Cheukting/mathqa huggingface dataset:
Question (physics): three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution q in the liquid in the tank after 3 minutes ?
Options: a ) 5 / 8 , b ) 6 / 8 , c ) 4 / 8 , d ) 2 / 8 , e ) 3 / 8
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by b in 3 minutes = 3 / 20 required ratio = 3 / 20 * 15 / 6 = 3 / 8 answer : e"
Answer: e
Question (general): when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 5 ] * [ 4 ] = ?
Options: a ) [ 33 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 5 ] * [ 4 ] = ( 2 * 5 + 1 ) ( 4 / 2 + 1 ) = [ 33 ] . ans - a"
Answer: a
Question (general): 765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns . how many chairs will be excluded to make this arrangement possible ?
Options: a ) 6 , b ) 36 , c ) 19 , d ) 27 , e ) none of these
Rationale: 27 ( 2 ) < 765 < 28 ( 2 ) ∴ required no . of chairs to be excluded = 765 – 729 = 36 answer b
Answer: b
Question (physics): a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 40 percent .
Options: a ) 120 , b ) 150 , c ) 175 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 40 percent 120 min . answer : a
Answer: a
Question (gain): if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 11 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 110 , b ) 106 , c ) 105 , d ) 107 , e ) 109
Rationale: "( 3500 * 1 * 3 ) / 100 = > 105 answer : c"
Answer: c
Question (general): x and y began business with rs . 10000 and rs . 8000 after 6 months , x advances rs . 2000 and y advances rs . 2000 more . at the end of the year , their profits amounted to rs . 2000 find the share of x and y respectively .
Options: a ) 10001000 , b ) 9001100 , c ) 1200800 , d ) 8001200 , e ) 1100 , 900
Rationale: ( 10 * 6 + 12 * 6 ) : ( 8 * 6 + 10 * 6 ) 11 : 9 x share = 11 / 20 * 2000 = 1100 . y share = 9 / 20 * 2000 = 900 . x and y share respectively is 1100 , 900 . answer : e
Answer: e
Question (general): in a group of ducks and cows , the total number of legs are 30 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 30 = > 2 x = 30 = > x = 15 d"
Answer: d
Question (other): the l . c . m of two numbers is 48 . the numbers are in the ratio 1 : 2 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 72
Rationale: "let the numbers be 1 x and 2 x . then , their l . c . m = 2 x . so , 2 x = 48 or x = 24 . the numbers are 24 and 48 . hence , required sum = ( 24 + 48 ) = 72 . answer : e"
Answer: e
Question (other): a certain fraction has the same ratio to 1 / 36 , as 4 / 7 does to 5 / 9 . what is this certain fraction ?
Options: a ) 1 / 35 , b ) 1 / 42 , c ) 1 / 49 , d ) 1 / 56 , e ) 1 / 63
Rationale: x / ( 1 / 36 ) = ( 4 / 7 ) / ( 5 / 9 ) x = 4 * 9 * 1 / 36 * 7 * 5 = 1 / 35 the answer is a .
Answer: a
Question (general): there are 780 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 130 , e ) 225
Rationale: "female = x male = 780 - x x / 2 + 780 - x / 4 = 1 / 3 * ( 780 ) = 260 x = 260 x / 2 = 130 is supposed to be the answer m is missing something correct option d"
Answer: d
Question (physics): two goods trains each 2000 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 228 , b ) 278 , c ) 192 , d ) 27 , e ) 21
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 2000 + 2000 = 4000 m . required time = 4000 * 6 / 125 = 192 sec . answer : c"
Answer: c
Question (gain): what sum of money will produce rs . 70 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 289 , b ) 500 , c ) 188 , d ) 666 , e ) 155
Rationale: "70 = ( p * 4 * 7 / 2 ) / 100 p = 500 answer : b"
Answer: b
Question (general): a man is 34 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 32 , e ) 40
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 34 ) + 2 = 2 ( x + 2 ) x + 36 = 2 x + 4 = > x = 32 . answer : d"
Answer: d
Question (general): a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 37 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : c"
Answer: c
Question (physics): a train running at a speed of 36 km / h passes an electric pole in 14 seconds . in how many seconds will the whole train pass a 360 - meter long platform ?
Options: a ) 44 , b ) 46 , c ) 48 , d ) 50 , e ) 52
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 14 * 10 = 140 m . the time taken to pass the platform = ( 140 + 360 ) / 10 = 50 seconds the answer is d ."
Answer: d
Question (general): if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Question (physics): a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m ?
Options: a ) 29798 , b ) 27908 , c ) 78902 , d ) 25000 , e ) 27000
Rationale: 27 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 27 = 1 / 100 * x = > x = 27000 answer : e
Answer: e
Question (general): one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 72 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 4
Rationale: "there are total 72 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 18 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 72 = 45 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 18 - b have read saramago but not kureishi . so , ( 18 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 72 = 18 + 45 - b + ( 18 - b - 1 ) b = 4 answer ( e )"
Answer: e
Question (physics): in traveling from a dormitory to a certain city , a student went 1 / 4 of the way by foot , 1 / 2 of the way by bus , and the remaining 10 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 10 , b ) 45 , c ) 30 , d ) 20 , e ) 40
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 4 x + 1 / 2 x + 10 x - 1 / 4 x - 1 / 2 x = 10 x = 40 km option : e"
Answer: e
Question (general): if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 4 = 1 / ( 16 * ( 10 ) ^ 4 ) , then m =
Options: a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 8
Rationale: "( 1 / 5 ) ^ m ( 1 / 4 ) ^ 4 = 1 / { 16 ( 10 ) ^ 4 } 16 ( 10 ) ^ 4 / 4 ^ 4 = 5 ^ m [ 16 ( 2 ^ 4 ) ( 5 ^ 4 ) ] / [ 2 ^ 8 ] = 5 ^ m 5 ^ 4 = 5 ^ m m = 4 d"
Answer: d
Question (general): in the faculty of reverse - engineering , 220 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 636 .
Rationale: answer is e : 636 solution : total number of students studying both are 423 + 220 - 134 = 509 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 509 , so 100 % is approx . 636 .
Answer: e
Question (physics): what would be the minimum number of pumps required to fill a tank of 1000 m 3 to 85 % in one hour ? the capacity of the pump is 150 m 3 / hour and operates at an efficiency of 75 % .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: volume handled by pump in one hour = 150 x . 75 = 112.5 volume of the tank that needs to be filled = 1000 x . 85 = 850 number of pumps needed = 850 / 112.5 = 7.55 â ‰ ˆ 8 answer : b
Answer: b
Question (gain): of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 60 percent was planted with grapes and 30 percent of the cleared land was planted with potato . if the remaining 360 acres of cleared land was planted with tomato , how many acres did the farmer own ?
Options: a ) 3250 , b ) 3450 , c ) 4000 , d ) 3750 , e ) 3800
Rationale: 60 % of 90 % = 54 % , 30 % 0 f 90 % = 27 % so the remaining 90 - 54 - 27 = 9 % = 360 acres or 10 % of 90 % = 9 % - - > 360 / 9 * 100 = 4000 acres answer ( c )
Answer: c
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 8 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 18 , d ) 16 , e ) 12
Rationale: "7 * 5 : 8 * x = 7 : 10 x = 16 answer : d"
Answer: d
Question (physics): a monkey ascends a greased pole 12 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these
Rationale: in 2 minutes , he ascends = 1 metre ∴ 10 metres , he ascends in 20 minutes . ∴ he reaches the top in 21 st minute . answer b
Answer: b
Question (general): what will be the remainder when 17 ^ 200 is divided by 18
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "17 ^ 200 % 18 ( 17 - 18 ) ^ 200 % 18 ( - 1 ) ^ 200 % 18 1 % 18 = 1 answer : a"
Answer: a
Question (general): sakshi invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?
Options: a ) rs . 4000 , b ) rs . 4500 , c ) rs . 5500 , d ) rs . 6000 , e ) rs . 6500
Rationale: let investment in 12 % stock be rs . x . then , investment in 15 % stock = rs . ( 12000 - x ) . 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x / 10 + 3 / 25 ( 12000 - x ) = 1360 5 x + 72000 - 6 x = 1360 x 50 x = 4000 . answer = a
Answer: a
Question (general): xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 5 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 11 / 8 , b ) 3 / 80 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 5 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 5 ) * ( 1 / 2 ) * ( 3 / 8 ) = 3 / 80 . ans . b ."
Answer: b
Question (other): in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 400 girls , the total number of students in the college is
Options: a ) 1040 , b ) 920 , c ) 980 , d ) 720 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 400 = > x = 80 total students = 8 x + 5 x = 13 x = 13 ( 80 ) = 1040 option a"
Answer: a
Question (general): the tax on a commodity is diminished by 18 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8.7 % , c ) 5.7 % , d ) 6.7 % , e ) 1 %
Rationale: "100 * 100 = 10000 82 * 115 = 9430 - - - - - - - - - - - 10000 - - - - - - - - - - - 570 100 - - - - - - - - - - - ? = > 5.7 % decrease answer : c"
Answer: c
Question (physics): a can do a job in 10 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 15 days , e ) none of these
Rationale: "explanation : 1 / 10 + 1 / 30 = 4 / 30 = 2 / 15 15 / 2 = 15 / 2 * 2 = 15 days answer : d"
Answer: d
Question (other): if jamie ' s income is rs 20000 , calculate his savings given that his income and expenditure are in the ratio 7 : 5 . ?
Options: a ) rs 7500 , b ) rs 4000 , c ) rs 2000 , d ) rs 8000 , e ) rs 7000
Rationale: let the income and the expenditure of the person be rs . 7 x and rs . 7 x respectively . income , 7 x = 28000 = > x = 4000 savings = income - expenditure = 7 x - 5 x = 2 x so , savings = rs . 8000 answer : d
Answer: d
Question (gain): a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 5 years . what is the sum ?
Options: a ) 82762 , b ) 12877 , c ) 82882 , d ) 80925 , e ) 80325
Rationale: "principal = ( 100 * 4016.25 ) / ( 1 * 5 ) = rs . 80325 . answer : e"
Answer: e
Question (general): on thrusday mabel handled 90 transactions . anthony handled 10 % more transaction than mabel , cal handled 2 / 3 rds of the transactions that anthony handled and jade handled 16 more transaction than cal . how much transaction did jade handled ?
Options: a ) 92 , b ) 80 , c ) 72 , d ) 82 , e ) 28
Rationale: mabel handled 90 transaction , anthony 10 % more transaction the mabel . anthony = 90 + 90 * 10 % , = 90 + 90 * 0.10 , = 90 + 9 , = 99 , cal handled 2 / 3 rds than anthony handled , cal = 2 / 3 * 99 = 66 , jade handled 16 more than cal . jade = 66 + 16 = 82 , jade handled = 82 tranasactions . correct answer : ( d )
Answer: d
Question (general): jar x is 1 / 3 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 5 / 6 , b ) 5 / 12 , c ) 7 / 12 , d ) 7 / 18 , e ) 11 / 18
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 3 + p / 4 = 7 p / 12 the answer is c ."
Answer: c
Question (general): a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 4 of the mixture is water , and the remaining 10 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 36
Rationale: "let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 4 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 4 ) x = ( 5 / 12 ) x = 10 x = 24 then answer will be a = 24"
Answer: a
Question (gain): 0.01 is what percent of 0.1 ?
Options: a ) 1 % , b ) 10 % , c ) 100 % , d ) 50 % , e ) 25 %
Rationale: "required percentage = 0.01 * 100 / 0.1 = 100 / 10 = 10 % answer is b"
Answer: b
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 26 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 150 m , c ) 289 m , d ) 299 m , e ) 219 m
Rationale: "speed = 300 / 26 = 150 / 13 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 150 / 13 = > x = 150 m . answer : b"
Answer: b
Question (general): 9 persons went to a hotel for taking their meals . 8 of them spent rs 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them ?
Options: a ) 117 , b ) 180 , c ) 150 , d ) 200 , e ) 250
Rationale: exp . let the total expenditure be x , then the average = x / 9 , 8 * 12 + [ x / 9 + 8 ] = x or [ x - x / 9 ] = 104 . 8 x / 9 = 104 , x = 104 * 9 / 8 = 117 . answer : a
Answer: a
Question (physics): a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 7 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 252 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 7 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 = sum of 7 terms in ap whose first term is 30 and last term is 42 = 7 / 2 [ 30 + 42 ] = 252 km . answer : c"
Answer: c
Question (general): the average ( arithmetic mean ) of 4 positive integers is 40 . if the average of 2 of these integers is 45 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 69 , c ) 100 , d ) 109 , e ) 115
Rationale: a + b + c + d = 160 a + b = 90 c + d = 70 greatest possible = 69 ( just less than 1 ) answer = b
Answer: b
Question (physics): what is the least number of square tiles required to pave the floor of a room 12 m 12 cm long and 1 m 20 cm broad ?
Options: a ) 1010 , b ) 804 , c ) 814 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1212 cm & 120 cm = 12 cm . area of each tile = ( 12 x 12 ) cm 2 ∴ required number of tiles = [ 1212 x 120 / 12 x 12 ] = 1010 . answer a"
Answer: a
Question (general): if 2 x = 3 √ 32 , then x is equal to :
Options: a ) 3 / 5 , b ) 5 / 3 , c ) 15 , d ) 25 , e ) none
Rationale: "sol . 2 x = 3 √ 32 ⇔ 2 x = ( 32 ) 1 / 3 = ( 25 ) 1 / 3 = 25 / 3 ⇔ x = 5 / 3 . answer b"
Answer: b
Question (physics): a train running at the speed of 48 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 120 meter , b ) 299 meter , c ) 666 meter , d ) 155 meter , e ) 144 meter
Rationale: "speed = 48 * ( 5 / 18 ) m / sec = 40 / 3 m / sec length of train ( distance ) = speed * time ( 40 / 3 ) * 9 = 120 meter answer : a"
Answer: a
Question (general): a cricket player whose bowling average was 20.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 101 , d ) 111 , e ) 128
Rationale: "average = total runs / total wickets total runs after last match = 20.5 w + 52 total wickets after last match = w + 5 ( 20.5 w + 52 ) / ( w + 5 ) = 20.5 - 0.5 = 20 w = 96 so total wickets aftr last match = w + 5 = 101 answer : c"
Answer: c
Question (gain): if a trader sold two cars each at rs . 325475 and gains 11 % on the first and loses 11 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.21 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.24 %
Rationale: "sp of each car is rs . 325475 , he gains 11 % on first car and losses 11 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 11 ) ( 11 ) / 100 % = 1.21 % answer : a"
Answer: a
Question (general): 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 36 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 15 days , b ) 18 days , c ) 21 days , d ) 24 days , e ) 27 days
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 36 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 36 / 60 oxen = 18 days the answer is b ."
Answer: b
Question (general): for any non - zero a and b that satisfy | ab | = ab and | a | = a | b - 4 | + | ab - b | = ?
Options: a ) ab - 4 , b ) 2 b - ab - 4 , c ) ab + 4 , d ) ab - 2 b + 4 , e ) 4 - ab
Rationale: | ab | = ab and | a | = - a = > b is also negative . so | b - 4 | + | ab - b | = ( b - 4 ) + ab - b ( as ab is positive and - b is positive , so expression is totally positive ) = b - 4 + ab - b = ab - 4 answer - a
Answer: a
Question (general): p software has coding line 5 % more than n , n software has coding line 1 / 3 more than m . m software has 90 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 126 , d ) 109 , e ) 110
Rationale: m s / w has 90 line of code n s / w has = 90 + 90 * 1 / 3 = 120 line of code p s / w 5 % more n ' code 120 + 6 = 126 answer : c
Answer: c
Question (geometry): the length of a rectangle is 4 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 100 square inches , d ) 89 square inches , e ) 92 square inches
Rationale: "if the width is 5 in and the length is 4 times the width , then the length is 4 * 5 = 20 in the area is given by 5 * 20 = 100 square inches correct answer c"
Answer: c
Question (physics): a and b go around a circular track of length 1800 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 186 sec , d ) 167 sec , e ) 360 sec
Rationale: time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1800 / ( 36 * 5 / 18 ) , 1800 / ( 54 * 5 / 18 ) } = lcm ( 180 , 120 ) = 360 sec . answer : e
Answer: e
Question (general): if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 3 x ^ 2 + 6 x , then f ( - 1 ) =
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: f ( - 1 ) = 3 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 3 ( - 1 ) ^ 2 + 6 ( - 1 ) = 3 + 4 - 3 - 6 = - 2 the answer is a .
Answer: a
Question (general): the greatest common divisor of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . what is the value of b ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 9 , e ) 6
Rationale: gcd of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . find x . best way to find n is substitute each of the answer and find out the correct one . only option d gave the correct answer . option d : 9 and find gcd or 7 ! , 10 ! and 13 ! . 7 ! itself is 5040 and 7 ! which is contained in the other two factorials . this satisfies the condition , hence answer is 9 . answer is d .
Answer: d
Question (physics): the length of a side of a hexagon is 10 inches . what is the perimeter ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 60
Rationale: "hexagon . it means 6 equal sides . p = 6 ( 10 ) = 60 inches answer e"
Answer: e