Cheukting/mathqa huggingface dataset:
Question (gain): if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 400 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 410 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 20,000 . now , put the value of x = 4000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 4000 + 5 % of 4000 = 4200 . 2 nd year , amount = 4200 + 5 % of 4200 = 4410 . we can see after 2 years interest = 4410 - 4000 = 410 . hence , it satisfies the question . hence d is the correct answer"
Answer: d
Question (gain): a cricket bat is sold for $ 900 , making a profit of $ 225 . the profit percentage would be
Options: a ) 24 % , b ) 25.5 % , c ) 33.33 % , d ) 36.3 % , e ) 40 %
Rationale: "225 / ( 900 - 225 ) = 33.33 % . answer : c"
Answer: c
Question (gain): a part of certain sum of money is invested at 16 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 5 : 4 , b ) 1 : 4 , c ) 3 : 1 , d ) 3 : 5 , e ) 3 : 4
Rationale: "12 : 16 = 3 : 4 answer : e"
Answer: e
Question (general): reduce 4128 / 4386 to its lowest terms
Options: a ) 14 / 13 , b ) 13 / 17 , c ) 16 / 17 , d ) 13 / 18 , e ) none of these
Rationale: explanation : hcf of 4128 and 4386 4128 ) 4386 ( 1 4128 - - - - - 258 ) 4128 ( 16 4128 - - - - 0 hence hcf of 4128 and 4386 is 258 . 4128 / 258 = 16 4386 / 258 = 17 4128 / 4386 = 16 / 17 answer : option c
Answer: c
Question (other): a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: probability of selecting first red marble = 2 / 5 probability of selecting second red marble without replacement = 1 / 4 final probability = 2 / 5 * 1 / 4 = 1 / 10 correct answer - a
Answer: a
Question (general): for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 40 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 40 4 n < 33 n < 8 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 8 ) combining the two - 1.5 < n < 8.25 n = 1 to 8 ( 48 integers ) and n = - 1 and 0 so 10 integers . a"
Answer: a
Question (physics): a contractor undertook to do a piece of work in 9 days . he employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days . find the number of men originally employed .
Options: a ) 15 , b ) 6 , c ) 13 , d ) 9 , e ) none of these
Rationale: let the number of men originally employed be x . 9 x = 15 ( x – 6 ) or x = 15 answer a
Answer: a
Question (general): the average of 11 results is 42 , if the average of first 5 results is 49 and that of the last 7 is 52 . find the fifth result ?
Options: a ) 145 , b ) 146 , c ) 147 , d ) 148 , e ) 149
Rationale: 1 to 11 = 11 * 42 = 462 1 to 5 = 5 * 49 = 245 5 to 11 = 7 * 52 = 364 5 th = 245 + 364 – 462 = 147 answer : c
Answer: c
Question (physics): a train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph , in 12 seconds . it also passes a railway platform in 45 seconds . the length of the platform is
Options: a ) 400 m , b ) 450 m , c ) 560 m , d ) 600 m , e ) 680 m
Rationale: length of the ist train = 2 x m and the length of the other train be x m ( 1 / 2 ) the relative speed of the train ( 48 + 42 ) = 90 kmph or 25 m / s time taken to cross one another = 12 s hence , 12 = 2 x + x / 25 solving , x = 100 m and 200 m now to determine the length of the platform 45 = 100 + length of the platform / speed of the ist train 45 = 100 + l / 240 / 18 ( 48 kmph = 240 / 118 m / s ) solving , we get l = 600 m answer : d
Answer: d
Question (probability): if x is to be chosen at random from the set { 1 , 2 , 3 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 5 / 6 . answer : e ."
Answer: e
Question (physics): if seven machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 84 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 7 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 14 / 3 = 10 / 3 * x x = 7 / 5 hour so 84 minutes answer : d"
Answer: d
Question (geometry): what is the % change in the area of a rectangle when its length increases by 60 % and its width decreases by 60 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 36 % decrease , d ) 1 % decrease , e ) insufficient data
Rationale: "( 16 / 10 ) * ( 4 / 10 ) = 64 / 100 of original area 64 / 100 is a 36 % decrease from 100 / 100 - > c"
Answer: c
Question (general): initially two cups of same volume are present with milk filled upto 3 / 5 th and 4 / 5 th of their volumes . water is then filled . then two mixtures are mixed . find the ratio of water to milk in the mixture
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: water content can b in 1 st and second is 2 / 5 and 1 / 5 total : 3 / 5 . the total milk content is 7 / 5 . the ratio is ( ( 3 / 5 ) / ( 7 / 5 ) ) = 3 / 7 . answer : c
Answer: c
Question (physics): convert 600 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 965604 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 600 mile = 600 * 1609.34 = 965604 meters answer is c"
Answer: c
Question (gain): heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 30 litres of tomato juice ?
Options: a ) 3.75 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 30 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 3.75 liters . answer : a"
Answer: a
Question (general): if x < y < z and y - x > 3 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 3 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 are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 3 , the least value for y - x must be 5 , the least value for x must be 2 , and , thus , the least possible value for y must be 7 ( y - 2 = 5 , y = 7 ) 2 < 7 < z , since z is odd , the least possible value for z is 9 z - x = 9 - 2 = 7 answer a"
Answer: a
Question (general): if an amount of rs 42900 is distributed equally amongst 22 persons , how much amount would each person get ?
Options: a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none
Rationale: required amount = 42900 / 22 = rs 1950 answer a
Answer: a
Question (physics): six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 50 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) 26
Rationale: "l . c . m of 2,4 , 6,8 , 10,12 is 120 . i . e after each 2 min they will toll together . so in 50 min they will toll 25 times . as they have initially tolled once , the answer will be 25 + 1 = 26 . answer : e"
Answer: e
Question (general): what least number must be subtracted from 9671 so that the remaining number is divisible by 5 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "on dividing 9671 by 5 , we get remainder = 1 . required number be subtracted = 1 answer : e"
Answer: e
Question (general): find the average of all prime numbers between 50 and 70
Options: a ) 90 , b ) 45 , c ) 60 , d ) 90 , e ) 26
Rationale: "prime numbers between 50 and 70 are 53 , 59 , 61 , 67 required average = ( 53 + 59 + 61 + 67 ) / 4 = 240 / 4 = 60 answer is c"
Answer: c
Question (general): the sum of ages of 5 children born at the intervals of 3 years each is 70 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 x = 8 . age of the youngest child = x = 8 years . e )"
Answer: e
Question (general): for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 120 ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 120 4 n < 113 n < 28 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 28 ( 48 integers ) and n = - 1 and 0 so 30 integers . e is the answer"
Answer: e
Question (general): the average of thirteen numbers is 9 . the average of first 6 numbers is 5 and the average of last 6 numbers is 7 . what is the middle number ?
Options: a ) 47 , b ) 45 , c ) 25 , d ) 37 , e ) 44
Rationale: the total of thirteen numbers = 13 x 9 = 117 the total of first 6 and last 6 numbers is = 6 x 5 + 6 x 7 = 72 so , the middle number is ( 117 - 72 ) = 45 b
Answer: b
Question (general): two heavily loaded sixteen - wheeler transport trucks are 1025 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 130 , c ) 150 , d ) 320 , e ) 145
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 1025 - 90 = 935 k ratio of speeds 9 : 8 - > 935 / 17 = 55 truck a = 90 + 55 * 9 = 585 truck b = 55 * 8 = 440 delta = 145 km answer e"
Answer: e
Question (general): find the sum of all 2 digit numbers divisible by 3 .
Options: a ) 1565 , b ) 1665 , c ) 1300 , d ) 1448 , e ) 1465
Rationale: "all 2 digit numbers divisible by 3 are 12,15 , 18,21 , … … … . . 99 this is an a . p with a = 12 , and d = 3 , let it contain n terms then , 12 + ( n – 1 ) * 3 = 99 , or n = ( 99 - 12 ) / 3 + 1 = 30 required sum = 30 / 2 * ( 12 + 99 ) = 15 * 111 = 1665 answer : b"
Answer: b
Question (general): 2 , 3 , 6 , 0 , 10 , - 3 , 14 , ( . . . )
Options: a ) - 6 , b ) 8 , c ) - 2 , d ) 4 , e ) 10
Rationale: "there are two series 2 , 6 , 10 , 14 , . . . ( adding 4 ) 3 , 0 , - 3 , . . . ( subtracting 3 ) hence , next term is - 3 - 3 = - 6 answer is a"
Answer: a
Question (gain): a man can row downstream at the rate of 12 km / hr and upstream at 8 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 6,3 , c ) 9,3 , d ) 10,2 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 12 + 8 ) = 10 km / hr rate of current = 1 / 2 ( 12 - 8 ) = 2 km / hr answer : option d"
Answer: d
Question (gain): the present population of a town is 1000 . population increase rate is 25 % p . a . find the population of town after 2 years ?
Options: a ) 1000 , b ) 2000 , c ) 1563 , d ) 2153 , e ) 1245
Rationale: "p = 1000 r = 25 % required population of town = p ( 1 + r / 100 ) ^ t = 1000 ( 1 + 25 / 100 ) ^ 2 = 1000 ( 5 / 4 ) ^ 2 = 1563 ( approximately ) answer is c"
Answer: c
Question (physics): the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.0 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1332 , c ) s . 999 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332 answer : b"
Answer: b
Question (general): two employees m and n are paid a total of $ 605 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 245 , b ) $ 255 , c ) $ 265 , d ) $ 275 , e ) $ 285
Rationale: "1.2 n + n = 605 2.2 n = 605 n = 275 the answer is d ."
Answer: d
Question (general): the weight of 4 dogs is determined to be 25 pounds , 31 pounds , 35 pounds and 33 pounds respectively . the weight of a fifth dog is determined to be y pounds . if the average ( arithmetic mean ) weight of the first 4 dogs is the same as that of all 5 dogs what is the value of y ?
Options: a ) 31 , b ) 33 , c ) 35 , d ) 37 , e ) 39
Rationale: total weight of the 4 dogs = ( 25 + 31 + 35 + 33 ) = 124 avg = 124 / 4 = 31 total weight of 5 dogs = 124 + y or 4 ( 31 ) + y average of 5 dogs as per question = 31 equation : 4 ( 31 ) + y = 5 ( 31 ) , or y = 31 . choose a
Answer: a
Question (gain): how many ounces of a 60 % salt solution must be added to 40 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 40 , c ) 50 , d ) 60.33 , e ) 70
Rationale: "let x = ounces of 60 % salt solution to be added . 2 * 40 + . 6 x = . 4 ( 40 + x ) x = 40 amswer b"
Answer: b
Question (physics): car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 60 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 13 : 7 , d ) 5 : 3 , e ) 6 : 11
Rationale: "car a travels 50 × 8 = 400 km car b travels 60 × 4 = 240 km the ratio is 400 : 240 = 40 : 24 = 5 : 3 the answer is d ."
Answer: d
Question (gain): if the cost price of 50 articles is equal to the selling price of 46 articles , then the gain or loss percent is ?
Options: a ) 22 , b ) 65 , c ) 78 , d ) 33 , e ) 8.69
Rationale: given that , cost price of 50 article is equal to selling price of 46 articles . let cost price of one article = rs . 1 selling price of 46 articles = rs . 50 but cost price of 46 articles = rs . 46 therefore , the trader made profit . \ percentage of profit = 4 / 46 * 100 = 8.69 % answer : e
Answer: e
Question (physics): johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 21 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 6.5 miles , d ) 8 miles , e ) 10 miles
Rationale: "answer : c ) 6.5 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 21 / ( 5 + 21 ) = 6.5 m / hr the distance between schoolhome should be half of that . ie . 6.5 miles answer c"
Answer: c
Question (general): if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 3 y ^ 2 = ?
Options: a ) 2 , b ) 48 , c ) 0 , d ) 10 , e ) 3
Rationale: 3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 3 y ^ 2 = 3 * 16 = 48 answer is b
Answer: b
Question (general): how many distinct 3 digit number less than 10
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "000,001 , 002,003 , 004,005 , 006,007 , 008,009 . 10 distinct 3 digit numbers less than 10 . answer : c"
Answer: c
Question (general): the average age of a group of persons going for picnic is 16 years . 20 new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is ?
Options: a ) 10 , b ) 20 , c ) 37 , d ) 26 , e ) 22
Rationale: let the initial number of persons be x . then , 16 x + 20 * 15 = 15.5 ( x + 20 ) < = > 0.5 x = 10 < = > x = 20 . answer : b
Answer: b
Question (gain): in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 2000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 20000 , b ) 25000 , c ) 24000 , d ) 23000 , e ) 22000
Rationale: "winner - looser 55 % - 45 % if 2000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 2,000 people compose 10 % of all voters , which means that the total number of votes is 20,000 . answer : a ."
Answer: a
Question (general): if 99 < x < 199 and 10 < y < 100 , then the product xy can not be equal to :
Options: a ) 19,104 , b ) 19,903 , c ) 19 , 356.732 , d ) 19,502 , e ) 19,880
Rationale: correct answer : ( b ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 99 * 10 . the largest value must be less than 199 * 100 . this means that 990 < xy < 19,900 . ( b ) is outside of this range , so it is not a possible product of xy .
Answer: b
Question (general): a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 39,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 14900 , d ) 16380 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 39000 × 21 / 50 = 16380 answer is d"
Answer: d
Question (general): if the operation € is defined for all x and y by the equation x € y = 3 * x * y , then 3 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 540 , e ) 660
Rationale: "working inside out , ( 4 € 5 ) = 3 * 4 * 5 = 60 3 € 60 = 3 * 3 * 60 = 540 hence , answer is d"
Answer: d
Question (physics): a person can swim in still water at 8 km / h . if the speed of water 4 km / h , how many hours will the man take to swim back against the current for 8 km ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 8 s = 4 us = 8 - 4 = 4 d = 4 t = 8 / 4 = 2 answer : a"
Answer: a
Question (other): thomas and matt has some money with them in the ratio of 3 : 4 . if their father gives rs . 30 to each of them then the ratio becomes 4 : 5 . what would be the ratio if thomas spend rs . 40 and matt spend rs . 20 from what they have now ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: let money of thomas and matt be x and y respectively . x / y = 3 / 4 = > x = 3 / 4 y ( x + 30 ) / ( y + 30 ) = 4 / 5 = > 5 x + 150 = 4 y + 120 = > 5 x = 4 y - 30 but x = 3 / 4 y 5 * 3 / 4 y = 4 y - 30 15 y = 16 y - 120 = > y = 120 = > x = 3 * 120 / 4 = > x = 90 ratio of their money , if thomas spend rs . 40 and matt spend rs . 20 = > ( 90 - 40 ) / ( 120 - 20 ) = 50 / 100 . = > 1 : 2 answer : a
Answer: a
Question (general): if the integer n has exactly 5 positive divisors , including 1 and n , how many positive divisors does √ n have ?
Options: a ) 6 , b ) 5 , c ) 2 , d ) 3 , e ) 4
Rationale: take the example of 16 . . . it has 3 positive divisors ( 1 , 2,4 , 8,16 ) now , take the example of 4 . . . it has only 3 divisors . . so d is the ans
Answer: d
Question (general): a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 480 ?
Options: a ) 249 , b ) 498 , c ) 239 , d ) 823 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 480 y = 2 x + 2 478 = 2 x x = 239 answer : c . 239"
Answer: c
Question (gain): bruce purchased 7 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 985 , b ) b ) 1050 , c ) c ) 1055 , d ) d ) 1065 , e ) e ) 1075
Rationale: cost of 7 kg grapes = 70 × 7 = 490 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 490 + 495 = 985 a
Answer: a
Question (general): if the sum of two positive integers is 26 and the difference of their squares is 52 , what is the product of the two integers ?
Options: a ) 108 , b ) 119 , c ) 128 , d ) 135 , e ) 168
Rationale: let the 2 positive numbers x and y x + y = 26 - - 1 x ^ 2 - y ^ 2 = 52 = > ( x + y ) ( x - y ) = 52 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 14 y = 12 product = 14 * 12 = 168 answer e
Answer: e
Question (general): fonzie , aunt bee and lapis paid $ 7000 , $ 8000 and $ 9000 respectively to buy a map to capt . plaidstache ' s treasure . when they found it , the treasure turned out to be worth a cool $ 900000 . how much of it should lapis get ?
Options: a ) $ 300000 , b ) $ 320000 , c ) $ 335000 , d ) $ 336500 , e ) $ 337500
Rationale: a = 7000 b = 8000 c = 9000 a share 7 parts , b share 8 parts & c share 9 parts total 24 parts - - - - - > 900000 - - - - > 1 part - - - - - - - > 37500 c share = 9 parts - - - - - > 337500 e
Answer: e
Question (general): for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 9 ] * [ 4 ] equivalent to ?
Options: a ) [ 108 ] , b ) [ 54 ] , c ) [ 36 ] , d ) [ 27 ] , e ) [ 18 ]
Rationale: "[ 9 ] * [ 4 ] = 27 * 2 = 54 = ( 1 / 2 ) ( 108 ) = [ 108 ] the answer is a ."
Answer: a
Question (physics): two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 4 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 5 , e ) 5.5
Rationale: "let x be the total time it takes for the cistern to fill . 4 / 10 + x / 15 = 1 x / 15 = 3 / 5 x = 9 after the first pipe is turned off , it takes 5 more minutes to fill the cistern . the answer is d ."
Answer: d
Question (physics): express 20 mps in kmph ?
Options: a ) 23 , b ) 88 , c ) 90 , d ) 72 , e ) 21
Rationale: 20 * 18 / 5 = 72 kmph answer : d
Answer: d
Question (gain): you hold some gold in a vault as an investment . over the past year the price of gold increases by 40 % . in order to keep your gold in the vault , you must pay 5 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 35 % , b ) 33 % , c ) 36 % , d ) 38 % , e ) 40 %
Rationale: "( 100 % + 40 % ) * ( 100 % - 5 % ) = 140 * 0.95 = 133 % an increase of 33 % your gold holdings have increased in value by 33 % . the answer is b"
Answer: b