options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
|---|---|---|---|---|---|
a ) 5.93 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) 8 | a | divide(subtract(264, multiply(20, 4.3)), 30) | in the first 20 overs of a cricket game , the run rate was only 4.3 . what should be the run rate in the remaining 30 overs to reach the target of 264 runs ? | "explanation : required run rate = ( 264 - ( 4.3 x 20 ) ) / 30 = 178 / 30 = 5.93 answer : a" | a = 20 * 4
b = 264 - a
c = b / 30
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a ) 62.5 , b ) 62.0 , c ) 62.6 , d ) 216.67 , e ) 62.2 | d | divide(multiply(add(150, divide(multiply(150, 30), const_100)), const_100), subtract(const_100, 10)) | at what price must an article costing rs . 150 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 30 % on the cost price ? | "cp = 150 sp = 150 * ( 130 / 100 ) = 195 mp * ( 90 / 100 ) = 195 mp = 216.67 answer : d" | a = 150 * 30
b = a / 100
c = 150 + b
d = c * 100
e = 100 - 10
f = d / e
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a ) 5.75 , b ) 5.7 , c ) 7.5 , d ) 5.74 , e ) 5.71 | c | multiply(divide(multiply(add(8, 2), subtract(8, 2)), add(add(8, 2), subtract(8, 2))), const_2) | a man can row 8 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ? | "m = 8 s = 2 ds = 10 us = 6 x / 10 + x / 6 = 1 x = 3.75 d = 3.75 * 2 = 7.5 answer : c" | a = 8 + 2
b = 8 - 2
c = a * b
d = 8 + 2
e = 8 - 2
f = d + e
g = c / f
h = g * 2
|
['a ) 4', 'b ) 8', 'c ) 16', 'd ) 24', 'e ) 2'] | b | divide(divide(64, const_4), const_2) | all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose three faces are coloured ? | there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having three faces coloured = no . of corners = 8 answer : b | a = 64 / 4
b = a / 2
|
a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 % | e | multiply(divide(multiply(divide(60, const_100), 525), multiply(const_100, power(const_4, const_2))), const_100) | an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ? | "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1260 ) * 100 = 25 % answer e" | a = 60 / 100
b = a * 525
c = 4 ** 2
d = 100 * c
e = b / d
f = e * 100
|
a ) 25 % , b ) 50 % , c ) 100 % , d ) 200 % , e ) 400 % | a | multiply(power(divide(const_1, const_2), const_2), const_100) | if the sides of a square are doubled in length , the area of the original square is now how many times as large as the area of the resultant square ? | let the original square have sides of length l and the new square have sides of length 2 l . the resulting areas are l ^ 2 for the original square and 4 l ^ 2 for the new square ( as the length of the side is square to get the area ) . the original square ' s area is l ^ 2 / 4 l ^ 2 or 25 % of the new square ' s area . choice a | a = 1 / 2
b = a ** 2
c = b * 100
|
a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 26 | e | add(16, 10) | there are 16 bees in the hive , then 10 more fly . how many bees are there in all ? | 16 + 10 = 26 . answer is e . | a = 16 + 10
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a ) 1240 , b ) 1120 , c ) 1190 , d ) 1462 , e ) none of these | d | add(612, divide(multiply(612, const_100), multiply(12, 6))) | the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 612 . what is the banker ' s discount ? | "explanation : td = ( bg × 100 ) / tr = ( 612 × 100 ) / ( 6 × 12 ) = rs . 850 bg = bd – td = > 612 = bd - 850 = > bd = 612 + 850 = 1462 answer : option d" | a = 612 * 100
b = 12 * 6
c = a / b
d = 612 + c
|
a ) 8 , b ) 18 , c ) 10 , d ) 12 , e ) 14 | a | divide(subtract(507, 19), 61) | if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ? | "we know dividend = divisor * quotient + remainder = = = > 507 = divisor * 61 + 19 = = = = = > 488 / 61 = divisor = = = > divisor = 8 ans - a" | a = 507 - 19
b = a / 61
|
a ) 4000 , b ) 5000 , c ) 6000 , d ) 7000 , e ) 8000 | d | subtract(add(5000, 4000), multiply(const_1000, const_2)) | the average salary of raj and roshan is rs . 4000 but the average salary of raj , roshan and thomas is rs . 5000 . what is the salary of thomas ? | total salary of raj and roshan = 2 x 4000 = 8000 total salary of raj roshan and thomas = 3 x 5000 = 15000 salary of thomas = 15000 - 8000 = rs . 7000 answer : d | a = 5000 + 4000
b = 1000 * 2
c = a - b
|
a ) 27 , b ) 36 , c ) 29 , d ) 90 , e ) 11 | d | subtract(multiply(divide(subtract(90, 45), subtract(const_12, 9)), const_12), 90) | gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 45 and the turban . find the price of the turban . | "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 45 . thus , 3434 ( 90 + x ) = 45 + x or 270 + 3 x = 180 + 4 x or x = 90 answer : d" | a = 90 - 45
b = 12 - 9
c = a / b
d = c * 12
e = d - 90
|
a ) 32.8 , b ) 180 , c ) 32.1 , d ) 32.2 , e ) 32.9 | b | add(divide(circumface(35), const_2), multiply(35, const_2)) | the radius of a semi circle is 35 cm then its perimeter is ? | "diameter 70 cm 1 / 2 * 22 / 7 * 70 + 70 = 180 answer : b" | a = circumface / (
b = a + 2
|
a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3333 | e | divide(multiply(2, const_100), 0.06) | an inspector rejects 0.06 % of the meters as defective . how many will he examine to reject 2 ? | "let the number of meters to be examined be x then , 0.06 % of x = 2 ( 6 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 3333 answer is e" | a = 2 * 100
b = a / 0
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a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) rs . 1600 | c | add(divide(divide(1404, const_2), divide(add(const_100, 8), const_100)), divide(divide(1404, const_2), divide(add(const_100, divide(8, const_2)), const_100))) | the present worth of rs . 1404 due in two equal half - yearly installments at 8 % per annum simple interest is : | "time = 1 / 2 yr r = 8 % let pw = x si = 1404 - x x * 1 / 2 * 8 / 100 = 1404 - x . ( ref problm 10 of si , rs aggarwal ) x = 1404 * 25 / 26 hence x = 1350 answer : c" | a = 1404 / 2
b = 100 + 8
c = b / 100
d = a / c
e = 1404 / 2
f = 8 / 2
g = 100 + f
h = g / 100
i = e / h
j = d + i
|
a ) 10.8 , b ) 18 , c ) 30 , d ) 20 , e ) none | d | multiply(72, const_0_2778) | a train moves with a speed of 72 kmph . its speed in metres per second is | "solution speed = 72 kmph = ( 72 x 5 / 18 ) m / sec = 20 m / sec . answer d" | a = 72 * const_0_2778
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a ) 0.2 , b ) 0.8 , c ) 0.6 , d ) 0.7 , e ) 0.9 | b | divide(multiply(40, 2), const_100) | 40 % of 2 is equal to | 40 % of 2 = ( 40 / 100 ) * 2 = 0.8 answer : option b | a = 40 * 2
b = a / 100
|
a ) 20 , b ) 31 , c ) 42 , d ) 40 , e ) 64 | d | divide(factorial(subtract(add(const_4, 4), const_1)), multiply(factorial(4), factorial(subtract(const_4, const_1)))) | how many positive integers less than 243 are multiple of 4 but not multiples of 6 ? | "240 / 4 = 60 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 60 - 20 = 40 answer : d" | a = 4 + 4
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
|
a ) 4 days , b ) 6 days , c ) 7 days , d ) 1 days , e ) 3 days | a | divide(subtract(const_1, add(multiply(divide(const_1, 5), const_2), multiply(divide(const_1, 10), const_2))), divide(const_1, 10)) | a can finish a piece of work in 5 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ? | "a 4 days 2 / 5 + ( 2 + x ) / 10 = 1 = > x = 4 days" | a = 1 / 5
b = a * 2
c = 1 / 10
d = c * 2
e = b + d
f = 1 - e
g = 1 / 10
h = f / g
|
a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 2400 | e | divide(6936, add(add(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(10, const_100))), subtract(const_1, divide(10, const_100))), const_1)) | vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6936 , how much amount did raghu invest ? | let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6936 = x = 6936 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2400 . answer : e | a = 10 / 100
b = 1 - a
c = 10 / 100
d = 1 + c
e = b * d
f = 10 / 100
g = 1 - f
h = e + g
i = h + 1
j = 6936 / i
|
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | b | divide(divide(20, const_2), const_2) | an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 59.4 meters . how many times did the ball bounce ? | "ans : 6 division of total diatance travelled will be 20 + 20 + 10 + 5 + 2.5 + 1.25 + 0.6 ans b" | a = 20 / 2
b = a / 2
|
a ) 5 , b ) 6 , c ) 10 , d ) 12 , e ) 28 | d | divide(80, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(80, 2))))), 2)) | a rectangular tiled patio is composed of 80 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 80 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ? | "r * c = 80 and ( 12 + 4 ) ( c - 2 ) = 80 - - > r = 12 and c = 7 . answer : d ." | a = negate + (
b = 4 ** 2
c = 80 * 2
d = 4 * c
e = b + d
f = math.sqrt(e)
g = a / f
h = 80 / g
|
a ) 91 , b ) 81 , c ) 1001 , d ) 1911 , e ) none | b | subtract(891, 810) | the maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is | olution required number of students . = h . c . f of 891 and 810 . â € ¹ = â € º 81 . answer b | a = 891 - 810
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a ) - 1 , b ) 2 , c ) - 2 , d ) 1 / 2 , e ) - 1 / 2 | c | divide(subtract(negate(3), 3), subtract(4, 1)) | what is the slope of a line on a standard xy - plane that passes through the point ( 1 , 3 ) and ( 4 , – 3 ) ? | plug the values for the coordinates into the formula for the slope of a line : slope = y 2 - y 1 / x 2 - x 1 = - 3 - 3 / 4 - 1 = - 6 / 3 = - 2 correct answer c ) - 2 | a = negate - (
b = a / 3
|
a ) 246 , b ) 248 , c ) 492 , d ) 15,128 , e ) 30,256 | c | multiply(multiply(122, subtract(124, 122)), subtract(124, 122)) | the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 124 different signs . if the company used 122 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 124 signs ? | "ok let ' s take a crack at this one . so basically we have 144 ^ 2 - 142 ^ 2 so then ( 144 + 142 ) ( 144 - 142 ) ( 246 ) ( 2 ) = 492 answer : c" | a = 124 - 122
b = 122 * a
c = 124 - 122
d = b * c
|
a ) 67 , b ) 10 , c ) 18 , d ) 26 , e ) 12 | b | divide(multiply(10, 5), subtract(10, 5)) | pipe a can fill a tank in 5 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ? | "let the leak can empty the full tank in x hours 1 / 5 - 1 / x = 1 / 10 = > 1 / x = 1 / 5 - 1 / 10 = 1 / 10 = > x = 10 . answer : b" | a = 10 * 5
b = 10 - 5
c = a / b
|
a ) 250 , b ) 500 , c ) 450 , d ) 550 , e ) 650 | b | multiply(20, 25) | a large box contains 20 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ? | "the number of chocolate bars is equal to 20 * 25 = 500 correct answer b" | a = 20 * 25
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a ) 240 / 1587 , b ) 240 / 1545 , c ) 240 / 1547 , d ) 240 / 1542 , e ) 240 / 1512 | c | multiply(divide(divide(5, 34), divide(7, 48)), divide(2, 13)) | find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 . | "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c" | a = 5 / 34
b = 7 / 48
c = a / b
d = 2 / 13
e = c * d
|
a ) 3 , b ) 15 , c ) 20 , d ) 2 , e ) 5 | b | multiply(const_100, divide(add(2, multiply(divide(5, const_100), 80)), 40)) | if 40 % of a number is greater than 80 % of 5 by 2 , what is the number ? | "explanation : 40 / 100 * x - 80 / 100 * 5 = 2 40 / 100 * x - 4 = 2 40 / 100 * x = 6 x = 6 * 100 / 40 x = 15 answer : option b" | a = 5 / 100
b = a * 80
c = 2 + b
d = c / 40
e = 100 * d
|
a ) 35.75 , b ) 36 , c ) 37 , d ) 38 , e ) 39 | a | add(divide(subtract(add(40, 1.5), 30), 2), 30) | each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 1.5 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ? | "james worked for 41 hours hence he earned 40 * x + 1 * 1.5 x = 41.5 x dollars ; we know that harry also earned the same 41.5 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 11.5 x additional dollars . since for each additional hour he gets 3 x dollars then he worked for 11.5 x / 2 x = 5.75 additional hours , so harry worked for total of 30 + 5.75 = 35.75 hours . answer : a ." | a = 40 + 1
b = a - 30
c = b / 2
d = c + 30
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a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34 | d | subtract(80, subtract(add(45, 33), 41)) | in a group of 80 people , 45 have visited iceland and 33 have visited norway . if 41 people have visited both iceland and norway , how many people have visited neither country ? | "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 80 = 45 + 33 - 41 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d" | a = 45 + 33
b = a - 41
c = 80 - b
|
a ) 1 / 32 , b ) 1 / 46656 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34 | b | multiply(multiply(multiply(divide(const_1, 6), divide(const_1, 6)), divide(const_1, 6)), divide(const_1, 6)) | seven 6 faced dice are thrown together . the probability that all the three show the same number on them is ? | "the three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways . hence the probability is 6 / 279936 = 1 / 46656 answer : b" | a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
|
a ) 110.86 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75 | a | subtract(multiply(divide(8000, 756), 10.5), divide(1, 4)) | the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 8000 , brokerage being 1 / 4 % , is : | "face value = rs . 8000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 8000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 111.11 = market value of rs . 100 stock = rs . 111.11 - re . 0.25 . = market value of rs . 100 stock = rs . 110.86 . answer : a" | a = 8000 / 756
b = a * 10
c = 1 / 4
d = b - c
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a ) rs . 7000 , b ) rs . 11000 , c ) rs . 8000 , d ) rs . 10000 , e ) rs . 9000 | e | divide(divide(multiply(3, multiply(4000, const_12)), 2), subtract(const_12, 4)) | p starts a business with rs . 4000 . after 4 months , q joins with p as his partner . after a year , the profit is divided in the ratio 2 : 3 . q ' s contribution in the capital is ? | solution : let ' s q ' s capital is x . p : q = ( 4000 * 12 ) : ( x : 8 ) = 2 : 3 . so q ' s share = ( 4000 * 12 / 8 x ) = 2 / 3 = > x = ( 4000 * 12 * 3 ) / ( 2 * 8 ) = rs . 9000 answer : option e | a = 4000 * 12
b = 3 * a
c = b / 2
d = 12 - 4
e = c / d
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a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32 | d | divide(const_2, choose(add(const_3, const_3), const_3)) | what is the probability of getting exactly 1 head in a single throw of five fair coins ? | "one possible case is htttt . p ( htttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 1 = 5 possible cases . p ( 1 head ) = 5 * 1 / 32 = 5 / 32 the answer is d ." | a = 3 + 3
b = math.comb(a, 3)
c = 2 / b
|
a ) 1430 , b ) 1302 , c ) - 2801 , d ) - 1388 , e ) none of these | d | add(multiply(negate(64), 29), 468) | - 64 * 29 + 468 = ? | = > - 64 * ( 30 - 1 ) + 468 ; = > - ( 64 * 30 ) + 64 + 468 ; = > - 1920 + 532 = - 1388 . correct option : d | a = negate * (
b = a + 29
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a ) 20 , b ) 31 , c ) 42 , d ) 53 , e ) 64 | c | divide(add(70, 14), const_2) | there are 70 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ? | "x + ( x - 14 ) = 70 - - > x = 42 . answer : c ." | a = 70 + 14
b = a / 2
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a ) 12 , b ) 21 , c ) 77 , d ) 99 , e ) 22 | b | inverse(divide(inverse(14), add(const_2, const_1))) | a is twice as good a work man as b and together they finish the work in 14 days . in how many days a alone can finish the work ? | "wc = 2 : 1 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 a can do the work in 21 days . answer : b" | a = 1/(14)
b = 2 + 1
c = a / b
d = 1/(c)
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | subtract(165826, multiply(floor(divide(165826, 4)), 4)) | find the least number must be subtracted from 165826 so that remaining no . is divisible by 4 ? | "on dividing 165826 by 4 we get the remainder 2 , so 2 should be subtracted b" | a = 165826 / 4
b = math.floor(a)
c = b * 4
d = 165826 - c
|
a ) 36 , b ) 66 , c ) 154 , d ) 264 , e ) 364 | c | divide(multiply(14, 396), 36) | hcf and lcm two numbers are 14 and 396 respectively . if one of the numbers is 36 , then the other number is ? | "14 * 396 = 36 * x x = 154 answer : c" | a = 14 * 396
b = a / 36
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a ) 28.8 sec , b ) 20.33 sec , c ) 60 sec , d ) 48 sec , e ) 49 sec | a | divide(240, multiply(subtract(60, 240), const_0_2778)) | a train 240 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 240 m long ? | "total length = 240 + 240 = 480 speed = 60 km / h = ( 60 * 5 ) / 18 = 50 / 3 m / s time = ( 480 * 3 ) / 50 = 28.8 sec . answer : a" | a = 60 - 240
b = a * const_0_2778
c = 240 / b
|
a ) 16 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 35 kmph | a | divide(multiply(40, 2), add(divide(40, 40), divide(multiply(2, 40), 20))) | a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 2 x km . | "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 2 x / ( x / 8 ) = 16 kmph answer : a" | a = 40 * 2
b = 40 / 40
c = 2 * 40
d = c / 20
e = b + d
f = a / e
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a ) 9 , b ) 1 , c ) 2 , d ) 4 , e ) 8 | a | add(8, const_1) | if x and y are positive integers , and y = x ^ 2 + 8 , the greatest common divisor of a and b can not be | if x is 1 , 2 , 4 , or 8 , then gcd of x and y is 1 , 2 , 4 , and 8 respectively . so , by poe the answer must be a . still : if x is a multiple of 9 , then y is 8 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : a . | a = 8 + 1
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a ) 550 , b ) 300 , c ) 650 , d ) 700 , e ) 750 | b | divide(const_3600, 12) | a light flashes every 12 seconds , how many times will it flash in ? of an hour ? | "1 flash = 12 sec for 1 min = 5 flashes so for 1 hour = 5 * 60 = 300 flashes . answer : b" | a = 3600 / 12
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a ) 7 / 11 , b ) 7 / 17 , c ) 8 / 17 , d ) 8 / 19 , e ) 11 / 19 | e | divide(35, add(68, 11)) | some of the 68 % solution of acid was removed and this was replaced with an equal amount of 11 % solution of acid . as a result , a 35 % solution of acid was obtained . what fraction of the original solution was replaced ? | "let x be the fraction of the original solution that was replaced . 0.68 * ( 1 - x ) + 0.11 ( x ) = 0.35 0.57 x = 0.33 x = 33 / 57 = 11 / 19 the answer is e ." | a = 68 + 11
b = 35 / a
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a ) 12 , b ) 17 , c ) 16 , d ) 13 , e ) 15 | c | add(divide(subtract(subtract(137, const_4), add(23, const_1)), 7), const_1) | how many natural numbers between 23 and 137 are divisible by 7 ? | "solution : these numbers are 28 , 35 , 42 , … . , 133 . this is in a . p . in which a = 28 , d = ( 35 - 28 ) = 7 and l = 133 . let the number of there terms be n . then , tn = 133 a + ( n - 1 ) d = 133 by solving this we will get n = 16 . answer c" | a = 137 - 4
b = 23 + 1
c = a - b
d = c / 7
e = d + 1
|
a ) 1228 , b ) 1423 , c ) 1632 , d ) 1834 , e ) 1932 | b | divide(add(9, subtract(multiply(5, const_2), 5)), add(9, add(9, subtract(multiply(5, const_2), 5)))) | ages of two sisters differ by 9 years . if 5 years ago , the elder one was twice as old the younger one , find their present age | explanation : let the age of younger sister be x , then elder sister ' s age is ( x + 9 ) = > 2 ( x - 5 ) = ( x + 9 - 5 ) [ 5 years before ] = > 2 x - 10 = x + 4 = > x = 14 . so older sister ' s age is x + 9 = 23 answer : option b | a = 5 * 2
b = a - 5
c = 9 + b
d = 5 * 2
e = d - 5
f = 9 + e
g = 9 + f
h = c / g
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a ) 30 , b ) 50 , c ) 60 , d ) 45 , e ) 70 | a | multiply(divide(3, 6), multiply(5, divide(multiply(4, 30), subtract(5, 4)))) | in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 6 , and the ratio of flour to baking soda is 5 to 1 . if there were 30 more pounds of baking soda in the room , the ratio of flour to baking soda would be 4 to 1 . how many pounds of sugar are stored in the room ? | "sugar : flour = 3 : 6 = 1 : 2 = 5 : 10 flour : soda = 5 : 1 = 10 : 2 ; thus we have that sugar : flour : soda = 5 x : 10 x : 2 x . also given that 10 x / ( 2 x + 30 ) = 4 / 1 - - > x = 60 - - > sugar = 5 x = 30 . answer : a" | a = 3 / 6
b = 4 * 30
c = 5 - 4
d = b / c
e = 5 * d
f = a * e
|
a ) 6 , b ) 10 , c ) 18 , d ) 24 , e ) 27 | b | divide(divide(100, const_2), add(const_1, const_4)) | there are 100 students in a certain geometry class . if one half of the students are boys and one fifth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ? | total students = 100 one half of the students are boys = 1 / 2 * 100 = 50 one fifth of the boys are under six feet tall = 1 / 5 * 50 = 10 . . . therefore number of boys in the class under six feet tall = 10 . . . answer b . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 5 of 1 / 2 of total students = 1 / 5 * 1 / 2 * 100 = 10 . . . answer b | a = 100 / 2
b = 1 + 4
c = a / b
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a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 % | a | multiply(divide(subtract(add(const_100, 60), add(const_100, 30)), add(const_100, 30)), const_100) | the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ? | "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 130 and $ 160 respectively . charles earns $ 30 more than robin who earns $ 130 . therefore , charles ' wage is 30 / 130 * 100 = 23.07 % . correct choice is ( a )" | a = 100 + 60
b = 100 + 30
c = a - b
d = 100 + 30
e = c / d
f = e * 100
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | a | floor(add(reminder(add(subtract(multiply(divide(47, const_100), 1442), multiply(divide(36, const_100), 1412)), 60), const_10), const_1)) | find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 60 = x ? | a ) 1 | a = 47 / 100
b = a * 1442
c = 36 / 100
d = c * 1412
e = b - d
f = e + 60
g = reminder + (
h = math.floor(g, 1)
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a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | c | divide(multiply(multiply(multiply(const_12, const_2), 6), subtract(multiply(const_12, const_4), const_4)), multiply(const_12, const_2)) | how many times are the hands of a clock at right angle in 6 hours ? | "in 12 hours , they are at right angles 22 times . in 6 hours , they are at right angles 11 times . answer : option c" | a = 12 * 2
b = a * 6
c = 12 * 4
d = c - 4
e = b * d
f = 12 * 2
g = e / f
|
a ) 8 days , b ) 10 days , c ) 12 days , d ) 4 days , e ) 12 days | a | divide(multiply(4, const_3), subtract(divide(add(divide(multiply(4, const_3), 3), add(divide(multiply(4, const_3), 4), divide(multiply(4, const_3), 6))), const_2), divide(multiply(4, const_3), 4))) | a and b can do a piece of work in 4 days , b and c in 6 days , c and a in 3 days . how long will c take to do it ? | "2 c = 1 / 6 + 1 / 3 – 1 / 4 = 1 / 4 c = 1 / 8 = > 8 days answer : a" | a = 4 * 3
b = 4 * 3
c = b / 3
d = 4 * 3
e = d / 4
f = 4 * 3
g = f / 6
h = e + g
i = c + h
j = i / 2
k = 4 * 3
l = k / 4
m = j - l
n = a / m
|
a ) 4 % , b ) 10 % , c ) 76.36 % , d ) 90.16 % , e ) 20 % | c | multiply(divide(subtract(divide(subtract(const_100, 45), const_100), subtract(divide(40, const_100), multiply(divide(45, const_100), divide(60, const_100)))), divide(subtract(const_100, 45), const_100)), const_100) | 45 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ? | "no of employees = 100 ( say ) men = 45 women = 55 men speaking french = 0.6 * 45 = 27 employees speaking french = 0.55 * 100 = 55 therefore women speaking french = 55 - 42 = 13 and women not speaking french = 55 - 13 = 42 % of women not speaking french = 42 / 55 * 100 = 76.36 % answer c" | a = 100 - 45
b = a / 100
c = 40 / 100
d = 45 / 100
e = 60 / 100
f = d * e
g = c - f
h = b - g
i = 100 - 45
j = i / 100
k = h / j
l = k * 100
|
a ) 55,200 , b ) 65,200 , c ) 75,200 , d ) 85,200 , e ) 95,200 | a | divide(add(multiply(add(const_4, const_1), const_100), 80), sqrt(const_100)) | a person spent rs . 6,040 from his salary on food and 5,000 on house rent . after that he was left with 80 % of his monthly salary . what is his monthly salary ? | "total money spent on food and house rent = 6,040 + 5,000 = 11,040 which is 100 - 80 = 20 % of his monthly salary ∴ his salary = 11040 x 100 / 20 = 55200 answer : a" | a = 4 + 1
b = a * 100
c = b + 80
d = math.sqrt(100)
e = c / d
|
a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96 | b | multiply(5, divide(const_1, subtract(divide(7, 8), divide(3, 4)))) | if henry were to add 5 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ? | 7 / 8 x - 3 / 4 x = 5 galls 1 / 8 * x = 5 gallons x = 40 gallons answer : b | a = 7 / 8
b = 3 / 4
c = a - b
d = 1 / c
e = 5 * d
|
a ) 1 : 3 , b ) 9 : 11 , c ) 1 : 1 , d ) 2 : 1 , e ) 11 : 3 | a | divide(subtract(const_100, 1), add(const_100, 11)) | the number of singles that a baseball player hit increased 11 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 1 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ? | "soln : - 1.11 s + 0.99 d = 1.02 [ s + d ] 0.09 s = 0.03 d s / d = 1 / 3 answer : a" | a = 100 - 1
b = 100 + 11
c = a / b
|
a ) 10 : 5 , b ) 15 : 9 , c ) 7 : 17 , d ) 19 : 23 , e ) not enough information given for the answer | e | divide(4, add(add(add(4, 3), 2), 4)) | trail mix consists of chex cereal , m & m ' s , raisins , and assorted nuts . if one serving consists of 4 cups chex cereal , 3 cups m & m ' s , 2 cups rains , and 4 cups assorted nuts , and the ratio of the chex is doubled to to the m & m ' s , what is the ratio of chex to the rest of the dish ? | the answer to this question is way too long for such a simple question , but there ' s really not enough information to tell , so the answer is e . | a = 4 + 3
b = a + 2
c = b + 4
d = 4 / c
|
a ) 168 , b ) 172 , c ) 170 , d ) 174 , e ) 176 | c | subtract(1856, add(6, multiply(gcd(1856, lcm(lcm(7, 12), 16)), lcm(lcm(7, 12), 16)))) | which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 16 is 6 ? | "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 6 will be { 336 + 6 , 336 x 2 + 6 , 336 x 3 + 6 , . . . } the largest such number less than or equal to 1856 is 336 x 5 + 6 or 1686 to obtain this you need to subtract 170 . c" | a = math.lcm(7, 12)
b = math.lcm(a, 16)
c = math.gcd(1856, b)
d = math.lcm(7, 12)
e = math.lcm(d, 16)
f = c * e
g = 6 + f
h = 1856 - g
|
a ) 92 / 8 , b ) 92 / 12 , c ) 92 / 13 , d ) 92 / 10 , e ) 92 / 11 | a | divide(96, 98) | find 96 × × 98 | "here both numbers are less than 100 . so they are deficient of - 4 and - 2 compared with 100 . so answer : a" | a = 96 / 98
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a ) 32 yrs , b ) 36 yrs , c ) 40 yrs , d ) 48 yrs , e ) none | c | divide(subtract(8, add(const_2, const_3)), subtract(divide(const_1, const_2), divide(const_2, add(const_2, const_3)))) | a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present ? | "explanation : let the mother ' s present age be x years . then , the person ' s present age = ( 2 / 5 ) * x years . ( ( 2 / 5 ) * x ) + 8 = ( 1 / 2 ) ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) x = 40 . answer : c" | a = 2 + 3
b = 8 - a
c = 1 / 2
d = 2 + 3
e = 2 / d
f = c - e
g = b / f
|
a ) 4 / 9 , b ) 5 / 11 , c ) 7 / 15 , d ) 9 / 22 , e ) 12 / 35 | c | multiply(divide(subtract(10, 3), 10), divide(subtract(subtract(10, 3), const_1), subtract(10, const_1))) | in a box of 10 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ? | "# defective pens = 3 # good pens = 7 probability of the 1 st pen being good = 7 / 10 probability of the 2 nd pen being good = 6 / 9 total probability = 7 / 10 * 6 / 9 = 7 / 15 the answer is c ." | a = 10 - 3
b = a / 10
c = 10 - 3
d = c - 1
e = 10 - 1
f = d / e
g = b * f
|
a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) none of these | c | add(add(multiply(const_2, 10), 10), 9) | in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is : | "explanation : let b ' s present age = x years . then , a ' s present age = ( x + 9 ) years . ( x + 9 ) + 10 = 2 ( x - 10 ) = > x + 19 = 2 x - 20 = > x = 39 . answer : c" | a = 2 * 10
b = a + 10
c = b + 9
|
a ) 77 % , b ) 73 % , c ) 79 % , d ) 83 % , e ) none | c | multiply(divide(add(add(multiply(700, subtract(const_1, divide(20, const_100))), multiply(500, subtract(const_1, divide(40, const_100)))), multiply(800, subtract(const_1, divide(10, const_100)))), add(add(700, 500), 800)), const_100) | in the recent , climate conference in new york , out of 700 men , 500 women , 800 children present inside the building premises , 20 % of the men , 40 % of the women and 10 % of the children were indians . find the percentage of people who were not indian ? | solution : number of indians men present there = 700 * 20 / 100 = 140 indian women = 500 * 40 / 100 = 200 indian children = 800 * 10 / 100 = 80 . total member present in climate conference = 700 + 500 + 800 = 2000 total indian = 200 + 140 + 80 = 420 hence , % of indian present there = 420 * 100 / 2000 = 21 % % of people who were not indian = 100 - 42 = 79 % . answer c | a = 20 / 100
b = 1 - a
c = 700 * b
d = 40 / 100
e = 1 - d
f = 500 * e
g = c + f
h = 10 / 100
i = 1 - h
j = 800 * i
k = g + j
l = 700 + 500
m = l + 800
n = k / m
o = n * 100
|
a ) 6 days , b ) 7 days , c ) 5 days , d ) 3 days , e ) 2 days | a | divide(const_1, add(divide(const_1, 9), divide(const_1, 18))) | a can do a work in 9 days and b can do the same work in 18 days . if they work together , in how many days will they complete the work ? | one day ' s work of a and b = 1 / 9 + 1 / 8 = ( 2 + 1 ) / 18 = 1 / 6 so , the time taken to complete the work is 6 days . answer : a | a = 1 / 9
b = 1 / 18
c = a + b
d = 1 / c
|
a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 180 | e | divide(multiply(660, const_3), add(const_10, const_1)) | the sum of the numbers is 660 . if the first number be twice the second and third number be one - third of the first , then the second number is : | "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 660 11 x / 3 = 660 x = 180 answer : e" | a = 660 * 3
b = 10 + 1
c = a / b
|
a ) 113 miles , b ) 432 miles , c ) 558 miles , d ) 887 miles , e ) 767 miles | c | subtract(1200, 642) | jim drove 642 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ? | "the number of miles to drive to finish his journey is given by 1200 - 642 = 558 miles correct answer c" | a = 1200 - 642
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a ) 90 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days | a | multiply(const_3, 30) | working together , jose and jane can complete an assigned task in 30 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose | "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 30 30 ( x + y ) = xy next , we ' re told 1 job takes 45 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 45 x + y = 90 so xy = 30 * 90 = 2700 the answer choices are : 90 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 90 days for jose and 30 days for jane . answer : a" | a = 3 * 30
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a ) 42 , b ) 36 , c ) 28 , d ) 20 , e ) 54 | e | multiply(const_3_6, divide(divide(add(120, 120), 8), const_2)) | two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 8 seconds , the speed of each train ( in km / hr ) is | "explanation : distance covered = 120 + 120 = 240 m time = 12 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 8 = 30 m / s speed of each train = v = 30 / 2 = 15 m / s = 15 × 36 / 10 km / hr = 54 km / hr answer : option e" | a = 120 + 120
b = a / 8
c = b / 2
d = const_3_6 * c
|
a ) 124 m 2 , b ) 132 m 2 , c ) 148 m 2 , d ) 152 m 2 , e ) none of these | b | subtract(rectangle_area(add(multiply(2, 2), 17), add(12, multiply(2, 2))), rectangle_area(17, 12)) | the floor of a rectangular room is 17 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is : | "area of the outer rectangle = 21 ã — 16 = 336 m 2 area of the inner rectangle = 17 ã — 12 = 204 m 2 required area = ( 336 â € “ 204 ) = 132 m 2 answer b" | a = 2 * 2
b = a + 17
c = 2 * 2
d = 12 + c
e = rectangle_area - (
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a ) 1136 , b ) 1728 , c ) 1216 , d ) 1484 , e ) none of these | b | divide(volume_cube(24), volume_cube(divide(2, const_100))) | how many cubes of 2 cm edge can be cut out of a cube of 24 cm edge | "explanation : number of cubes = ( 24 x 24 x 24 ) / ( 2 x 2 x 2 ) = 1728 answer : b" | a = volume_cube / (
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a ) 5737.5 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these | a | divide(multiply(const_100, 4016.25), multiply(14, 5)) | a sum fetched total simple interest of 4016.25 at the rate of 14 p . c . p . a . in 5 years . what is the sum ? | "let the sums be p . now , 70 % of p = 4016.25 or , p = 5737.5 answer a" | a = 100 * 4016
b = 14 * 5
c = a / b
|
a ) 288 , b ) 225 , c ) 881 , d ) 1277 , e ) 121 | b | multiply(21, multiply(54, const_0_2778)) | a train passes a station platform in 36 sec and a man standing on the platform in 21 sec . if the speed of the train is 54 km / hr . what is the length of the platform ? | "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 21 = 315 m . let the length of the platform be x m . then , ( x + 315 ) / 36 = 15 = > x = 225 m . answer : b" | a = 54 * const_0_2778
b = 21 * a
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a ) 25 % , b ) 40 % , c ) 60 % , d ) 75 % , e ) 90 % | d | divide(subtract(36, add(24, const_1)), subtract(divide(40, const_100), divide(add(24, const_1), const_100))) | seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 24 % ryegrass and 75 % fescue . if a mixture of x and y contains 36 % ryegrass , what percent of the weight of the mixture is from mixture x ? | 36 % is 12 % - points above 25 % and 4 % - points below 40 % . thus the ratio of mixture y to mixture x is 1 : 3 . the percent of mixture x is 3 / 4 = 75 % . the answer is d . | a = 24 + 1
b = 36 - a
c = 40 / 100
d = 24 + 1
e = d / 100
f = c - e
g = b / f
|
a ) 30 and 75 , b ) 35 and 70 , c ) 40 and 65 , d ) 45 and 60 , e ) 55 and 70 | d | divide(180, 15) | hcf of two numbers is 15 and their lcm is 180 . if their sum is 105 , then the numbers are | "explanation : let the numbers be 15 a and 15 b . then , 15 a + 15 b = 105 or a + b = 7 . . ( i ) lcm = 15 ab = 180 ab = 12 . . ( ii ) solving equations ( i ) and ( ii ) , we get a = 4 , b = 3 so , the numbers are 15 × 4 and 15 × 3 , i . e . , 60 and 45 answer : d" | a = 180 / 15
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a ) $ 33.75 , b ) $ 47.25 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 66.00 | e | add(multiply(7.5, 5.5), multiply(multiply(subtract(10.5, 7.5), 1.5), 5.5)) | lloyd normally works 7.5 hours per day and earns $ 5.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ? | daily working hour * regular rate + overtime * increased rate 7.5 * 5.5 + 3 * 5.5 * 1.5 = 66.00 answer e | a = 7 * 5
b = 10 - 5
c = b * 1
d = c * 5
e = a + d
|
a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 40 | b | divide(multiply(subtract(divide(60, const_4), divide(20, const_4)), const_60), 20) | the cyclist going at a constant rate of 20 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 60 miles per hour . the motor - cyclist stops to wait for the cyclist 10 minutes after passing her , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ? | "for the 10 minutes the motor - cyclist continues to overtake the cyclist , she is going at 40 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 20 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 40 / 20 * 10 or 20 minutes answer is ( b )" | a = 60 / 4
b = 20 / 4
c = a - b
d = c * const_60
e = d / 20
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a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | c | add(multiply(multiply(const_3, const_2), 4), 5) | how many 4 digit numbers divisible by 4 can be made with digits 1 , 2 , 3 , 4 , 5 if the repetition of digits is not allowed ? | a number is divisible by 4 if the last 2 numbers are divisible by 4 ( divisible by 2 twice ) ending can be 12 24 32 42 52 case : ending with 12 , 24,32 , 42,54 first digit - 3 choices second digit - 2 choices third digit - 1 choice fourth digit - 1 choice 6 possible choices for each ending ( e . g . 3412,3512 , 3212 , 4512 , 5312 , 5412 ) total number of 4 digit numbers divisible by 4 = 6 * 5 = 30 answer : c | a = 3 * 2
b = a * 4
c = b + 5
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a ) 15 , b ) 13 , c ) 11 , d ) 14 , e ) 18 | b | subtract(add(multiply(14, const_2), 5), add(3, 17)) | x and y are positive integers . when x is divided by 17 , the remainder is 3 , and when x is divided by 19 , the remainder is 1 . when y is divided by 14 , the remainder is 5 , and when y is divided by 21 , the remainder is 12 . what is the least possible value of y - x ? | when x is divided by 17 , the remainder is 3 : so , the possible values of x are : 3 , 20 , 37,54 , etc . when x is divided by 19 , the remainder is 1 : so , the possible values of x are : 1,20 . . . stop . since both lists include 20 , the smallest possible value of x is 20 . when y is divided by 14 , the remainder is 5 : so , the possible values of y are : 5 , 19 , 33,47 etc . when y is divided by 21 , the remainder is 12 : so , the possible values of y are : 12 , 33 , . . . stop . since both lists include 33 , the smallest possible value of y is 33 since the smallest possible values of x and y are 20 and 33 respectively , the smallest possible value of y - x is 13 . so , b is the correct answer to the original question . | a = 14 * 2
b = a + 5
c = 3 + 17
d = b - c
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a ) 10 , b ) 20 , c ) 85 , d ) 86 , e ) 88 | b | divide(1200, const_60) | how many hours are there in 1200 minutes ? | we know that there are 60 minutes in 1 hour . divide the number of minutes by the number of minutes in 1 hour . we get , divide 1200 by 601200 ÷ 60 = 20 so there are 20 hours in 1200 minutes . answer is b | a = 1200 / const_60
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a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64 | c | add(divide(200, add(const_4, const_1)), divide(200, multiply(add(const_4, const_1), add(const_4, const_1)))) | how many terminating zeroes t does 200 ! have ? | you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c | a = 4 + 1
b = 200 / a
c = 4 + 1
d = 4 + 1
e = c * d
f = 200 / e
g = b + f
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a ) rs . 32000 , b ) rs . 96000 , c ) rs . 128000 , d ) rs . 500000 , e ) none of these | b | multiply(224000, divide(3, add(4, 3))) | brindavan express leave chennai central station every day at 07.50 am and goes to bangalore city railway station . this train is very popular among the travelers . on 25 th july 2012 number of passengers traveling by i class and ii class was in the ratio 1 : 4 . the fare for this travel is in the ratio 3 : 1 . the total fare collected was rs . 224000 / . ( rs . two lakhs 20 4 1000 only ) . what was the fare collected from i class passengers on that day ? | solution : let the number of passenger traveling by first class be x . then , number of passenger traveling by second class will be 4 x . but the fare is in the ratio 3 : 1 in other words , if 3 y fare is collected per i class passenger , y would be collected per ii class passenger . fares of i class passengers : fares of ii class passengers = x * 3 y : 4 x * y = 3 : 4 the above ratio can be interpreted as follows . if total fare is 3 + 4 = 7 , then i class passengers should pay rs . 3 similarly , we can calculate the fare of i class passengers when total was 224000 total fare i class fare 7 3 224000 ? = 224000 * ( 3 / 7 ) = rs . 96000 . answer : option b | a = 4 + 3
b = 3 / a
c = 224000 * b
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a ) 15 / 4 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9 | a | divide(const_1, add(divide(const_1, 5), divide(const_1, 15))) | worker a takes 5 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ? | "one day work of a = 1 / 5 one day work of b = 1 / 15 so one day work of a and b together = 1 / 5 + 1 / 15 = 4 / 15 so total days required = 15 / 4 answer : a" | a = 1 / 5
b = 1 / 15
c = a + b
d = 1 / c
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a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 240 | e | multiply(add(14, const_1), add(add(14, const_1), const_1)) | there are 14 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ? | "the total number of stations = 16 from 16 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 16 p ₂ ways . 16 p ₂ = 16 * 15 = 240 . answer : e" | a = 14 + 1
b = 14 + 1
c = b + 1
d = a * c
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a ) 550 , b ) 570 , c ) 590 , d ) 610 , e ) 630 | b | multiply(divide(add(12, 48), const_2), divide(add(subtract(48, 12), 2), 2)) | in a theater , the first row has 12 seats and each row has 2 more seats than previous row . if the last row has 48 seats , what is the total number of seats in the theater ? | "the number of seats in the theater is 12 + ( 12 + 2 ) + . . . + ( 12 + 36 ) = 19 ( 12 ) + 2 ( 1 + 2 + . . . + 18 ) = 19 ( 12 ) + 2 ( 18 ) ( 19 ) / 2 = 19 ( 12 + 18 ) = 19 ( 30 ) = 570 the answer is b ." | a = 12 + 48
b = a / 2
c = 48 - 12
d = c + 2
e = d / 2
f = b * e
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a ) 15 , b ) 18 , c ) 21 , d ) 12 , e ) 19 | a | subtract(divide(subtract(multiply(6, 22), 7), const_4), 7) | the average age of a family of 6 members is 22 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ? | "present age of total members = 6 x 22 = 132 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 132 - 42 = 90 therefore , avg age at the birth of youngest member = 90 / 6 = 15 . answer : a" | a = 6 * 22
b = a - 7
c = b / 4
d = c - 7
|
a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 77.12 , e ) 81.6 | d | multiply(add(add(7.5, 8.1), 8.5), 3.2) | in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.1 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ? | "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.1 + 8.5 ) = 24 point of value of the dive = 24.1 * 3.2 = 77.12 answer d" | a = 7 + 5
b = a + 8
c = b * 3
|
['a ) 14 percent increase', 'b ) 5 percent increase', 'c ) 24 percent increase', 'd ) 13 percent increase', 'e ) 11 percent increase'] | a | multiply(divide(subtract(multiply(add(const_100, 20), subtract(const_100, 5)), multiply(const_100, const_100)), multiply(const_100, const_100)), const_100) | calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 20 % and its breadth is decreased by 5 % ? | let l and b be 100 each 100 * 100 = 10000 l increase by 20 % = 120 b decrease by 5 % = 95 120 * 95 = 11400 14 percent increase answer : a | a = 100 + 20
b = 100 - 5
c = a * b
d = 100 * 100
e = c - d
f = 100 * 100
g = e / f
h = g * 100
|
['a ) 3', 'b ) 4', 'c ) 5', 'd ) 6', 'e ) 7'] | c | subtract(14, power(const_3, const_2)) | how many differently shaped triangles exist in which no two sides are of the same length , each side is of integral unit length and the perimeter of the triangle is less than 14 units ? | explanation : let the lengths of the sides be a , b and c . given , triagle ' s perimeter < 14 = > a + b + c < 14 - - - - - - - - - - ( i ) from triangle inequality theorem , c < a + b = > 2 c < a + b + c . - - - - - - - - - - ( ii ) from ( i ) and ( ii ) , 2 c < a + b + c < 14 . = > c < 7 - - - - - - - - - - ( iii ) = > by similarity , we can say that length of any side must be less than 7 . keeping these in mind , we can find the following possibilities : - ( 2 , 3,4 ) ( 2 , 4,5 ) ( 2 , 5,6 ) ( 3 , 4,5 ) ( 3 , 4,6 ) = > total 5 possibilities . answer : c | a = 3 ** 2
b = 14 - a
|
a ) 870 m 3 , b ) 277 m 3 , c ) 270 m 3 , d ) 220 m 3 , e ) 170 m 3 | c | multiply(quadrilateral_area(12, 1, 4), 9) | a swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side . its volume is ? | "volume will be length * breadth * height , but in this case two heights are given so we will take average , volume = ( 12 ∗ 9 ∗ ( 1 + 42 ) ) m 312 ∗ 9 ∗ 2.5 m 3 = 270 m 3 answer : c" | a = quadrilateral_area * (
|
a ) 15 , b ) 21 , c ) 37 , d ) 19 , e ) 21 | c | divide(subtract(multiply(500, 54), 10350), subtract(500, 50)) | a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 54 . find the number of notes of rs . 50 denomination . | "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 54 - x now , 50 * x + 500 * ( 54 - x ) = 10350 50 x + 27000 - 500 x = 10350 - 450 x = - 16650 x = 37 . no . of 50 rupees note = 37 . answer : option c" | a = 500 * 54
b = a - 10350
c = 500 - 50
d = b / c
|
a ) 18 , b ) 30 , c ) 35 , d ) 40 , e ) 45 | a | subtract(multiply(divide(15, const_100), 180), multiply(divide(const_1, const_3), multiply(divide(15, const_100), 180))) | one - third less than 15 % of 180 is equal to : | "lots of ways to tackle this . 15 % of 180 = 27 1 / 3 of 27 = 9 so , 1 / 3 less than 27 is equal to 27 - 9 = 18 answer : a" | a = 15 / 100
b = a * 180
c = 1 / 3
d = 15 / 100
e = d * 180
f = c * e
g = b - f
|
a ) 5000 , b ) 500 , c ) 50000 , d ) 50 , e ) 0.5 | a | divide(2.5, divide(0005, 2.5)) | evaluate 2.5 / . 0005 | "explanation : 2.5 * 10000 / 5 = 25000 / 5 = 5000 option a" | a = 5 / 2
b = 2 / 5
|
a ) 20000 , b ) 10000 , c ) 25000 , d ) 35000 , e ) 30000 | d | multiply(63000, subtract(const_1, divide(multiply(30000, multiply(2, multiply(2, const_3))), add(multiply(45000, subtract(multiply(2, multiply(2, const_3)), 2)), multiply(30000, multiply(2, multiply(2, const_3))))))) | tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 63000 after completion of one year . what will be jose ' s share of profit ? | "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 63000 = 35000 d" | a = 2 * 3
b = 2 * a
c = 30000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 45000 * f
h = 2 * 3
i = 2 * h
j = 30000 * i
k = g + j
l = c / k
m = 1 - l
n = 63000 * m
|
a ) 70.6 % , b ) 74.5 % , c ) 78.4 % , d ) 82.1 % , e ) 86.9 % | c | multiply(const_100, subtract(const_1, divide(volume_cube(multiply(const_1, const_4)), volume_cube(5)))) | a wooden cube whose edge length is 5 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ? | "there are a total of 5 * 5 * 5 = 125 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 3 * 3 * 3 = 27 cubes . the number of cubes with at least one side painted red is 125 - 27 = 98 cubes the probability that a cube has at least one side painted red is 98 / 125 which is 78.4 % the answer is c ." | a = 1 * 4
b = volume_cube / (
c = 1 - b
d = 100 * c
|
a ) 64 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 % | b | multiply(divide(add(const_100, 40), add(add(const_100, 40), const_100)), const_100) | in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 40 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ? | "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 140 / 100 = 84 in june total income = 84 + 40 = 124 % of mrs lee ' s income = 84 / 124 = 67.74 ( b )" | a = 100 + 40
b = 100 + 40
c = b + 100
d = a / c
e = d * 100
|
a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 24 | e | divide(subtract(multiply(86, 3), multiply(69, 2)), subtract(multiply(3, 3), multiply(2, 2))) | if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 86 , how much does one shirt cost ? | "3 j + 2 s = 69 2 j + 3 s = 86 - - - - - - - - - - - - - - - - 5 j + 5 s = 155 - - - - ( divide by 5 ) - - - > j + s = 31 3 j + 2 s = j + 2 ( j + s ) = j + 62 = 69 - - - > j = 7 3 * 7 + 2 s = 69 21 + 2 s = 69 2 s = 48 s = 24 answer : e" | a = 86 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
|
a ) 30 % gain , b ) 30 % loss , c ) 32 % loss , d ) 40 % loss , e ) 50 % loss | c | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 25), 17)), divide(multiply(const_100, 25), 17))) | if the cost price of 17 articles is same as the selling price of 25 articles . find the gain or loss percentage ? | "explanation : 17 cp = 25 sp cost price cp = 25 selling price sp = 17 formula = ( sp - cp ) / cp * 100 = ( 17 - 25 ) / 25 * 100 = 32 % loss answer : option c" | a = 100 * 25
b = a / 17
c = 100 - b
d = 100 * 25
e = d / 17
f = c / e
g = 100 * f
|
a ) $ 700 , b ) $ 754 , c ) $ 770 , d ) $ 782 , e ) $ 893 | c | multiply(divide(812, add(const_1, divide(16, const_100))), add(const_1, divide(10, const_100))) | tough and tricky questions : word problems . if bill ' s salary increased by 16 percent , he would earn $ 812 per month . if instead , his salary were to increase by only 10 percent , how much money r would he earn per month ? | official solution : ( c ) if bill ’ s salary increased by 16 % he would earn $ 812 . algebraically , this can be written as : $ 812 = 1.16 s , where s is his current salary . then s = $ 812 / 1.16 = $ 700 . now that we know his current salary is $ 700 , we can calculate what his salary would be if it were increased by 10 % . we know that 10 % of $ 700 is $ 70 , so his salary would be : r = $ 700 + $ 70 = $ 770 . the correct answer is choice ( c ) . | a = 16 / 100
b = 1 + a
c = 812 / b
d = 10 / 100
e = 1 + d
f = c * e
|
a ) 80 , b ) 28 , c ) 90 , d ) 26 , e ) 11 | a | subtract(divide(8925, 85), 25) | a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 25 per metre of cloth . what is the cost price of one metre of cloth ? | "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 25 = rs . 80 . answer : a" | a = 8925 / 85
b = a - 25
|
a ) 440 , b ) 540 , c ) 443 , d ) 740 , e ) 250 | c | divide(multiply(480, 4), divide(add(multiply(3, 4), 1), 3)) | an aeroplane covers a certain distance of 480 kmph in 4 hours . to cover the same distance in 4 1 / 3 hours , it must travel at a speed of | "speed of aeroplane = 480 kmph distance travelled in 4 hours = 480 * 4 = 1920 km speed of aeroplane to acver 1920 km in 13 / 3 = 1920 * 3 / 13 = 443 km answer c ." | a = 480 * 4
b = 3 * 4
c = b + 1
d = c / 3
e = a / d
|
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