 hours avg speed = total distance / t = 720 / 13 = 55 mph = b"


Question: a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 20.00 ?

<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 - 30</gadget>
<output>70</output>

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(7/10) * 20</gadget>
<output>14</output>

<gadget id="calculator">(4/5) * 14</gadget>
<output>56/5 = around 11.2</output>
<result>56/5 = around 11.2</result>

Choices:
A. $ 10.00
B. $ 11.20
C. $ 14.40
D. $ 16.00
E. $ 18.00

multiply(divide(subtract(const_100, 20), const_100), multiply(divide(subtract(const_100, 30), const_100), 20.00))

Explanation: "for retail price = $ 20 first maximum discounted price = 20 - 30 % of 20 = 20 - 6 = 14 price after additional discount of 20 % = 14 - 20 % of 14 = 14 - 2.8 = 11.2 answer : option b"


Question: if 20 liters of chemical x are added to 80 liters of a mixture that is 15 % chemical x and 85 % chemical y , then what percentage of the resulting mixture is chemical x ?

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

<gadget id="calculator">(3/20) * 80</gadget>
<output>12</output>

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

Choices:
A. 30 %
B. 32 %
C. 35 %
D. 38 %
E. 40 %

add(20, multiply(divide(15, const_100), 80))

Explanation: "the amount of chemical x in the solution is 20 + 0.15 ( 80 ) = 32 liters . 32 liters / 100 liters = 32 % the answer is b ."


Question: a set consists of 12 numbers , all are even or multiple of 5 . if 4 numbers are even and 10 numbers are multiple of 5 , how many numbers is multiple of 10 ?

<gadget id="calculator">12 - 10</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 0
B. 1
C. 2
D. 3
E. 5

Explanation: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 12 = 4 + 10 - { both } + 0 ; { both } = 2 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : c ."


Question: two employees x and y are paid a total of rs . 506 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

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

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

<gadget id="calculator">506 * 10</gadget>
<output>5_060</output>

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

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

<gadget id="calculator">5_060 / 22</gadget>
<output>230</output>
<result>230</result>

Choices:
A. s . 250
B. s . 280
C. s . 290
D. s . 299
E. s . 230

divide(multiply(506, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 506 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 506 ⇒ y [ 12 / 10 + 1 ] = 506 ⇒ 22 y / 10 = 506 ⇒ 22 y = 5060 ⇒ y = 5060 / 22 = 460 / 2 = rs . 230 e"


Question: the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years . the age of the 15 th student is

<gadget id="calculator">15 * 15</gadget>
<output>225</output>

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

<gadget id="calculator">10 * 16</gadget>
<output>160</output>

<gadget id="calculator">56 + 160</gadget>
<output>216</output>

<gadget id="calculator">225 - 216</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 9 years
B. 11 years
C. 14 years
D. 21 years
E. 9 years

subtract(multiply(15, 15), add(multiply(4, 14), multiply(10, 16)))

Explanation: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 4 + 16 x 10 ) ] = ( 225 - 216 ) = 9 years . answer e"


Question: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 40 , find the sum of money ?

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

<gadget id="calculator">100 + 65</gadget>
<output>165</output>

<gadget id="calculator">165 + 40</gadget>
<output>205</output>

<gadget id="calculator">1 * 205</gadget>
<output>205</output>
<result>205</result>

Choices:
A. 288
B. 262
C. 72
D. 205
E. 267

multiply(divide(40, 40), add(add(const_100, 65), 40))

Explanation: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 40 41 - - - - ? = > rs . 205 answer : d"


Question: two trains leave the train station at the same time . one train , on the blue line , heads east - while the other , on the red line , heads west . if the train on the blue line averages 40 km / hr and the other train averages 40 km / hr - how long will it take for the trains to be 100 km apart ?

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

<gadget id="calculator">50 / 40</gadget>
<output>5/4 = around 1.25</output>
<result>5/4 = around 1.25</result>

Choices:
A. 2 hours
B. 2.25 hours
C. 1 hour
D. 1.25 hours
E. not enough information

Explanation: each train is averaging 40 km / hour in an opposite direction . after 1 hour , they will be 80 km apart , and after 1.25 hours , they will be 100 km apart . ( 80 * 1.25 = 100 ) answer is d


Question: a certain college ' s enrollment at the beginning of 1992 was 30 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?

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

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

<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">130 * (11/10)</gadget>
<output>143</output>

<gadget id="calculator">143 - 100</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 43 %
B. 45 %
C. 50 %
D. 35 %
E. 38 %

subtract(multiply(add(const_100, 30), divide(add(const_100, 10), const_100)), const_100)

Explanation: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 130 and enrollment in 1993 will be 130 * 1.1 = 143 increase in 1993 from 1991 = 143 - 100 = 43 answer : a"


Question: a can give b 120 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?

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

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

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

<gadget id="calculator">1_000 - 120</gadget>
<output>880</output>

<gadget id="calculator">800_000 / 880</gadget>
<output>10_000/11 = around 909.090909</output>

<gadget id="calculator">1_000 - (10_000/11)</gadget>
<output>1_000/11 = around 90.909091</output>
<result>1_000/11 = around 90.909091</result>

Choices:
A. 90.09 meters
B. 111.12 meters
C. 112.12 meters
D. 113.12 meters
E. none of these

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 120)))

Explanation: "explanation : a runs 1000 meters while b runs 880 meters and c runs 800 meters . therefore , b runs 880 meters while c runs 800 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 800 ) / 880 = 909.09 meters thus , b can give c ( 1000 - 909.09 ) = 90.09 meters start answer : a"


Question: a merchant marks his goods up by 30 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?

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

<gadget id="calculator">130 * 20</gadget>
<output>2_600</output>

<gadget id="calculator">2_600 / 100</gadget>
<output>26</output>

<gadget id="calculator">130 - 26</gadget>
<output>104</output>

<gadget id="calculator">104 - 100</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 8 %
B. 10 %
C. 21 %
D. 15 %
E. 4 %

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

Explanation: "let the price be 100 . the price becomes 130 after a 30 % markup . now a discount of 20 % on 130 . profit = 104 - 100 4 % answer e"


Question: the owner of a furniture shop charges his customer 42 % more than the cost price . if a customer paid rs . 8300 for a computer table , then what was the cost price of the computer table ?

<gadget id="calculator">42 / 100</gadget>
<output>21/50 = around 0.42</output>

<gadget id="calculator">1 + (21/50)</gadget>
<output>71/50 = around 1.42</output>

<gadget id="calculator">8_300 / (71/50)</gadget>
<output>415_000/71 = around 5_845.070423</output>
<result>415_000/71 = around 5_845.070423</result>

Choices:
A. rs . 5725
B. rs . 5845
C. rs . 6275
D. rs . 6725
E. none of these

divide(8300, add(const_1, divide(42, const_100)))

Explanation: cp = sp * ( 100 / ( 100 + profit % ) ) = 8300 ( 100 / 142 ) = rs . 5845 . answer : b


Question: an article with cost price of 320 is sold at 18 % profit . what is the selling price ?

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

<gadget id="calculator">320 * (9/50)</gadget>
<output>288/5 = around 57.6</output>

<gadget id="calculator">320 + (288/5)</gadget>
<output>1_888/5 = around 377.6</output>
<result>1_888/5 = around 377.6</result>

Choices:
A. 198
B. 200
C. 204
D. 378
E. 347

add(320, multiply(320, divide(18, const_100)))

Explanation: "sp = 1.18 * 320 = 378 answer : d"


Question: given that 100.48 = x , 100.70 = y and xz = y 2 , then the value of z is close to :

<gadget id="calculator">100.7 - 100</gadget>
<output>0.7</output>

<gadget id="calculator">0.7 * 2</gadget>
<output>1.4</output>

<gadget id="calculator">100.48 - 100</gadget>
<output>0.48</output>

<gadget id="calculator">1.4 / 0.48</gadget>
<output>2.916667</output>
<result>2.916667</result>

Choices:
A. 2.2
B. 8.2
C. 2.9
D. 2.1
E. 2.6

divide(multiply(subtract(100.70, const_100), const_2), subtract(100.48, const_100))

Explanation: "xz = y 2 10 ( 0.48 z ) = 10 ( 2 x 0.70 ) = 101.40 0.48 z = 1.40 z = 140 = 35 = 2.9 ( approx . ) 48 12 answer : c"


Question: how many digits are required to number a book containing 250 pages ?

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

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

<gadget id="calculator">90 * 2</gadget>
<output>180</output>

<gadget id="calculator">9 + 180</gadget>
<output>189</output>

<gadget id="calculator">250 - 100</gadget>
<output>150</output>

<gadget id="calculator">150 + 1</gadget>
<output>151</output>

<gadget id="calculator">151 * 3</gadget>
<output>453</output>

<gadget id="calculator">189 + 453</gadget>
<output>642</output>
<result>642</result>

Choices:
A. 756
B. 642
C. 492
D. 372
E. 250

add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(250, const_100), const_1), const_3))

Explanation: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 250 - ( 90 + 9 ) = 151 pages will require 151 * 3 = 453 digits . the total number of digits is 9 + 180 + 453 = 642 . the answer is b ."


Question: at scratch and dents rent - a - car , it costs $ 34.95 a day plus $ 0.23 per mile to rent a car . at rent - a - lemon , the charge is $ 25.00 a day plus $ 1.31 per mile . if you need to rent a car for 3 days , how many miles ( to nearest tenth ) must you drive for a car from both agencies to cost the same amount ?

<gadget id="calculator">34.95 * 3</gadget>
<output>104.85</output>

<gadget id="calculator">25 * 3</gadget>
<output>75</output>

<gadget id="calculator">104.85 - 75</gadget>
<output>29.85</output>

<gadget id="calculator">1.31 - 0.23</gadget>
<output>1.08</output>

<gadget id="calculator">29.85 / 1.08</gadget>
<output>27.638889</output>
<result>27.638889</result>

Choices:
A. 25.7 miles
B. 26.2 miles
C. 27.6 miles
D. 27.9 miles
E. 29.9 miles

divide(subtract(multiply(34.95, 3), multiply(25, 3)), subtract(1.31, 0.23))

Explanation: for sad : saddaily = $ 34.95 / day sadmile = $ 0.23 / mile for ral : raldaily = $ 25.00 / day ralmile = $ 1.31 / mile we want the raltotal = sadtotal , so we get ( raldaily * days ) + ( ralmile * miles ) = ( saddaily * days ) + ( sadmile * miles ) = > miles = ( ( saddaily * days ) - ( raldaily * days ) ) / ( ralmiles - sadmiles ) = ( ( saddaily - raldaily ) * days ) / ( ralmiles - sadmiles ) miles = ( ( $ 34.95 * 3 ) - ( $ 25.00 * 3 ) ) / ( $ 1.31 - $ 0.23 ) = 27.6 miles c . 27.6 miles


Question: pipe a can fill a tank in 9 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?

<gadget id="calculator">12 * 9</gadget>
<output>108</output>

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

<gadget id="calculator">108 / 3</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 36
B. 88
C. 18
D. 26
E. 12

divide(multiply(12, 9), subtract(12, 9))

Explanation: "let the leak can empty the full tank in x hours 1 / 9 - 1 / x = 1 / 12 = > 1 / x = 1 / 9 - 1 / 12 = 1 / 12 = > x = 36 . answer : a"


Question: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 16 is divided by 12 .

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

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

<gadget id="calculator">16 + 25</gadget>
<output>41</output>

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

<gadget id="calculator">41 - 36</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 5
B. 1
C. 0
D. 8
E. 7

subtract(add(16, power(add(const_1, const_4), const_2)), multiply(12, 3))

Explanation: every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 16 = 36 n ^ 2 + 12 n + 1 + 16 = 36 n ^ 2 + 12 n + 12 + 5 if p = 6 n - 1 , then p ^ 2 + 16 = 36 n ^ 2 - 12 n + 1 + 16 = 36 n ^ 2 - 12 n + 12 + 5 when divided by 12 , it must leave a remainder of 5 . the answer is a .


Question: if x is 20 percent greater than 55 , then x =

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

<gadget id="calculator">(1/5) * 55</gadget>
<output>11</output>

<gadget id="calculator">55 + 11</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 68
B. 70.4
C. 86
D. 66
E. 108

add(55, multiply(divide(20, const_100), 55))

Explanation: x is 20 % greater than 55 means x is 1.2 times 55 ( in other words 55 + 20 / 100 * 55 = 1.2 * 55 ) therefore , x = 1.2 * 55 = 66 answer : d


Question: find the value of 72519 x 9999 = y ?

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

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

Choices:
A. 354517481
B. 457687783
C. 246567689
D. 725117481
E. 565776879

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


Question: a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 49 / 64 . how many marbles are in the bag ?

<gadget id="calculator">49 / 64</gadget>
<output>49/64 = around 0.765625</output>

<gadget id="calculator">(49/64) ** (1/2)</gadget>
<output>7/8 = around 0.875</output>

<gadget id="calculator">1 - (7/8)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">12 / (1/8)</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 24
B. 48
C. 60
D. 96
E. 84

divide(12, subtract(const_1, sqrt(divide(49, 64))))

Explanation: "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 49 / 64 - - > ( x - 12 ) ^ 2 = 49 / 64 x ^ 2 square rooting u have x - 12 / x = 7 / 8 or x = 96 d"


Question: average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ?

<gadget id="calculator">15 * 43</gadget>
<output>645</output>

<gadget id="calculator">7 * 41</gadget>
<output>287</output>

<gadget id="calculator">7 * 45</gadget>
<output>315</output>

<gadget id="calculator">287 + 315</gadget>
<output>602</output>

<gadget id="calculator">645 - 602</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 41
B. 39
C. 43
D. 45
E. 47

subtract(multiply(15, 43), add(multiply(7, 41), multiply(7, 45)))

Explanation: option ' c '


Question: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 432 . 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">432 / (1/25)</gadget>
<output>10_800</output>
<result>10_800</result>

Choices:
A. 2277
B. 2667
C. 3600
D. 9766
E. 10800

divide(432, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1)))

Explanation: p = 432 ( 100 / 5 ) ^ 2 = > p = 10800 answer : e


Question: a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is π r during the first 30 seconds , π r / 2 during next one minute , π r / 4 during next 2 minutes , π r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for the previous round ?

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

Choices:
A. 4
B. 8
C. 16
D. 32
E. 36

Explanation: explanation : there is more than 1 way to approach the solution ; however , i will detail the easiest way to go about it here . we want to find the ratio of time taken for nth round : time taken for ( n - 1 ) th round it will be same as finding the ratio of time taken for 2 nd round : time taken for 1 st round . 1 round = circumference of the circle = 2 π r 1 st round : speed = π r for 30 seconds . so , total distance travelled = π r / 2 . speed = π r / 2 for 1 minute . so , total distance travelled = π r / 2 . speed = π r / 4 for 2 minutes . so , total distance travelled = π r / 2 . speed = π r / 8 for 4 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 7.5 minutes . 2 nd round : speed = π r / 16 for 8 minutes . so , total distance travelled = π r / 2 . speed = π r / 32 for 16 minutes . so , total distance travelled = π r / 2 . speed = π r / 64 for 32 minutes . so , total distance travelled = π r / 2 . speed = π r / 128 for 64 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 120 minutes . ratio is 120 : 7.5 = 16 : 1 . answer : c


Question: . a car covers a distance of 1028 km in 4 hours . find its speed ?

<gadget id="calculator">1_028 / 4</gadget>
<output>257</output>
<result>257</result>

Choices:
A. 104
B. 255
C. 266
D. 257
E. 276

Explanation: "1028 / 4 = 257 kmph answer : d"


Question: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t ?

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

Choices:
A. t = 16
B. t = 32
C. t = 64
D. 128
E. 512

Explanation: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"


Question: an enterprising businessman earns an income of re 5 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 10 th day of business , he earns an income of :

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

<gadget id="calculator">50 - 5</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 21
B. 22
C. 20
D. 45
E. 30

Explanation: 2 nd day he earns = 3 ( 2 – 5 ) 3 rd day he earns = 3 ( 3 – 5 ) on 20 th day he earns 3 ( 20 - 5 ) = 45 rupees answer : d


Question: a student chose a number , multiplied it by 3 , then subtracted 138 from the result and got 102 . what was the number he chose ?

<gadget id="calculator">102 + 138</gadget>
<output>240</output>

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

Choices:
A. 80
B. 120
C. 130
D. 140
E. 150

Explanation: "solution : let xx be the number he chose , then 3 ⋅ x − 138 = 102 3 x = 240 x = 80 answer a"


Question: two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively find the time taken by the slower train to pass the driver of the faster one .

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

<gadget id="calculator">1_000 * 75</gadget>
<output>75_000</output>

<gadget id="calculator">75_000 / 3_600</gadget>
<output>125/6 = around 20.833333</output>

<gadget id="calculator">500 / (125/6)</gadget>
<output>24</output>

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

Choices:
A. 12 sec
B. 24 sec
C. 48 sec
D. 60 sec
E. none

multiply(divide(500, divide(multiply(const_1000, add(45, 30)), const_3600)), const_2)

Explanation: solution relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec total distance covered = ( 500 + 500 ) m = 1000 m required time = ( 1000 x 6 / 125 ) sec = 48 sec answer c


Question: the population of a village is 14300 . it increases annually at the rate of 15 % p . a . what will be its population after 2 years ?

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

<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>

<gadget id="calculator">(23/20) ** 2</gadget>
<output>529/400 = around 1.3225</output>

<gadget id="calculator">14_300 * (529/400)</gadget>
<output>75_647/4 = around 18_911.75</output>
<result>75_647/4 = around 18_911.75</result>

Choices:
A. 18911
B. 18788
C. 19898
D. 14000
E. 14400

multiply(14300, power(add(const_1, divide(15, const_100)), 2))

Explanation: formula : ( after = 100 denominator ago = 100 numerator ) 14300 × 115 / 100 × 115 / 100 = 18911 a


Question: what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 20 ?

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

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

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

Choices:
A. - 1
B. 6
C. 7
D. 12
E. 14

add(add(const_4, 3), subtract(3, const_4))

Explanation: "first of all | x - 3 | ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + | x - 3 | = 20 . when x < 3 , x - 3 is negative , thus | x - 3 | = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 , x - 3 is non - negative , thus | x - 3 | = x - 3 . in this case we ' ll have ( x - 3 ) ^ 2 + ( x - 3 ) = 20 - - > x = - 2 or x = 7 . discard x = - 2 because it ' s not in the range we consider ( > = 3 ) . thus there are two solutions : x = - 1 and x = 7 - - > the sum = 6 . answer : b ."


Question: a closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity . when the tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . when the tank is placed on its side on level ground , what is the height , in feet , of the surface of the water above the ground ?

<gadget id="calculator">36 * pi</gadget>
<output>36*pi = around 113.097336</output>

<gadget id="calculator">(36*pi) / 4</gadget>
<output>9*pi = around 28.274334</output>

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

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

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

sqrt(divide(divide(multiply(36, const_pi), 4), const_pi))

Explanation: 36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d


Question: shopkeeper rise price by 33 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?

<gadget id="calculator">100 + 33</gadget>
<output>133</output>

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

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

<gadget id="calculator">133 * (9/10)</gadget>
<output>1_197/10 = around 119.7</output>

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

<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">(1_197/10) * (17/20)</gadget>
<output>20_349/200 = around 101.745</output>

<gadget id="calculator">(20_349/200) - 100</gadget>
<output>349/200 = around 1.745</output>
<result>349/200 = around 1.745</result>

Choices:
A. 1.745 %
B. 4.745 %
C. 3.745 %
D. 6.745 %
E. 7.745 %

subtract(multiply(multiply(add(const_100, 33), divide(subtract(const_100, 10), const_100)), divide(subtract(const_100, 15), const_100)), const_100)

Explanation: "let d initial price be 100 33 % rise now price = 133 / 100 * 100 = 133 10 % discount then price = 133 * 90 / 100 = 119.7 15 % discount then price = 119.7 * 85 / 100 = 101.745 so gain = 101.745 - 100 = 1.745 gain % = gain * 100 / cp = = > 1.745 * 100 / 100 = 1.745 % answer : a"


Question: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13 . if the shop carries 352 dogs and bunnies total in stock , how many dogs are there ?

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

<gadget id="calculator">352 / 16</gadget>
<output>22</output>

<gadget id="calculator">22 * 3</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 42
B. 66
C. 98
D. 112
E. 154

Explanation: "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 13 x total dogs and bunnies = 16 x . and we are given that 16 x = 352 . hence x = 22 . dogs = 3 x = 3 * 22 = 66 ( option b )"


Question: when the price of an article was reduced by 25 % its sale increased by 80 % . what was the net effect on the sale ?

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

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

<gadget id="calculator">180 * 75</gadget>
<output>13_500</output>

<gadget id="calculator">13_500 / 100</gadget>
<output>135</output>

<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 35 % increase
B. 44 % decrease
C. 60 % increase
D. 66 % increase
E. 66 % decrease

subtract(divide(multiply(add(80, const_100), subtract(const_100, 25)), const_100), const_100)

Explanation: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 25 % , the new price is 0.75 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.75 p ) ( 1.8 n ) = 1.35 np , which is 1.35 times the old revenue , so is 35 % greater . answer : a"


Question: 5 years ago , the average age of a and b was 15 years . average age of a , b and c today is 20 years . how old will c be after 14 years ?

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

<gadget id="calculator">15 * 2</gadget>
<output>30</output>

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

<gadget id="calculator">35 + 5</gadget>
<output>40</output>

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

<gadget id="calculator">20 + 14</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 30
B. 34
C. 40
D. 50
E. 60

add(subtract(multiply(20, const_3), add(add(multiply(15, const_2), 5), 5)), 14)

Explanation: explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b


Question: one fourth of a solution that was 10 % sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?

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

<gadget id="calculator">100 * (4/25)</gadget>
<output>16</output>

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

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

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

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

<gadget id="calculator">75 * (1/10)</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">16 - (15/2)</gadget>
<output>17/2 = around 8.5</output>

<gadget id="calculator">(17/2) / 25</gadget>
<output>17/50 = around 0.34</output>

<gadget id="calculator">(17/50) * 100</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 34 %
B. 24 %
C. 22 %
D. 18 %
E. 8.5 %

multiply(divide(subtract(multiply(const_100, divide(16, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(10, const_100))), multiply(divide(const_1, const_4), const_100)), const_100)

Explanation: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : a ."


Question: a can give b 100 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?

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

<gadget id="calculator">1_000 - 120</gadget>
<output>880</output>

<gadget id="calculator">1_000 * 880</gadget>
<output>880_000</output>

<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>

<gadget id="calculator">880_000 / 900</gadget>
<output>8_800/9 = around 977.777778</output>

<gadget id="calculator">1_000 - (8_800/9)</gadget>
<output>200/9 = around 22.222222</output>
<result>200/9 = around 22.222222</result>

Choices:
A. 10.22 meters
B. 11.22 meters
C. 22.22 meters
D. 33.22 meters
E. none of these

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 120)), subtract(multiply(const_100, const_10), 100)))

Explanation: "explanation : a runs 1000 meters while b runs 900 meters and c runs 880 meters . therefore , b runs 900 meters while c runs 880 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 880 ) / 900 = 977.778 meters thus , b can give c ( 1000 - 977.77 ) = 22.22 meters start answer : c"


Question: a train 450 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :

<gadget id="calculator">450 / 1_000</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">25 + 2</gadget>
<output>27</output>

<gadget id="calculator">(9/20) / 27</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">3_600 * (1/60)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 30 sec
B. 32 sec
C. 36 sec
D. 38 sec
E. 60 sec

multiply(const_3600, divide(divide(450, const_1000), add(25, 2)))

Explanation: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 450 × 2 / 15 ) sec = 60 sec answer : e"


Question: a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?

<gadget id="calculator">45 - 35</gadget>
<output>10</output>

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

Choices:
A. 4 inches
B. 6 inches
C. 5 inches
D. 8 inches
E. 10 inches

Explanation: you need to divide the width and length of the rectangular to equal pieces where l = w you can solve this using gcf 35 = 5 * 7 45 = 3 * 3 * 5 gcf = 5 p . s you can make squares with side of 5 answer : c


Question: the function f ( p ) represents the number of ways that prime numbers can be uniquely summed to form a certain number p such that p = a + b + c + d … where those summed variables are each prime and a ≤ b ≤ c ≤ d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?

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

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

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

Explanation: so we can start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d


Question: in what time will a train 175 m long cross an electric pole , it its speed be 144 km / hr ?

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

<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>

<gadget id="calculator">175 / 40</gadget>
<output>35/8 = around 4.375</output>
<result>35/8 = around 4.375</result>

Choices:
A. 2.58 sec
B. 2.91 sec
C. 4.37 sec
D. 2.9 sec
E. 1.8 sec

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 175 / 40 = 4.37 sec . answer : c"


Question: a student chose a number , multiplied it by 5 , then subtracted 275 from the result and got 135 . what was the number he chose ?

<gadget id="calculator">135 + 275</gadget>
<output>410</output>

<gadget id="calculator">410 / 5</gadget>
<output>82</output>
<result>82</result>

Choices:
A. 80
B. 82
C. 84
D. 86
E. 88

Explanation: "let x be the number he chose , then 5 ⋅ x − 275 = 135 5 x = 410 x = 82 correct answer b"


Question: in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?

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

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

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

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

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

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

<gadget id="calculator">18 + 6</gadget>
<output>24</output>

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

<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 36
B. 34
C. 32
D. 30
E. 28

add(add(multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 3), 6), multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 2))

Explanation: "let c be the capacity of the can . ( 3 / 5 ) * ( c - 6 ) + 6 = ( 2 / 3 ) * c 9 c - 54 + 90 = 10 c c = 36 the answer is a ."


Question: susan drives from city a to city b . after two hours of driving she noticed that she covered 80 km and calculated that , if she continued driving at the same speed , she would end up been 15 minutes late . so she increased her speed by 10 km / hr and she arrived at city b 36 minutes earlier than she planned . find the distance between cities a and b .

<gadget id="calculator">36 / 60</gadget>
<output>3/5 = around 0.6</output>

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

<gadget id="calculator">40 + 10</gadget>
<output>50</output>

<gadget id="calculator">80 / 50</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(3/5) - (8/5)</gadget>
<output>-1</output>

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

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

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

<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>

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

<gadget id="calculator">(1/40) - (1/50)</gadget>
<output>1/200 = around 0.005</output>

<gadget id="calculator">(3/4) / (1/200)</gadget>
<output>150</output>

<gadget id="calculator">150 + 100</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 223
B. 376
C. 250
D. 378
E. 271

add(divide(subtract(add(subtract(divide(36, const_60), divide(80, add(divide(80, const_2), 10))), const_2), divide(15, const_60)), subtract(divide(const_1, divide(80, const_2)), divide(const_1, add(divide(80, const_2), 10)))), const_100)

Explanation: let xx be the distance between a and b . since susan covered 80 km in 2 hours , her speed was v = 802 = 40 v = 802 = 40 km / hr . if she continued at the same speed she would be 1515 minutes late , i . e . the planned time on the road is x 40 − 1560 x 40 − 1560 hr . the rest of the distance is ( x − 80 ) ( x − 80 ) km . v = 40 + 10 = 50 v = 40 + 10 = 50 km / hr . so , she covered the distance between a and b in 2 + x − 80502 + x − 8050 hr , and it was 36 min less than planned . therefore , the planned time was 2 + x − 8050 + 36602 + x − 8050 + 3660 . when we equalize the expressions for the scheduled time , we get the equation : x 40 − 1560 = 2 + x − 8050 + 3660 x 40 − 1560 = 2 + x − 8050 + 3660 x − 1040 = 100 + x − 80 + 3050 x − 1040 = 100 + x − 80 + 3050 x − 104 = x + 505 x − 104 = x + 505 5 x − 50 = 4 x + 2005 x − 50 = 4 x + 200 x = 250 x = 250 so , the distance between cities a and b is 250 km . answer : c


Question: a train running at the speed of 40 km / hr crosses a pole in 9 sec . what is the length of the train ?

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

<gadget id="calculator">40_000 / 3_600</gadget>
<output>100/9 = around 11.111111</output>

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

Choices:
A. 100 m
B. 150 m
C. 187 m
D. 167 m
E. 197 m

multiply(divide(multiply(40, const_1000), const_3600), 9)

Explanation: "speed = 40 * 5 / 18 = 100 / 9 m / sec length of the train = speed * time = 100 / 9 * 9 = 100 m answer : a"


Question: what is the remainder if 7 ^ 16 is divided by 100 ?

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

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

<gadget id="calculator">50 - 49</gadget>
<output>1</output>
<result>1</result>

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

subtract(divide(100, const_2), multiply(7, 7))

Explanation: "7 ^ 16 can be written as ( 7 ^ 4 ) ^ 4 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 4 by 100 , the reminder is 1 ^ 4 = 1 answer : d"


Question: a large box contains 17 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?

<gadget id="calculator">17 * 25</gadget>
<output>425</output>
<result>425</result>

Choices:
A. 250
B. 350
C. 425
D. 550
E. 650

Explanation: "the number of chocolate bars is equal to 17 * 25 = 425 correct answer c"


Question: what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?

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

Choices:
A. 12
B. 18
C. 15
D. 6
E. 9

Explanation: explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d


Question: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 6 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?

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

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

<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 5 : 1
B. 30 : 2
C. 15 : 2
D. 20 : 2
E. 25 : 2

Explanation: "u / i = 6 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 30 : 18 : 2 i . e . u : b = 30 : 2 answer : option b"


Question: a man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 3 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?

<gadget id="calculator">3 / 60</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">15 - 9</gadget>
<output>6</output>

<gadget id="calculator">(1/20) * 6</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) / 9</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">60 * (1/30)</gadget>
<output>2</output>
<result>2</result>

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

multiply(const_60, divide(multiply(divide(3, const_60), subtract(15, 9)), 9))

Explanation: when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 3 * 15 / 60 = 15 / 20 miles and the man walks the distance mm , which is 3 * 9 / 60 = 9 / 20 mile . the difference of 15 / 20 - 9 / 20 = 3 / 10 miles ( mw ) will be covered by the man in ( 3 / 10 ) / 9 = 1 / 30 of an hour , which is 2 minutes . answer b .


Question: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 20 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?

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

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

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

<gadget id="calculator">(4/5) * 3</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">(2/5) + (12/5)</gadget>
<output>14/5 = around 2.8</output>

<gadget id="calculator">3 - (12/5)</gadget>
<output>3/5 = around 0.6</output>

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

<gadget id="calculator">(3/5) + (8/5)</gadget>
<output>11/5 = around 2.2</output>

<gadget id="calculator">(14/5) - (11/5)</gadget>
<output>3/5 = around 0.6</output>

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

<gadget id="calculator">(3/5) / 5</gadget>
<output>3/25 = around 0.12</output>

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

Choices:
A. 2 %
B. 5 %
C. 8 %
D. 10 %
E. 12 %

multiply(divide(subtract(add(multiply(divide(20, const_100), 2), multiply(divide(80, const_100), 3)), add(subtract(3, multiply(divide(80, const_100), 3)), subtract(2, multiply(divide(20, const_100), 2)))), add(3, 2)), const_100)

Explanation: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 20 % of democrats ( 40 * 0.2 = 8 ) voted for candidate x , means that out of total of 100 voters ; 56 ( 48 + 8 ) voters voted for candidate x and 44 voted for candidate y . thus we can infer that candidate x is expected to win the election by 12 ( 56 - 44 ) votes . therefore candidate x is expected to win the election by ( 12 / 100 ) votes which is equivalent to 12 % . i think the answer is e ."


Question: the sides of a square region , measured to the nearest centimeter , are 10 centimeters long . the least possible value of the actual area of the square region is

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

<gadget id="calculator">10 - (1/4)</gadget>
<output>39/4 = around 9.75</output>

<gadget id="calculator">(39/4) - (1/4)</gadget>
<output>19/2 = around 9.5</output>

<gadget id="calculator">(19/2) ** 2</gadget>
<output>361/4 = around 90.25</output>
<result>361/4 = around 90.25</result>

Choices:
A. 96.25 sq cm
B. 98.25 sq cm
C. 92.25 sq cm
D. 100.25 sq cm
E. 90.25 sq cm

power(subtract(subtract(10, const_0_25), const_0_25), const_2)

Explanation: "though there might be some technicalities concerning the termnearest ( as 9.5 is equidistant from both 9 and 10 ) the answer still should be : 9.5 ^ 2 = 90.25 . answer : e"


Question: if tim had lunch at $ 50.50 and he gave 10 % tip , how much did he spend ?

<gadget id="calculator">50.5 * 10</gadget>
<output>505</output>

<gadget id="calculator">505 / 100</gadget>
<output>101/20 = around 5.05</output>

<gadget id="calculator">50.5 + (101/20)</gadget>
<output>55.55</output>
<result>55.55</result>

Choices:
A. $ 30.60
B. $ 60.60
C. $ 70.60
D. $ 55.55
E. $ 50.60

Explanation: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 10 / 100 ) * 50.50 = $ 5.05 total spent 50.50 + 5.05 = $ 55.55 correct answer d"


Question: a 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .

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

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

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

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

<gadget id="calculator">500 - 240</gadget>
<output>260</output>
<result>260</result>

Choices:
A. 260 m
B. 220 m
C. 230 m
D. 240 m
E. 250 m

subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 240)

Explanation: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 240 / 9 = 500 / 9 x = 260 ans is 260 m answer : a"


Question: company a imported 12,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?

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

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

<gadget id="calculator">(1/10) * (2/5)</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">10 + 2</gadget>
<output>12</output>

<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(1/25) * (6/5)</gadget>
<output>6/125 = around 0.048</output>

<gadget id="calculator">(6/125) * 100</gadget>
<output>24/5 = around 4.8</output>

<gadget id="calculator">(24/5) * 100</gadget>
<output>480</output>
<result>480</result>

Choices:
A. 420
B. 480
C. 1050
D. 1680
E. 2100

multiply(multiply(multiply(multiply(divide(10, const_100), divide(40, const_100)), divide(add(10, const_2), 10)), const_100), const_100)

Explanation: answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 10 % brass widgets leads to 4 % blue brass widgets out of the total 10,550 widgets . 12,000 / 100 * 4 = 480 . answer b .


Question: mr . das decided to walk down the escalator of a mall . he found that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stair she would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom , find out the height of the stair way insteps ?

<gadget id="calculator">34 - 26</gadget>
<output>8</output>

<gadget id="calculator">30 - 18</gadget>
<output>12</output>

<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">20 + 26</gadget>
<output>46</output>

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

<gadget id="calculator">46 - 40</gadget>
<output>6</output>
<result>6</result>

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

subtract(add(multiply(divide(subtract(34, 26), subtract(30, 18)), 30), 26), multiply(const_4, const_10))

Explanation: here when he step down 26 steps he has 30 seconds for remaining steps . if he step down 34 stairs he has only 18 sec . 30 - 18 = 12 12 secs for 8 steps . . 18 secs for 12 steps . 12 + 34 = 46 so ans is 46 . . answer : b


Question: solution x is 30 % chemical a and 70 % chemical b by volume . solution y is 40 % chemical a and 60 % chemical b by volume . if a mixture of x and y is 36 % chemical a , what percent of the mixture is solution x ?

<gadget id="calculator">40 - 36</gadget>
<output>4</output>

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

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

<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>

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

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

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

multiply(divide(divide(subtract(40, 36), subtract(36, 30)), add(divide(subtract(40, 36), subtract(36, 30)), const_1)), const_100)

Explanation: "the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.36 ( x + y ) x = 2 y / 3 x / ( x + y ) = ( 2 y / 3 ) / ( 5 y / 3 ) = 2 / 5 = 40 % . the answer is c ."


Question: jim ’ s taxi service charges an initial fee of $ 2.45 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?

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

<gadget id="calculator">3.6 / (2/5)</gadget>
<output>9</output>

<gadget id="calculator">0.35 * 9</gadget>
<output>3.15</output>

<gadget id="calculator">2.45 + 3.15</gadget>
<output>5.6</output>
<result>5.6</result>

Choices:
A. $ 3.15
B. $ 4.45
C. $ 4.80
D. $ 5.05
E. $ 5.6

Explanation: "let the fixed charge of jim ’ s taxi service = 2.45 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.45 + ( 3.6 / . 4 ) * . 35 = 2.45 + 9 * . 35 = 5.6 $ answer e"