Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
values |
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a train 600 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ? | "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 600 + x ) / 60 = 65 / 3 x = 700 m . answer : e" | a ) 298 m , b ) 279 m , c ) 500 m , d ) 289 m , e ) 700 m | e | divide(600, multiply(subtract(78, 1), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ? | let the original speed be s and time be t if new speed = s ã — 3 / 4 , then new time would be t ã — 4 / 3 ( d = st = constant ) . given , 3 t / 4 â ˆ ’ t = 20 t / 3 â ‡ ’ t = 60 minutes = 1 hour answer : a | a ) 2 hr , b ) 1 hr , c ) 3 hr , d ) 1.5 hr , e ) 2.5 hr | a | divide(multiply(multiply(divide(multiply(20, 3), 4), 4), const_2), const_60) | multiply(n0,n2)|divide(#0,n1)|multiply(n1,#1)|multiply(#2,const_2)|divide(#3,const_60) | physics |
andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.86 . what is the median gasoline price ? | "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.86 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.86 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b" | a ) $ 1 , b ) $ 1.86 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15 | b | min(divide(add(add(add(add(add(add(1.75, 1.61), 1.79), 2.11), 1.96), 2.09), 1.86), 7), 1.86) | add(n1,n2)|add(n3,#0)|add(n4,#1)|add(n5,#2)|add(n6,#3)|add(n7,#4)|divide(#5,n0)|min(n7,#6)| | general |
how many odd numbers between 10 and 1,100 are the squares of integers ? | "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 15 numbers . answer : ... | a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16 | d | add(10, const_4) | add(n0,const_4)| | geometry |
a man deposits $ 1000 in a bank at 2 % per annum and $ 1500 in uti at 7 % per annum . find the rate of interest for the whole sum . | "following the above formula , we have the rate of interest for the whole sum = ( 1000 * 2 ) + ( 1500 * 7 ) / 1000 + 1500 = 12500 / 2500 = 5 % . answer is a" | a ) 5 % , b ) 8 % , c ) 3 % , d ) 7 % , e ) 1 % | a | multiply(const_100, divide(subtract(add(p_after_gain(2, 1000), p_after_gain(7, 1500)), add(1000, 1500)), 1500)) | add(n0,n2)|p_after_gain(n1,n0)|p_after_gain(n3,n2)|add(#1,#2)|subtract(#3,#0)|divide(#4,n2)|multiply(#5,const_100)| | gain |
a pump can fill a tank with water in 6 hours . because of a leak , it took 12 hours to fill the tank . the leak can drain all the water in ? | work done by the leak in 1 hour = 1 / 6 - 1 / 12 = 1 / 12 leak will empty the tank in 12 hours answer is a | a ) 12 hr , b ) 11 hr , c ) 13 hr , d ) 14 hr , e ) 16 hr | a | divide(multiply(6, 12), subtract(12, 6)) | multiply(n0,n1)|subtract(n1,n0)|divide(#0,#1) | physics |
if 10 x = 8 y = 14 z , then what is a possible sum of positive integers x , y , and z ? | "10 x = 8 y = 14 z 5 x = 4 y = 7 z 5 ( 4 * 7 ) = 4 ( 5 * 7 ) = 7 ( 5 * 4 ) addition = 28 + 20 + 35 = 83 answer would be multiple of 83 which is 166 answer : b" | a ) 52 , b ) 166 , c ) 84 , d ) 122 , e ) 168 | b | divide(multiply(multiply(8, 14), 10), const_4) | multiply(n1,n2)|multiply(n0,#0)|divide(#1,const_4)| | general |
if x and y are positive integers and 9 + x + y + xy = 23 , what is the value of x + y ? | "try each answer choices . for a : 9 + 3 + xy = 23 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 9 + 5 + xy = 23 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 9 + 6 + xy = 23 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 9 + 8 + xy = 23 ; xy = 6 ( no comb... | a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9 | c | add(23, const_1) | add(n1,const_1)| | general |
a container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ? | container 1 has 15 ounces in the ratio 1 : 2 or , x + 2 x = 15 gives x ( alcohol ) = 5 and remaining water = 10 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 5 + 2 and water = 10 + 6 ratio thus alcohol / water = 7 / 16 answer e | a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 16 | e | divide(add(multiply(15, divide(1, add(1, 2))), multiply(8, divide(1, add(1, 3)))), subtract(add(15, 8), add(multiply(15, divide(1, add(1, 2))), multiply(8, divide(1, add(1, 3)))))) | add(n1,n2)|add(n1,n5)|add(n0,n3)|divide(n1,#0)|divide(n1,#1)|multiply(n0,#3)|multiply(n3,#4)|add(#5,#6)|subtract(#2,#7)|divide(#7,#8) | other |
how many plants will be there in a circular bed whose outer edge measure 31 cms , allowing 4 cm 2 for each plant ? | circumference of circular bed = 31 cm area of circular bed = ( 31 ) 2 â „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 31 ) 2 â „ 4 ï € ã · 4 = 19.11 = 19 ( approx ) answer a | ['a ) 19', 'b ) 750', 'c ) 24', 'd ) 120', 'e ) none of these'] | a | divide(circle_area(divide(31, multiply(2, const_pi))), const_4) | multiply(n2,const_pi)|divide(n0,#0)|circle_area(#1)|divide(#2,const_4) | physics |
3 cannons are firing at a target . if their individual probabilities to hit the target are 0.5 , 0.2 , and 0.3 respectively , what is the probability that none of the cannons will hit the target after one round of fire ? prob . that all the cannons will hit the target = . 06 prob . that none of the cannons will hit = 1... | the probability that eachdoesn ' thit is : 0.5 , 0.8 , and 0.7 . when we have multiple independent events , we multiply the probabilities : . 5 * . 8 * . 7 = 0.28 . option : e | a ) 0.06 , b ) 0.12 , c ) 0.21 , d ) 0.29 , e ) 0.28 | e | multiply(multiply(subtract(const_1, 0.3), subtract(const_1, 0.2)), subtract(const_1, 0.5)) | subtract(const_1,n3)|subtract(const_1,n2)|subtract(const_1,n1)|multiply(#0,#1)|multiply(#3,#2) | general |
if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , whe... | "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 18 years investment will become $ 5,000 * 2 = $ 10... | a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000 | a | multiply(multiply(5000, const_2), const_2) | multiply(n1,const_2)|multiply(#0,const_2)| | general |
2 / 5 of 3 / 7 of 23 / 11 of ? = 64 × 3 | "explanation : 2 / 5 & time ; 3 / 7 & time ; 20 / 11 & time ; x = 192 x = 192 & time ; 11 & time ; 7 & time ; 5 / 2 & time ; 3 & time ; 20 = 616 answer : option c" | a ) 511 , b ) 419 , c ) 616 , d ) 636 , e ) 686 | c | multiply(multiply(multiply(divide(2, 5), divide(3, 7)), divide(7, 11)), 64) | divide(n3,n5)|divide(n0,n1)|divide(n2,n3)|multiply(#1,#2)|multiply(#0,#3)|multiply(n6,#4)| | general |
the annual interest rate earned by an investment increased by 11 percent from last year to this year . if the annual interest rate earned by the investment this year was 22 percent , what was the annual interest rate last year ? | "let i = interest rate i ( this year ) = i ( last year ) + 0.11 i ( last year ) = 1.11 i ( last year ) 22 = 1.11 x i ( last year ) i ( last year ) = 22 / 1.1 = 220 / 11 = 20 % answer : d" | a ) 17 % , b ) 19 % , c ) 18 % , d ) 20 % , e ) 22 % | d | divide(multiply(22, const_100), add(22, const_100)) | add(n1,const_100)|multiply(n1,const_100)|divide(#1,#0)| | gain |
if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability that this product will be a multiple of 45 ? | there are 3 single digit multiple of 3 , that is , 3 , 69 . there are 8 prime nos less than 20 - 23 , 57 , 1113 , 1719 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability = 1 / 24 . answer c . | a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14 | c | divide(const_1, add(20, const_4)) | add(n1,const_4)|divide(const_1,#0) | general |
if p ^ 2 – 13 p + 40 = h , and p is a positive integer between 1 and 10 , inclusive , what is the probability that h < 0 ? | p 2 – 13 p + 40 = h so ( p – 8 ) ( p – 5 ) = h for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included becau... | a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10 | b | divide(const_2, 10) | divide(const_2,n4) | general |
abcd is a square where ab = â ˆ š 4004 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd . | "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4004 / 2 = 2002 . correct answer b" | a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000 | b | divide(4004, const_2) | divide(n0,const_2)| | geometry |
two - third of a positive number and 16 / 216 of its reciprocal are equal . the number is : | let the number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 = 1 / 9 x = 1 / 3 answer : c | a ) 5 / 12 , b ) 12 / 5 , c ) 1 / 3 , d ) 144 / 25 , e ) 146 / 25 | c | sqrt(divide(multiply(16, const_3), multiply(216, const_2))) | multiply(n0,const_3)|multiply(n1,const_2)|divide(#0,#1)|sqrt(#2) | general |
if x < y < z and y - x > 9 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ? | we have : 1 ) x < y < z 2 ) y - x > 9 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c ... | a ) 6 , b ) 7 , c ) 8 , d ) 13 , e ) 10 | d | add(add(9, const_2), const_2) | add(n0,const_2)|add(#0,const_2) | general |
in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are marketing majors ? | "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are marketing majors is r = 7 . the answer is c ." | a ) 3 , b ) 5 , c ) 7 , d ) 11 , e ) 17 | c | divide(1365, multiply(multiply(add(const_2, const_3), add(add(const_2, const_3), const_2)), add(const_10, const_3))) | add(const_10,const_3)|add(const_2,const_3)|add(#1,const_2)|multiply(#1,#2)|multiply(#0,#3)|divide(n0,#4)| | gain |
if x = 8 and y = − 2 , what is the value of ( x − 2 y ) ^ y ? | "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.007 answer : b" | a ) − 100 , b ) 0.007 , c ) 0.25 , d ) 4 , e ) 8 | b | divide(divide(2, 2), const_1000) | divide(n1,n1)|divide(#0,const_1000)| | general |
a train running at the speed of 60 km / hr crosses a pole in 5 seconds . find the length of the train . | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 5 = 83.33 meter . answer : a" | a ) 83.33 , b ) 882 , c ) 772 , d ) 252 , e ) 121 | a | multiply(divide(multiply(60, const_1000), const_3600), 5) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
on a purchase of $ 118 , a store offered a payment plan consisting of a $ 18 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ? | "12 * 10 + 18 = 138 ( 18 / 118 ) * 100 = 15.3 answer : e" | a ) 16.7 % , b ) 16.2 % , c ) 16.5 % , d ) 15.5 % , e ) 15.3 % | e | multiply(divide(subtract(add(multiply(10, 12), 18), multiply(10, 12)), 118), const_100) | multiply(n2,n3)|add(n1,#0)|subtract(#1,#0)|divide(#2,n0)|multiply(#3,const_100)| | gain |
if 70 honey bees make 70 grams of honey in 70 days , then 1 honey bee will make 1 gram of honey in how many days ? | "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 70 : : 70 : x honey 70 : 1 = > 1 x 70 x x = 70 x 1 x 70 = > x = 70 . answer : e" | a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 70 | e | divide(1, divide(1, 70)) | divide(n3,n0)|divide(n3,#0)| | physics |
3 times the first of 3 consecutive odd integers is 3 more than twice the third . the third integer is ? | let the three integers be x , x + 2 and x + 4 . then , 3 x = 2 ( x + 4 ) + 3 x = 11 . third integer = x + 4 = 15 . option a | a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 26 | a | add(add(multiply(const_2, const_4), 3), const_4) | multiply(const_2,const_4)|add(n0,#0)|add(#1,const_4) | general |
two trains , each 100 m long , moving in opposite directions , cross other in 10 sec . if one is moving twice as fast the other , then the speed of the faster train is ? | let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 10 = 3 x = > x = 20 / 3 . so , speed of the faster train = 40 / 3 = 40 / 3 * 18 / 5 = 48 km / hr . answer : c | a ) 76 km / hr , b ) 66 km / hr , c ) 48 km / hr , d ) 67 km / hr , e ) 22 km / hr | c | divide(multiply(multiply(divide(add(100, 100), multiply(10, add(const_1, const_2))), const_2), const_3600), const_1000) | add(n0,n0)|add(const_1,const_2)|multiply(n1,#1)|divide(#0,#2)|multiply(#3,const_2)|multiply(#4,const_3600)|divide(#5,const_1000) | physics |
if a certain number is divided by 9 , the quotient , dividend , and divisor , added together , will amount to 69 . what is the number ? | let x = the number sought . then x / 9 + x + 9 = 69 . and x = 54 . e | a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 54 | e | divide(multiply(subtract(69, 9), 9), add(9, const_1)) | add(n0,const_1)|subtract(n1,n0)|multiply(n0,#1)|divide(#2,#0) | general |
a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did b get in a profit of rs . 2400 ? | "let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 b ' s share in the profit of rs . 2400 = 15 ( 2400 / 60 ) = rs . 600 . answer... | a ) s . 532 , b ) s . 600 , c ) s . 822 , d ) s . 812 , e ) s . 810 | b | multiply(2400, divide(1, 3)) | divide(n0,n1)|multiply(n6,#0)| | general |
if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ? | "50 * 10 = 500 66 * 5 = 330 830 / 15 = 55.33 answer : d" | a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above | d | divide(add(multiply(10, 50), multiply(5, 66)), add(10, 5)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)| | gain |
if the price of a book is first decreased by 25 % and then increased by 20 % , then the decrease in the price will be ? | "let the original price be $ 100 new final price = 120 % of ( 75 % of $ 100 ) = 120 / 100 * 75 / 100 * 100 = $ 90 decrease is 10 % answer is b" | a ) 20 % , b ) 10 % , c ) 25 % , d ) 18 % , e ) 30 % | b | subtract(const_100, multiply(multiply(divide(subtract(const_100, divide(multiply(const_100, 25), const_100)), const_100), divide(add(const_100, divide(multiply(const_100, 20), const_100)), const_100)), const_100)) | multiply(n0,const_100)|multiply(n1,const_100)|divide(#0,const_100)|divide(#1,const_100)|add(#3,const_100)|subtract(const_100,#2)|divide(#5,const_100)|divide(#4,const_100)|multiply(#6,#7)|multiply(#8,const_100)|subtract(const_100,#9)| | general |
the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ? | "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 35 + 20 ) kg = 55 kg the answer is e ." | a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg | e | add(multiply(2.5, 8), 35) | multiply(n0,n1)|add(n2,#0)| | general |
from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 2 hours at 8 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 4 kilometers per hour , how many hours longer is the journey of ferry q compared with ... | the distance traveled by ferry p is 16 km . then the distance traveled by ferry q is 48 km . ferry q travels at a speed of 12 kph . the time of the journey for ferry q is 48 / 12 = 4 hours , which is 2 hours more than ferry p . the answer is b . | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | subtract(divide(multiply(const_3, multiply(8, 2)), add(8, 4)), 2) | add(n1,n2)|multiply(n0,n1)|multiply(#1,const_3)|divide(#2,#0)|subtract(#3,n0) | physics |
a car takes 6 hours to cover a distance of 324 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 6 distence = 324 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 324 / 9 = 36 kmph d )" | a ) 50 kmph , b ) 60 kmph , c ) 65 kmph , d ) 36 kmph , e ) none | d | divide(324, divide(multiply(6, 3), 2)) | multiply(n0,n2)|divide(#0,n3)|divide(n1,#1)| | physics |
in a renowned city , the average birth rate is 4 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day . | "every 2 seconds , 2 persons are added ( 4 - 2 ) . every second 1 person are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option a" | a ) 86,400 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200 | a | multiply(multiply(subtract(4, 2), const_3600), const_12) | subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)| | general |
steve traveled the first 5 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ? | average speed = total distance / total time = ( 40 * 5 + 80 * 3 ) / ( 5 + 3 ) = 440 / 5 = 88 answer : b | a ) 53.33 mph , b ) 88 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph | b | add(divide(add(multiply(80, 3), multiply(40, 5)), add(3, 5)), subtract(divide(const_100, const_3), const_0_33)) | add(n0,n2)|divide(const_100,const_3)|multiply(n2,n3)|multiply(n0,n1)|add(#2,#3)|subtract(#1,const_0_33)|divide(#4,#0)|add(#6,#5) | physics |
if circles x and y have the same area and circle x has a circumference of 20 π , half of the radius of circle y is : | "x b é radius of circle x ý b é radius of circle y given : pi * x ^ 2 = pi * ý ^ 2 also , 2 * pi * x = 20 * pi x = 10 thus ý = 10 y / 2 = 5 ans : b" | a ) 16 , b ) 5 , c ) 4 , d ) 2 , e ) 1 | b | divide(divide(20, const_2), const_2) | divide(n0,const_2)|divide(#0,const_2)| | geometry |
what is theleast number should be added to 1056 , so the sum of the number is completely divisible by 23 ? | ( 1056 / 23 ) gives remainder 21 21 + 2 = 23 , so we need to add 2 b | a ) 20 , b ) 23 , c ) 25 , d ) 27 , e ) 28 | b | add(subtract(23, reminder(1056, 23)), subtract(23, const_3)) | reminder(n0,n1)|subtract(n1,const_3)|subtract(n1,#0)|add(#2,#1) | general |
ravi and sunil are partners in a business . ravi invests rs . 20,000 for 8 months and sunil invested rs . 16000 for 10 months then after one year ratio of their profits will be | "= ( 15000 * 8 ) : ( 8000 * 10 ) = 160000 : 160000 = 1 : 1 answer : a" | a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4 | a | divide(multiply(multiply(multiply(multiply(const_4, const_3), multiply(10, const_2)), const_100), 8), multiply(16000, 10)) | multiply(const_3,const_4)|multiply(n3,const_2)|multiply(n2,n3)|multiply(#0,#1)|multiply(#3,const_100)|multiply(n1,#4)|divide(#5,#2)| | gain |
tanks c and b are each in the shape of a right circular cylinder . the interior of tank c has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank c is what percent of the capacity of tank b ? | b . for c , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi c / b = 160 pi / 200 pi = 0.8 | ['a ) 75 %', 'b ) 80 %', 'c ) 100 %', 'd ) 120 %', 'e ) 125 %'] | b | multiply(divide(volume_cylinder(divide(8, const_2), 10), volume_cylinder(divide(10, const_2), 8)), const_100) | divide(n1,const_2)|divide(n0,const_2)|volume_cylinder(#0,n0)|volume_cylinder(#1,n1)|divide(#2,#3)|multiply(#4,const_100) | physics |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , the how old is b ? | "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 ⇒ 5 x = 20 ⇒ x = 4 . hence , b ' s age = 2 x = 8 years . answer : c" | a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10 | c | divide(multiply(subtract(22, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general |
in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 78 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? | "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 78 % of 250 = 195 are boys who play soccer . girls who play soccer = 55 . total girls who do not play soccer = 108 - 55 = 53 . correct option : c" | a ) 69 . , b ) 73 . , c ) 53 , d ) 91 , e ) 108 | c | subtract(subtract(420, 312), subtract(250, divide(multiply(250, 78), const_100))) | multiply(n2,n3)|subtract(n0,n1)|divide(#0,const_100)|subtract(n2,#2)|subtract(#1,#3)| | gain |
the price of 3 pants and 6 t - shirts is rs . 1500 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ? | let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - -... | a ) 700 , b ) 300 , c ) 250 , d ) 550 , e ) 800 | e | multiply(divide(1500, add(multiply(divide(subtract(12, 6), subtract(3, 1)), 3), 6)), 8) | subtract(n4,n1)|subtract(n0,n3)|divide(#0,#1)|multiply(n0,#2)|add(n1,#3)|divide(n2,#4)|multiply(n5,#5) | general |
rs . 770 were divided among a , b , c in such a way that a had rs . 40 more than b and c had rs 30 more than a . how much was b â € ™ s share ? | let b gets rs x . then we can say a gets rs ( x + 40 ) and c gets rs ( x + 70 ) . x + 40 + x + x + 70 = 770 3 x = 660 x = 220 . b â € ™ s share = rs ( 220 + 70 ) = rs . 290 d | a ) rs . 260 , b ) rs . 270 , c ) rs . 280 , d ) rs . 290 , e ) rs . 300 | d | add(add(divide(subtract(770, add(add(40, 40), 30)), const_3), 30), 40) | add(n1,n1)|add(n2,#0)|subtract(n0,#1)|divide(#2,const_3)|add(n2,#3)|add(n1,#4) | general |
what is the greatest of 3 consecutive integers whose sum is 39 ? | "39 / 3 = 13 the three numbers are 12 , 13 , and 14 . the answer is a ." | a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | a | add(divide(subtract(39, 3), 3), const_2) | subtract(n1,n0)|divide(#0,n0)|add(#1,const_2)| | physics |
john and jacob set out together on bicycle traveling at 15 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ... | john ' s speed - 15 miles / hr jacob ' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . ... | a ) 3 , b ) 3 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 1 1 / 4 | e | divide(add(subtract(15, 9), subtract(9, subtract(multiply(divide(40, const_60), 15), multiply(divide(40, const_60), 9)))), subtract(multiply(divide(40, const_60), 15), multiply(divide(40, const_60), 9))) | divide(n2,const_60)|subtract(n0,n1)|multiply(n0,#0)|multiply(n1,#0)|subtract(#2,#3)|subtract(n1,#4)|add(#1,#5)|divide(#6,#4) | physics |
23 × 19 × ? ÷ 19 ÷ 17 = 115 | "explanation : 23 × 19 × ? ÷ 19 ÷ 17 = 115 = > ( 23 × 19 × ? ) / ( 19 × 17 ) = 115 = > ? = ( 115 × 19 × 17 ) / ( 23 × 19 ) = 85 answer : option c" | a ) 65 , b ) 75 , c ) 85 , d ) 95 , e ) 45 | c | multiply(23, 19) | multiply(n0,n1)| | general |
a city with a population of 97500 is to be divided into 6 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ? | the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 97,500 = p + 5 ( 1.1 ) p 6.5 p = 97,5000 p = 15,000 the answer is a . | a ) 15,000 , b ) 15,500 , c ) 16,000 , d ) 16,500 , e ) 17,000 | a | divide(divide(97500, add(multiply(divide(add(const_100, const_10), const_100), subtract(6, const_1)), const_1)), const_1000) | add(const_10,const_100)|subtract(n1,const_1)|divide(#0,const_100)|multiply(#2,#1)|add(#3,const_1)|divide(n0,#4)|divide(#5,const_1000) | general |
pipe a can fill a tank in 10 hr , pipe b in 20 hr and pipe c in 40 hr . if all the pipes are open in how many hours will tank be filled ? | part filled by ( a + b + c ) in 1 hour = 1 / 10 + 1 / 20 + 1 / 40 = 7 / 40 all the 3 pipes together will fill the tank in 17 min approximately answer is d | a ) 1 hr , b ) 30 min , c ) 15 min , d ) 17 min , e ) 10 min | d | multiply(add(add(divide(10, 10), divide(10, 20)), divide(10, 40)), 10) | divide(n0,n0)|divide(n0,n1)|divide(n0,n2)|add(#0,#1)|add(#3,#2)|multiply(n0,#4) | physics |
a 40 kg metal bar made of alloy of tin and silver lost 4 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ? | you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 4 kg when 40 kg alloy is immersed . this is a loss of ( 4 / 40 ) * 100 = 10 % . this is aavg the loss of tin... | a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3 | e | divide(divide(subtract(4, multiply(divide(0.375, 5), 40)), subtract(divide(1.375, 10), divide(0.375, 5))), subtract(40, divide(subtract(4, multiply(divide(0.375, 5), 40)), subtract(divide(1.375, 10), divide(0.375, 5))))) | divide(n5,n4)|divide(n3,n2)|multiply(n0,#0)|subtract(#1,#0)|subtract(n1,#2)|divide(#4,#3)|subtract(n0,#5)|divide(#5,#6) | other |
in a sports club with 28 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ? | "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 28 38 - 2 x + x = 28 38 - x = 28 x = 10 so 8 members play both badminton and tennis . d" | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | d | subtract(add(add(17, 19), 2), 28) | add(n1,n2)|add(n3,#0)|subtract(#1,n0)| | other |
village x has a population of 74000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ? | "let the population of two villages be equal after p years then , 74000 - 1200 p = 42000 + 800 p 2000 p = 32000 p = 16 answer is b ." | a ) 15 , b ) 16 , c ) 11 , d ) 18 , e ) 13 | b | divide(subtract(74000, 42000), add(800, 1200)) | add(n1,n3)|subtract(n0,n2)|divide(#1,#0)| | general |
the radius of a semi circle is 6.5 cm then its perimeter is ? | "36 / 7 r = 6.5 = 33.4 answer : c" | a ) 32.7 , b ) 32.4 , c ) 33.4 , d ) 32.8 , e ) 32.1 | c | add(divide(circumface(6.5), const_2), multiply(6.5, const_2)) | circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)| | physics |
a number x is 3 times another number y . the percentage that y is less than x is | "say y = 1 and x = 3 . then y = 1 is less than x = 3 by ( 3 - 1 ) / 3 * 100 = 2 / 3 * 100 = 66.6 % . answer : b ." | a ) 12.5 % , b ) 66.6 % , c ) 80 % , d ) 11 % , e ) 1 % | b | multiply(divide(subtract(3, const_1), 3), const_100) | subtract(n0,const_1)|divide(#0,n0)|multiply(#1,const_100)| | general |
two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 36 kmph . in how much time will the trains cross each other ? | "d relative speed = ( 54 + 36 ) * 5 / 18 = 5 * 5 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec ." | a ) 12 sec , b ) 13 sec , c ) 15 sec , d ) 16 sec , e ) 17 sec | d | divide(100, multiply(add(54, 36), const_0_2778)) | add(n3,n4)|multiply(#0,const_0_2778)|divide(n2,#1)| | physics |
if a car had traveled 20 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 60 km , at what speed did it travel ? | "time = distance / speed difference in time = 1 / 2 hrs 60 / x - 60 / ( x + 20 ) = 1 / 2 substitute the value of x from the options . - - > x = 40 - - > 60 / 40 - 60 / 60 = 3 / 2 - 1 = 1 / 2 answer : b" | a ) 35 kmh , b ) 40 kmh , c ) 50 kmh , d ) 60 kmh , e ) 65 kmh | b | divide(subtract(sqrt(add(multiply(multiply(const_2, multiply(60, 20)), const_4), power(20, const_2))), 20), const_2) | multiply(n0,n2)|power(n0,const_2)|multiply(#0,const_2)|multiply(#2,const_4)|add(#3,#1)|sqrt(#4)|subtract(#5,n0)|divide(#6,const_2)| | physics |
a student has to obtain 33 % of the total marks to pass . he got 59 marks and failed by 40 marks . the maximum marks are ? | "let the maximum marks be x then , 33 % of x = 59 + 40 33 x / 100 = 99 x = 300 answer is b" | a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 175 | b | divide(add(59, 40), divide(33, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | general |
the ratio of the volumes of two cubes is 1728 : 1331 . what is the ratio of their total surface areas ? | "explanation : ratio of the sides = ³ √ 1728 : ³ √ 1331 = 12 : 11 ratio of surface areas = 12 ^ 2 : 11 ^ 2 = 144 : 121 answer : option a" | a ) 144 : 121 , b ) 141 : 127 , c ) 144 : 191 , d ) 181 : 161 , e ) 81 : 182 | a | power(divide(1728, 1331), divide(const_1, const_3)) | divide(n0,n1)|divide(const_1,const_3)|power(#0,#1)| | geometry |
the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 4 years is | "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 4 = rs 9724 answer : c" | a ) s . 9621 , b ) s . 6921 , c ) s . 9724 , d ) s . 6261 , e ) s . 6361 | c | multiply(8000, power(add(const_1, divide(5, const_100)), 4)) | divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | gain |
there are 6 working days in a regular week and for each day , the working hours are 10 . a man earns rs . 2.10 per hour for regular work and rs . 4.20 per hour for overtime . if he earns rs . 525 in 4 weeks , how many hours did he work ? | egular working hours in 4 weeks = ( 4 × 6 × 10 ) = 240 hours amount earned by working in these regular working hours = 240 × 2.10 = rs . 504 additional amount he earned = 525 - 504 = rs . 21 hours he worked overtime = 21 / 4.2 = 210 / 42 = 5 hours total hours he worked = 240 + 5 = 245 hours answer is e . | a ) 225 , b ) 235 , c ) 215 , d ) 255 , e ) 245 | e | add(multiply(multiply(4, 6), 10), divide(subtract(525, multiply(multiply(multiply(4, 6), 10), 2.1)), 4.2)) | multiply(n0,n5)|multiply(n1,#0)|multiply(n2,#1)|subtract(n4,#2)|divide(#3,n3)|add(#4,#1) | physics |
due to construction , the speed limit along an 7 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | "7 / 35 - 7 / 55 = 7 / 5 * ( 11 - 7 ) / 77 = 7 / 5 * 4 / 77 * 60 min = 7 * 12 * 4 / 77 = 336 / 77 ~ 4.3 answer - c" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | c | max(multiply(subtract(add(55, 7), const_1), subtract(divide(7, 35), divide(7, 55))), const_4) | add(n0,n1)|divide(n0,n2)|divide(n0,n1)|subtract(#0,const_1)|subtract(#1,#2)|multiply(#3,#4)|max(#5,const_4)| | physics |
if the price of gasoline increases by 25 % and a driver intends to spend only 5 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ? | "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.05 ( p * x ) y = ( 1.05 / 1.25 ) x = 0.84 x which is a reduction of 16 % . the answer is b ." | a ) 20 % , b ) 16 % , c ) 15 % , d ) 12 % , e ) 10 % | b | multiply(divide(subtract(add(25, const_100), add(5, const_100)), add(25, const_100)), const_100) | add(n0,const_100)|add(n1,const_100)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100)| | general |
the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 9 = rs . 8154 answer : option e" | a ) 4000 , b ) 345 , c ) 5673 , d ) 6530 , e ) 8154 | e | multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 9) | add(n0,n1)|multiply(n2,const_2)|multiply(n4,n5)|multiply(n5,n6)|multiply(#0,#1)|multiply(n5,#3)|subtract(#4,#2)|subtract(#6,#5)|multiply(n3,#7)| | geometry |
d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 25 : 144 and bc = 13 cm , then find the length of de . | "abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 169 / 25 side of abc / side of ade = 13 / 5 so the length of de = 5 answer - b" | a ) 12 , b ) 5 , c ) 14 , d ) 11 , e ) 15 | b | multiply(sqrt(divide(144, add(144, 25))), 13) | add(n0,n1)|divide(n1,#0)|sqrt(#1)|multiply(n2,#2)| | geometry |
there are 24 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ? | "the total number of stations = 26 from 26 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 26 p 2 ways . 26 p 2 = 26 * 25 = 650 answer : c" | a ) 800 , b ) 820 , c ) 650 , d ) 870 , e ) 900 | c | multiply(add(24, const_2), subtract(add(24, const_2), const_1)) | add(n0,const_2)|subtract(#0,const_1)|multiply(#0,#1)| | physics |
jaclyn buys $ 50 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter | "explanation : i = ( p x r x t ) / 100 answer : a" | a ) 1187.5 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these | a | divide(divide(multiply(multiply(const_100, const_100), 9.5), const_100), const_4) | multiply(const_100,const_100)|multiply(n2,#0)|divide(#1,const_100)|divide(#2,const_4)| | gain |
x does a work in 30 days . y does the same work in 45 days . in how many days they together will do the same work ? | "x ' s 1 day ' s work = 1 / 30 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 30 + 1 / 45 ) = 1 / 18 both together will finish the work in 18 days . correct option is a" | a ) 18 , b ) 12 , c ) 20 , d ) 30 , e ) 15 | a | inverse(add(divide(const_1, 30), divide(const_1, 45))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2)| | physics |
how many positive integer solutions does the equation 2 x + 3 y = 100 have ? | "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 3 ) = 15.5 answer : c" | a ) 50 , b ) 33 , c ) 16 , d ) 35 , e ) 14 | c | divide(3, 2) | divide(n1,n0)| | general |
if 3 : 7 : : x : 21 , then find the value of x | explanation : treat 3 : 7 as 3 / 7 and x : 21 as x / 21 , treat : : as = so we get 3 / 7 = x / 21 = > 7 x = 63 = > x = 9 option e | a ) 7 , b ) 8 , c ) 11 , d ) 6 , e ) 9 | e | divide(add(multiply(7, 3), 7), 21) | multiply(n0,n1)|add(n1,#0)|divide(#1,n2)| | general |
how many pieces of 0.42 meteres can be cut from a rod 36.5 meteres long | "explanation : we need so simple divide 36.5 / 0.42 , = ( 3650 / 42 ) = 86 option c" | a ) 30 , b ) 40 , c ) 86 , d ) 89 , e ) 95 | c | divide(36.5, 0.42) | divide(n1,n0)| | physics |
if the cost price is 94 % of sp then what is the profit % | "sol . sp = rs 100 : then cp = rs 94 : profit = rs 6 . profit = { ( 6 / 94 ) * 100 } % = 6.25 % answer is e ." | a ) 5.07 % , b ) 6 % , c ) 5.7 % , d ) 6.50 % , e ) 6.25 % | e | multiply(divide(subtract(const_100, 94), 94), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
if a is a positive integer , and if the units digit of a ^ 2 is 1 and the units digit of ( a + 1 ) ^ 2 is 0 , what is the units digit of ( a + 2 ) ^ 2 ? | "if the units digit of a ^ 2 is 1 , then the units digit of a is either 1 or 9 . if the units digit of ( a + 1 ) ^ 2 is 0 , then the units digit of a + 1 is 0 . to satisfy both conditions , the units digit of a must be 9 . then a + 2 has the units digit of 1 , thus the units digit of ( a + 2 ) ^ 2 will be 1 . the answe... | a ) 1 . , b ) 3 . , c ) 5 . , d ) 7 . , e ) 9 . | a | power(add(multiply(1, 2), 2), 2) | multiply(n0,n1)|add(n0,#0)|power(#1,n0)| | general |
a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a heig... | in order to fill up the tank , same volume is shifted from one tank to the other . pi r 1 ^ 2 h 1 = pi r 2 ^ 2 h 2 5 * 5 * 10 = 100 * 100 * h 2 h 2 = . 025 ft e is the answer | ['a ) 2.5 ft', 'b ) 1 ft', 'c ) 0.5 ft', 'd ) 0.25 ft', 'e ) 0.025 ft'] | e | divide(volume_cylinder(5, 10), circle_area(100)) | circle_area(n0)|volume_cylinder(n2,n3)|divide(#1,#0) | geometry |
a person saved $ 10 in buying an item on sale . if he spent $ 100 for the item , approximately how much percent he saved in the transaction ? | actual price = 100 + 10 = $ 110 saving = 10 / 110 * 100 = 100 / 11 = 10 % approximately answer is b | a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 % | b | add(floor(multiply(divide(10, add(10, 100)), const_100)), const_1) | add(n0,n1)|divide(n0,#0)|multiply(#1,const_100)|floor(#2)|add(#3,const_1) | general |
two family reunions are happening at the same hotel , the oates reunion and the yellow reunion . all 100 guests at the hotel attend at least one of the reunions . if 42 people attend the oates reunion and 65 people attend the yellow reunion , how many people attend both reunions ? | no of people in oates reunion = 42 no of people in yellow reunion = 65 attending both = x all guests attend at least one . therefore , 100 = 42 + 65 - ( both ) both = 7 answer b | a ) 2 , b ) 7 , c ) 10 , d ) 16 , e ) 22 | b | subtract(add(42, 65), 100) | add(n1,n2)|subtract(#0,n0) | other |
in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? | "number of newborns that can die in first month = 1 / 10 * 200 = 20 survived = 180 number of newborns that can die in second month = 1 / 10 * 180 = 18 survived = 162 number of newborns that can die in third month = 1 / 10 * 162 = 16 survived = 146 answer : b" | a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 170 | b | multiply(multiply(multiply(200, subtract(1, divide(1, 10))), subtract(1, divide(1, 10))), subtract(1, divide(1, 10))) | divide(n1,n2)|subtract(n1,#0)|multiply(n3,#1)|multiply(#2,#1)|multiply(#3,#1)| | probability |
the surface of a cube is 150 sq cm . find its volume ? | "6 a 2 = 150 = 6 * 25 a = 5 = > a 3 = 125 cc answer : c" | a ) 8 cc , b ) 9 cc , c ) 125 cc , d ) 4 cc , e ) 6 cc | c | volume_cube(sqrt(divide(150, add(const_2, const_4)))) | add(const_2,const_4)|divide(n0,#0)|sqrt(#1)|volume_cube(#2)| | geometry |
two numbers are in the ratio of 5 : 7 . if 7 is subtracted from each number , they are in the ratio of 2 : 3 . what are the two numbers ? | "( 5 x - 7 ) : ( 7 x - 7 ) = 2 y : 3 y 5 x - 7 = 2 y 7 x - 7 = 3 y 49 - 35 = 15 y - 14 y 14 = y 5 x - 7 = 28 x = 7 the two numbers are 5 x and 7 x which are 35 and 49 . the answer is a ." | a ) 35 , 49 , b ) 40 , 56 , c ) 45 , 63 , d ) 50 , 70 , e ) 55 , 77 | a | subtract(multiply(multiply(subtract(multiply(3, 7), multiply(2, 7)), 5), divide(7, 5)), multiply(subtract(multiply(3, 7), multiply(2, 7)), 5)) | divide(n1,n0)|multiply(n2,n4)|multiply(n2,n3)|subtract(#1,#2)|multiply(n0,#3)|multiply(#0,#4)|subtract(#5,#4)| | other |
a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 40 - sided polygon have ? | "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 40 . plugging it in , we get 740 diagonals ! answer ( b ) ." | a ) 875 , b ) 740 , c ) 1425 , d ) 2025 , e ) 2500 | b | divide(multiply(subtract(40, const_3), 40), const_2) | subtract(n0,const_3)|multiply(n0,#0)|divide(#1,const_2)| | geometry |
in covering a distance of 24 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is : | "let abhay ' s speed be x km / hr . then , 24 / x - 24 / 2 x = 3 6 x = 24 x = 4 km / hr . answer : option a" | a ) 4 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 7.8 kmph | a | divide(subtract(24, divide(24, 2)), add(1, 2)) | add(n1,n2)|divide(n0,n1)|subtract(n0,#1)|divide(#2,#0)| | physics |
20 workers can finish a work in 30 days . after how many days should 5 workers leave the job so the work is completed in 35 days ? | work done by 15 workers in 35 days = 15 * 35 = 525 men days . now , work remaining = 600 – 525 = 75 men days and we have 5 workers . so 5 workers will work for 75 / 5 = 15 days . answer : c | a ) 7 , b ) 6 , c ) 15 , d ) 4 , e ) 3 | c | divide(subtract(multiply(20, 30), multiply(subtract(20, 5), 35)), 5) | multiply(n0,n1)|subtract(n0,n2)|multiply(n3,#1)|subtract(#0,#2)|divide(#3,n2) | physics |
a glass was filled with 10 ounces of water , and 0.02 ounce of the water evaporated each day during a 30 - day period . what percent of the original amount of water evaporated during this period ? | "in 30 days 30 * 0.02 = 0.6 ounces of water evaporated , which is 0.6 / 10 â ˆ — 100 = 6 of the original amount of water . answer : c ." | a ) 0.006 % , b ) 0.06 % , c ) 6 % , d ) 2 % , e ) 60 % | c | multiply(divide(multiply(0.02, 30), 10), const_100) | multiply(n1,n2)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a train 284 m in length crosses a telegraph post in 18 seconds . the speed of the train is ? | "s = 284 / 18 * 18 / 5 = 57 kmph answer : c" | a ) 77 kmph , b ) 55 kmph , c ) 57 kmph , d ) 58 kmph , e ) 76 kmph | c | multiply(const_3_6, divide(284, 18)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be 3 times as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ? | r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d . | a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108 | d | multiply(add(divide(subtract(add(8, 2), multiply(3, 2)), subtract(3, const_1)), add(8, 2)), subtract(add(divide(subtract(add(8, 2), multiply(3, 2)), subtract(3, const_1)), add(8, 2)), divide(8, const_2))) | add(n0,n1)|divide(n0,const_2)|multiply(n1,n2)|subtract(n2,const_1)|subtract(#0,#2)|divide(#4,#3)|add(#0,#5)|subtract(#6,#1)|multiply(#6,#7) | general |
a mixture of 120 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ? | number of liters of water in 120 liters of the mixture = 20 % of 120 = 20 / 100 * 120 = 24 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 24 + p ) and total volume of mixture is ( 120 + p ) . ( 24 + p ) = 25 / 100 * ( 120 + p ) 96 + 4 p = 120 + p ... | a ) 2 liters , b ) 3 liters , c ) 8 liters , d ) 5 liters , e ) 7 liters | c | divide(subtract(multiply(divide(25, const_100), 120), multiply(divide(20, const_100), 120)), subtract(const_1, divide(25, const_100))) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(const_1,#0)|subtract(#2,#3)|divide(#5,#4) | general |
5 friends visited a fruit stall , and everyone decided to contribute equally to the total bill of $ 100 . if one of the friends had a coupon for 6 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ? | at the non - discounted price , each friend would pay $ 20 , as $ 100 divided by 5 friends is $ 20 per friend . but if the bill is 6 % off , then each friend would pay 6 % less . 6 % of $ 20 is $ 1.2 , so each friend saves $ 1.2 and pays the remaining 18.8 correct option : option b | a ) 18 , b ) 18.8 , c ) 19 , d ) 17.8 , e ) 17.9 | b | divide(subtract(100, divide(multiply(6, 100), const_100)), 5) | multiply(n1,n2)|divide(#0,const_100)|subtract(n1,#1)|divide(#2,n0) | general |
a certain country is divided into 5 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 15 the total number of progressives in the entire country , what fraction of t... | "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 15 the total number of traditionalists is 5 p / 15 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ." | a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4 | e | subtract(1, divide(divide(5, 15), add(divide(5, 15), 1))) | divide(n0,n2)|add(n1,#0)|divide(#0,#1)|subtract(n1,#2)| | general |
an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22050 / - in 3 years at the same rate of interest . find the rate percentage ? | "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22050 / - - 17640 / - = rs . 4410 / - rate of interest = ( 4410 / 17640 ) × ( 100 / 1 ) = > 25 % answer : option e" | a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 25 % | e | multiply(divide(subtract(22050, 17640), 17640), const_100) | subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)| | general |
which number can we add to 859722 to get a number exactly divisible by 456 ? | "859722 / 456 = 1885 with a remainder of 162 . we need to add 456 - 162 = 294 the answer is a ." | a ) 294 , b ) 306 , c ) 318 , d ) 338 , e ) 362 | a | subtract(456, reminder(859722, 456)) | reminder(n0,n1)|subtract(n1,#0)| | general |
find the l . c . m of 12 , 25 , 24 and 20 . | "explanation : 6 x 2 x 2 x 5 x 5 = 600 answer : option b" | a ) 240 , b ) 600 , c ) 320 , d ) 150 , e ) 250 | b | multiply(multiply(power(const_3, const_3), multiply(power(const_2, const_3), power(add(const_4, const_1), const_2))), divide(divide(divide(divide(divide(24, const_2), const_2), const_3), add(const_4, const_1)), add(const_4, const_1))) | add(const_1,const_4)|divide(n2,const_2)|power(const_2,const_3)|power(const_3,const_3)|divide(#1,const_2)|power(#0,const_2)|divide(#4,const_3)|multiply(#2,#5)|divide(#6,#0)|multiply(#7,#3)|divide(#8,#0)|multiply(#10,#9)| | physics |
walking with 4 / 5 of my usual speed , i miss the bus by 3 minutes . what is my usual time ? | speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 3 4 - - - - - - - - - ? è 12 answer : e | a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min | e | multiply(divide(3, divide(5, 4)), 5) | divide(n1,n0)|divide(n2,#0)|multiply(n1,#1) | physics |
what is the probability of getting a sum 9 from two throws of a dice ? | "in two throws of a dice , n ( s ) = ( 6 x 6 ) = 36 . let e = event of getting a sum = { ( 3 , 6 ) , ( 4 , 5 ) , ( 5 , 4 ) , ( 6 , 3 ) } . p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 . answer : c" | a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) none of these | c | divide(const_2, choose(add(const_3, const_3), const_3)) | add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)| | probability |
in the hillside summer camp there are 100 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ? | "given there are 100 students , 90 % of 50 = 90 boys and remaining 10 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 1000 to existing 90 then the count will be 190 and the girls number will be 10 a... | a ) 150 . , b ) 145 . , c ) 100 . , d ) 30 . , e ) 25 . | c | add(multiply(divide(subtract(const_100, 5), const_100), 100), multiply(divide(5, const_100), 100)) | divide(n2,const_100)|subtract(const_100,n2)|divide(#1,const_100)|multiply(n0,#0)|multiply(n0,#2)|add(#4,#3)| | general |
what is the sum of the integers from - 185 to 195 inclusive ? | "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = - 185 + 195 / 2 = 5 number of items ( n ) = b - a + 1 = 195 - ( - 185 ) + 1 = 195 + 186 = 381 . sum = average * n = 5 * 381 = 1905 . answer is d" | a ) 0 , b ) 5 , c ) 375 , d ) 1905 , e ) 965 | d | divide(multiply(185, 195), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general |
a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 2 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? | "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 6 possible orderings the probabbility is the same . so... | a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 6 / 22 | e | divide(multiply(choose(5, 2), choose(3, 1)), choose(add(add(5, 4), 3), 3)) | add(n1,n2)|choose(n1,n4)|choose(n0,n5)|add(n0,#0)|multiply(#1,#2)|choose(#3,n0)|divide(#4,#5)| | probability |
10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is ? | total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be years . then , age of... | a ) 1 , b ) 7 , c ) 3 , d ) 9 , e ) 2 | c | divide(subtract(subtract(multiply(24, add(4, 2)), add(multiply(24, 4), multiply(10, 4))), 2), const_2) | add(n1,n3)|multiply(n1,n2)|multiply(n0,n1)|add(#1,#2)|multiply(n2,#0)|subtract(#4,#3)|subtract(#5,n3)|divide(#6,const_2) | general |
a certain quantity of 70 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ? | let ' s say that the total original mixture a is 100 ml the original mixture a thus has 70 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 70 ml and 25 ml is 45 ml per 100 ml of m... | a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9 | e | inverse(add(divide(subtract(35, 25), subtract(70, 35)), const_1)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|add(#2,const_1)|inverse(#3) | other |
f 1 ( x ) f 1 ( x ) = 2 x - 1 and fn ( x ) = f 1 ( fn − 1 ( x ) ) fn ( x ) = f 1 ( fn − 1 ( x ) ) for n ≥ ≥ 2 . find f 5 ( 2 ) | answer : a | a ) 7 , b ) 6 , c ) 78 , d ) 9 , e ) 1 | a | add(2, 5) | add(n2,n9) | general |
of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 22 boys and 38 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ? | "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you ... | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | e | subtract(subtract(22, subtract(10, 4)), 6) | subtract(n2,n7)|subtract(n4,#0)|subtract(#1,n6)| | other |
real - estate salesman z is selling a house at a 10 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 10 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 10 percent discount .... | "let the retail price be = x selling price of z = 0.90 x selling price of x = 0.90 * 0.90 x = 0.81 x selling price of y = ( ( 0.90 x + 0.81 x ) / 2 ) * 0.90 = 0.86 x * 0.90 = 0.77 x 0.77 x = k * 0.81 x k = 0.77 / 0.81 = 77 / 81 answer : c" | a ) 38 / 6 , b ) 38 / 5 , c ) 77 / 81 , d ) 38 / 7 , e ) 38 / 10 | c | multiply(divide(divide(multiply(divide(add(subtract(const_100, 10), multiply(subtract(const_100, 10), divide(subtract(const_100, 10), const_100))), const_2), subtract(const_100, 10)), const_100), multiply(subtract(const_100, 10), divide(subtract(const_100, 10), const_100))), const_10) | subtract(const_100,n1)|subtract(const_100,n0)|subtract(const_100,n2)|divide(#0,const_100)|multiply(#3,#1)|add(#4,#1)|divide(#5,const_2)|multiply(#6,#2)|divide(#7,const_100)|divide(#8,#4)|multiply(#9,const_10)| | general |
find the distance covered by a man walking for 42 min at a speed of 10 km / hr ? | "distance = 10 * 42 / 60 = 7 km answer is a" | a ) 7 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km | a | divide(multiply(42, divide(multiply(10, const_1000), const_60)), const_1000) | multiply(n1,const_1000)|divide(#0,const_60)|multiply(n0,#1)|divide(#2,const_1000)| | physics |
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