regisss/math_qa huggingface dataset:
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 34 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "34 % is 9 % - points above 25 % and 6 % - points below 40 % . thus the ratio of mixture y to mixture x is 2 : 3 . the percent of mixture x is 3 / 5 = 60 % . the answer is d ."
Answer: d
Problem: in a triangle abc , ab = 6 , bc = 8 and ac = 10 . a perpendicular dropped from b , meets the side ac at d . a circle of radius bd ( with centre b ) is drawn . if the circle cuts ab and bc at p and q respectively , then ap : qc is equal to
Options: a ) 1 : 1
b ) 3 : 2
c ) 4 : 1
d ) 3 : 8
e ) 2 : 5
Rationale: explanation : triangle abc and triangle adb are similar , ac / ab = bc / bd 10 / 6 = 8 / r r = 24 / 5 bp = bq = bd = r = 24 / 5 ap = ab - r = 6 - 24 / 5 = 6 / 5 cq = bc - r = 8 - 24 / 5 = 16 / 5 ap : cq = 6 / 16 = 3 : 8 answer : d
Answer: d
Problem: find the mean proportional between 49 & 81 ?
Options: a ) 59 , b ) 61 , c ) 63 , d ) 65 , e ) 67
Rationale: formula = √ a × b a = 49 and b = 81 √ 49 × 81 = 7 × 9 = 63 c
Answer: c
Problem: the average monthly income of p and q is rs . 6050 . the average monthly income of q and r is rs . 7050 and the average monthly income of p and r is rs . 8000 . the monthly income of p + q + r is :
Options: a ) 41100 , b ) 42000 , c ) 21100 , d ) 42200 , e ) 21000
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 6050 x 2 ) = 12100 . . . . ( i ) q + r = ( 7050 x 2 ) = 14100 . . . . ( ii ) p + r = ( 8000 x 2 ) = 16000 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 42200 or p + q + r = 21100 . . . . ( iv ) ( p + q + r ) ' s monthly income = rs . 21100 . answer : c"
Answer: c
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 4 = 20 . thus there are 320 - 20 = 300 such numbers . answer : d ."
Answer: d
Problem: in one hour , a boat goes 9 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 2 , b ) 4 , c ) 7 , d ) 12 , e ) 15
Rationale: "sol . speed in still water = 1 / 2 ( 9 + 5 ) kmph = 7 kmph . answer c"
Answer: c
Problem: a 70 cm long wire is to be cut into two pieces so that one piece will be 2 / 3 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 35 , b ) 20 , c ) 28 , d ) 36 , e ) 30
Rationale: "1 : 2 / 3 = 3 : 2 2 / 5 * 70 = 28 answer : c"
Answer: c
Problem: 165 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 66 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 165 = 99 liters water = 66 liters 99 : ( 66 + p ) = 3 : 4 198 + 3 p = 396 = > p = 66 66 liters of water are to be added for the ratio become 3 : 4 . answer : a"
Answer: a
Problem: raman mixed 54 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129 , b ) 287 , c ) 196 , d ) 188 , e ) 112
Rationale: "explanation : cp per kg of mixture = [ 54 ( 150 ) + 36 ( 125 ) ] / ( 54 + 36 ) = rs . 140 sp = cp [ ( 100 + profit % ) / 100 ] = 140 * [ ( 100 + 40 ) / 100 ] = rs . 196 . answer : c"
Answer: c
Problem: average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 25 % the new mean is $ 850 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "0.25 x = 4 ( 850 - 800 ) 0.25 x = 200 x = 800 answer a"
Answer: a
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 5 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 50 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 5 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 5 × 2 / 100 = 500 his overall gain in 2 years = rs . 500 - rs . 400 = rs . 100 his overall gain in 1 year = 100 / 2 = rs . 50 answer : option a"
Answer: a
Problem: a chemist mixes one liter of pure water with x liters of a 30 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 30 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 30 - 15 ) / ( 15 - 0 ) = 1 / 1 1 / x = 1 / 1 x = 1 answer : d"
Answer: d
Problem: the surface of a cube is 96 sq cm . find its volume ?
Options: a ) 8 cc
b ) 9 cc
c ) 2 cc
d ) 4 cc
e ) 64 cc
Rationale: 6 a 2 = 96 = 6 * 16 a = 4 = > a 3 = 64 cc answer : e
Answer: e
Problem: the largest four digit number which is a perfect cube , is :
Options: a ) 7000 , b ) 8000 , c ) 9261 , d ) 9999 , e ) none of these
Rationale: "explanation : 21 * 21 * 21 = 9261 option c"
Answer: c
Problem: the angle between two hands at 3.45 is
Options: a ) 110 degree , b ) 115 degree , c ) 112 1 / 2 degree , d ) 117 degree , e ) 157 1 / 2 degree
Rationale: "theta degree = 11 / 2 m - 30 h = 11 / 2 ( 45 ) - 30 ( 3 ) = 247.5 - 90 = 157.5 or 157 1 / 2 degree answer : e"
Answer: e
Problem: pipe a and pipe b fill water into a tank of capacity 2000 litres , at a rate of 200 l / min and 50 l / min . pipe c drains at a rate of 25 l / min . pipe a is open for 1 min and closed , then pipe b is open for 2 min and closed . further the pipe c is opened and drained for another 2 min . this process is repeated until the tank is filled . how long will it take to fill the tank ?
Options: a ) 14 min , b ) 18 min , c ) 25 min , d ) 32 min , e ) 40 min
Rationale: "tank capacity : 2000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 2000 l tank : 2000 / 250 = 8 time taken to fill : 8 * total time = 8 * 5 = 40 ( option e )"
Answer: e
Problem: a wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 52.9 % , b ) 55.4 % , c ) 58.3 % , d ) 61.7 % , e ) 64.5 %
Rationale: "there are a total of 9 * 9 * 9 = 729 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 7 * 7 * 7 = 343 cubes . the number of cubes with at least one side painted red is 729 - 343 = 386 cubes the probability that a cube has at least one side painted red is 386 / 729 which is about 52.9 % the answer is a ."
Answer: a
Problem: the sector of a circle has radius of 21 cm and central angle 110 o . find its perimeter ?
Options: a ) 91.5 , b ) 91.4 , c ) 91.7 , d ) 82.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 110 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 40.3 + 42 = 82.3 cm answer : d"
Answer: d
Problem: how many positive integers less than 25 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 2 odd multiples of 5 : { 5 , 15 } 10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 2 + 10 - 1 = 20 . answer : e ."
Answer: e
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.27 , c ) 6.23 , d ) 6.29 , e ) 6.39
Rationale: "required run rate = [ 282 - ( 3.2 * 10 ) ] / 40 = 250 / 40 = 6.25 ' answer : a"
Answer: a
Problem: company m produces two kinds of stereos : basic and deluxe . of the stereos produced by company m last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 5 / 22 , b ) 4 / 22 , c ) 3 / 22 , d ) 9 / 22 , e ) 7 / 22
Rationale: # of basic stereos was 3 / 4 of total and # of deluxe stereos was 1 / 4 of total , let ' s assume total = 16 , then basic = 12 and deluxe = 4 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 12 * 1 = 12 and total time for deluxe would be 4 * 7 / 5 = 28 / 5 - - > total time for both of them would be 12 + 28 / 5 = 88 / 5 - - > deluxe / total = 28 / 5 / 88 / 5 = 28 / 88 = 7 / 22 e
Answer: e
Problem: rectangular tile each of size 80 cm by 40 cm must be laid horizontally on a rectangular floor of size 130 cm by 230 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 6 , b ) 2 , c ) 8 , d ) 9 , e ) 7
Rationale: "area of tile = 80 * 40 = 3200 area of floor = 130 * 230 = 29900 no of tiles = 29900 / 3200 = 9.34 so , the no of tile = 9 answer : d"
Answer: d
Problem: find large number from below question the difference of two numbers is 1395 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1671
Rationale: "let the smaller number be x . then larger number = ( x + 1395 ) . x + 1395 = 6 x + 15 5 x = 1380 x = 276 large number = 276 + 1395 = 1671 e"
Answer: e
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1740 ?
Options: a ) rs . 1000 , b ) rs . 1550 , c ) rs . 1510 , d ) rs . 1500 , e ) none of these
Rationale: "explanation : 1740 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1500 answer : option d"
Answer: d
Problem: the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "average = 50 , sum of temperatures = 50 * 5 = 250 as the min temperature is 45 , max would be 250 - 4 * 45 = 70 - - > the range = 70 ( max ) - 45 ( min ) = 25 answer : b ."
Answer: b
Problem: a grocer has a sale of rs . 800 , rs . 900 , rs . 1000 , rs . 700 and rs . 800 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 850 ?
Options: a ) s . 440 , b ) s . 850 , c ) s . 450 , d ) s . 900 , e ) s . 950
Rationale: "total sale for 5 months = rs . ( 800 + 900 + 1000 + 700 + 800 ) = rs . 4200 required sale = rs . [ ( 850 x 6 ) - 4200 ] = rs . ( 5100 - 4200 ) = rs . 900 . option d"
Answer: d
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 767 , e ) 408
Rationale: "1 h - - - - - 2 ? - - - - - - 60 12 h rs = 16 + 18 = 34 t = 12 d = 34 * 12 = 408 answer : e"
Answer: e
Problem: a can finish a piece of work in 5 days . b can do it in 16 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "2 / 4 + ( 2 + x ) / 16 = 1 = > x = 6 days answer : c"
Answer: c
Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 54 ^ 100 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "54 = 3 ^ 3 * 2 . 54 ^ 100 = 3 ^ 300 * 2 ^ 100 the answer is c ."
Answer: c
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 5 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 36 / 625 , b ) 48 / 625 , c ) 64 / 625 , d ) 98 / 625 , e ) 128 / 625
Rationale: "one case is : 1 / 5 * 1 / 5 * 4 / 5 * 4 / 5 * 4 / 5 = 64 / 3125 the total number of possible cases is 5 c 2 = 10 p ( event a occurs exactly twice ) = 10 * ( 64 / 3125 ) = 128 / 625 the answer is e ."
Answer: e
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . if it takes 48 days for the patch to cover the entire lake , how long would it take for the patch to cover half of the lake ?
Options: a ) 45 , b ) 56 , c ) 47 , d ) 57 , e ) 49
Rationale: "explanation : with all the talk of doubling and halves , your brain jumps to the conclusion that to solve the problem of when the lily patch covers half the lake , all you have to do is divide the number of days it took to fill the lake ( 48 ) in half . it ' s understandable but wrong . the problem says that the patch doubles in size every day , which means that on any day , the lily patch was half the size the day before . so if the patch reaches the entire size of the lake on the 48 th day , it means the lily pad was half the size of the lake on day 47 . correct answer is c ) 47"
Answer: c
Problem: the least common multiple of positive integer d and 3 - digit integer n is 690 . if n is not divisible by 3 and d is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and d is 690 = 2 * 3 * 5 * 23 . d is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to d . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Problem: in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 172,700 , b ) 172,800 , c ) 172,900 , d ) 173,000 , e ) 173,100
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 3 = 4 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 4 = 172,800 . hence b ."
Answer: b
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 54 sec . the length of each train is ?
Options: a ) 50 , b ) 26 , c ) 75 , d ) 28 , e ) 21
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 54 = 25 / 9 = > x = 75 . answer : c"
Answer: c
Problem: a number is doubled and 8 is added . if the resultant is trebled , it becomes 84 . what is that number ?
Options: a ) 10 , b ) 6 , c ) 8 , d ) none of these , e ) can not be determined
Rationale: "solution let the number be x . then , 3 ( 2 x + 8 ) ‹ = › 84 ‹ = › 2 x + 8 = 28 ‹ = › 2 x = 20 x = 10 . answer a"
Answer: a
Problem: a train 100 m in length crosses a telegraph post in 12 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 30 kmph , c ) 54 kmph , d ) 18 kmph , e ) 19 kmph
Rationale: "s = 100 / 12 * 18 / 5 = 30 kmph answer : b"
Answer: b
Problem: by selling a book for 250 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 208 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 250 × 100 / 120 = 208 option ' b '"
Answer: b
Problem: 50 liters of a mixture contains milk and water in the ratio 3 : 2 . if 5 liters of this mixture be replaced by 5 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 6 : 5 , b ) 6 : 2 , c ) 6 : 4 , d ) 7 : 4 , e ) 7 : 2
Rationale: "quantity of milk in 50 liters if mix = 50 * 3 / 5 = 30 liters quantity of milk in 55 liters of new mix = 30 + 5 = 35 liters quantity of water in it = 55 - 35 = 20 liters ratio of milk and water in new mix = 35 : 20 = 7 : 4 answer is d"
Answer: d
Problem: the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 48 , what is the perimeter of the garden in feet ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "let x be the length of one side of the square garden . x ^ 2 = 8 x + 48 x ^ 2 - 8 x - 48 = 0 ( x - 12 ) ( x + 4 ) = 0 x = 12 , - 4 p = 4 ( 12 ) = 48 the answer is d ."
Answer: d
Problem: the average of 10 numbers is calculated as 5 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "10 * 5 + 36 – 26 = 60 / 10 = 6 answer : e"
Answer: e
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 14 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 9 , b ) 14 , c ) 21 , d ) 28 , e ) 42
Rationale: 3.456789 ^ 14 has 6 * 14 = 84 decimal places . 10 ^ 56 moves the decimal place to the right 56 places . ( 10 ^ 4 * 3.456789 ) ^ 14 has 84 - 56 = 28 digits after the decimal point . the answer is d .
Answer: d
Problem: find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 5 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 5 = 2 / 1 = 4 : 5 answer is d"
Answer: d
Problem: how many digits are required to write numbers between 1 to 100 .
Options: a ) 196 , b ) 158 , c ) 192 , d ) 200 , e ) none
Rationale: "explanation : single digits are from 1 to 9 = 9 digits doubt digits are from 10 to 99 = 90 x 2 = 180 digits 100 needs 3 digits . total 192 digits correct option : c"
Answer: c
Problem: a , b , c can complete a piece of work in 16 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 48 / 15 , c ) 7 / 9 , d ) 10 , e ) 24 / 7
Rationale: a + b + c 1 day work = 1 / 16 + 1 / 6 + 1 / 12 = 15 / 48 a , b , c together will complete the job in 48 / 15 days answer is b
Answer: b
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 100,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 100 ( 100,000 / 1,000 = 100 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 100 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 7 = 128 , i . e . the population has to double 7 times . since it takes the population 2 minutes to double once it takes 7 * 2 minutes = 14 minutes to double 7 times . thus , solution c = 14 is correct ."
Answer: c
Problem: certain stocks in january were 10 % less than they were in february and 20 % greater than they were in march . what was the percentage decrease in the stocks from february to march ?
Options: a ) 5 % , b ) 10 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: let j , f , m be the values of the stock in jan , feb and march . thus , per the question , j = 0.9 f = 1.2 m - - - - > m = 0.75 f thus the % decrease from f to m = ( f - m ) / ( f ) * 100 = ( f - 0.75 f ) / f * 100 = 0.25 * 100 = 25 % , d is the correct answer .
Answer: d
Problem: to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 15 hours a day ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 20 , e ) 19.2
Rationale: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 15 = 300 therefore number of days = 5760 / 300 = 19.2 days ans = e"
Answer: e
Problem: a scuba diver descends at a rate of 80 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 4000 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 70 minutes , b ) 72 minutes , c ) 50 minutes , d ) 66 minutes , e ) 67 minutes
Rationale: "time taken to reach = 4000 / 80 = 50 minutes answer : c"
Answer: c
Problem: the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 784 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 784 x ^ 2 = 196 x = 14 length = 4 * 14 = 56 difference = 56 - 14 = 42 c is the answer"
Answer: c
Problem: two water pumps , working simultaneously at their respective constant rates , took exactly 5 hours to fill a certain swimming pool . if the constant rate of one pump was 1.5 times the constant rate of the other , how many hours would it have taken the slower pump to fill the pool if it had worked alone at its constant rate ?
Options: a ) 8.5 , b ) 10.5 , c ) 12.5 , d ) 14.5 , e ) 16.5
Rationale: let x be the rate of the slower pump . then 1.5 x is the rate of the faster pump . both pumps together can fill 1 / 5 of the pool each hour . 2.5 x = 1 / 5 x = 1 / 12.5 = 2 / 25 the slower pump could fill the pool in 25 / 2 = 12.5 hours . the answer is c .
Answer: c
Problem: a certain box has 8 cards and each card has one of the integers from 1 to 8 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 8 cards ?
Options: a ) 1 / 8 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 28
Rationale: "the average of the numbers is 4.5 the total number of ways to choose 2 cards from 8 cards is 8 c 2 = 28 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } the probability is 2 / 28 = 1 / 14 the answer is c ."
Answer: c
Problem: a positive number x is multiplied by 4 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: sq rt ( 4 x / 3 ) = x = > 4 x / 3 = x ^ 2 = > x = 4 / 3 ans - c
Answer: c
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 100 total = 100 + 100 = 200 answer ( d )"
Answer: d
Problem: a 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 270 / 9 = 500 / 9 x = 230 ans is 230 m answer : c"
Answer: c
Problem: car z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 375.2 , c ) 400 , d ) 408 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 51 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40.8 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40.8 miles / gallon * 10 gallons = 408 miles . answer d ."
Answer: d
Problem: at what rate percent on simple interest will rs . 1800 amount to rs . 2000 in 5 years ?
Options: a ) 4 % , b ) 3 6 / 7 % , c ) 2 6 / 7 % , d ) 3.47 % , e ) 6 %
Rationale: "explanation : 250 = ( 1800 x 5 xr ) / 100 r = 3.47 % answer : option d"
Answer: d
Problem: what is 0.02 percent of 12,356 ?
Options: a ) 0.247 , b ) 2.47 , c ) 24.7 , d ) 0.0247 , e ) 0.00247
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.02 ( 1 / 100 ) 12,356 . the answer is 2.47 . hence , the correct answer is b .
Answer: b
Problem: of 45 applicants for a job , 21 had at least 4 years ' experience , 27 had degrees , and 5 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 3 , e ) 2
Rationale: "45 - 5 = 40 40 - 21 - 27 = - 8 then 8 are in the intersection between 4 years experience and degree . answer : b"
Answer: b
Problem: 12,21 , 48,87 , __
Options: a ) 176 , b ) 186 , c ) 184 , d ) 174 , e ) 164
Rationale: "21 = 12 * 2 - 3 48 = 21 * 2 + 6 87 = 48 * 2 - 9 so next number is 87 * 2 + 12 = 186 answer : b"
Answer: b
Problem: a man rows his boat 90 km downstream and 5 ` km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 7 kmph , b ) 5 kmph , c ) 2 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 51 / ( 3 ) = 17 kmph the speed of the stream = ( 30 - 17 ) / 2 = 7 kmph answer : a"
Answer: a
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 45 % on his income , while mindy pays a rate of only 25 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 29 % , b ) 31 % , c ) 33 % , d ) 35 % , e ) 37 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 1.0 x = 1.45 x 1.45 x / 5 x = 0.29 the answer is a ."
Answer: a
Problem: reema took a loan of rs 1100 with simple interest for as many years as the rate of interest . if she paid rs . 704 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 1100 ∗ r ∗ r / 100 = 704 = > r 2 = 64 = > r = 8 % option d"
Answer: d
Problem: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 a for the digits ?
Options: a ) 30 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 number of possibilities = 3 * 3 * 3 = 27 . then , just add up the number of 1 digits numbers = 3 , so total is 27 + 3 = 30 . answer : a"
Answer: a
Problem: in a company , 52 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 65 % , b ) 70 % , c ) 75 % , d ) 80 % , e ) 85 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 48 % of all employees are women , so non - union women are 48 % - 18 % = 30 % 40 % of all employees are non - union . the percent of non - union employees who are women is 30 % / 40 % = 75 % the answer is c ."
Answer: c
Problem: how long does a lorry 200 m long traveling at 80 kmph takes to cross a bridge of 200 m in length ?
Options: a ) 15 , b ) 17 , c ) 15 , d ) 16 , e ) 18
Rationale: d = 200 + 200 = 400 m s = 80 * 5 / 18 = 200 / 9 t = 400 * 9 / 200 = 18 sec answer : e
Answer: e
Problem: pradeep has to obtain 20 % of the total marks to pass . he got 160 marks and failed by 25 marks . the maximum marks are
Options: a ) 1925 , b ) 600 , c ) 925 , d ) 1325 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 20 % of x = 160 + 25 = > 20 / 100 x = 185 x = ( 18500 / 20 ) x = 925 . answer : c"
Answer: c
Problem: 1480 men have provisions for 14 days . if 460 more men join them , for how many days will the provisions last now ?
Options: a ) 9.9 , b ) 8.0 , c ) 12.5 , d ) 12.2 , e ) 12.1
Rationale: "1480 * 13 = 1940 * x x = 9.9 answer : a"
Answer: a
Problem: what is the difference between the c . i . on rs . 5000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) rs . 2.04 , b ) rs . 2.09 , c ) rs . 2.06 , d ) rs . 2.22 , e ) rs . 2.08
Rationale: "c . i . when interest is compounded yearly = [ 5000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 5000 * 26 / 25 * 51 / 50 = rs . 5304 c . i . when interest is compounded half - yearly = [ 5000 * ( 1 + 2 / 100 ) 2 ] = ( 5000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 5306.04 difference = ( 5306.04 - 5304 ) = rs . 2.04 . answer : a"
Answer: a
Problem: the sum of three consecutive even numbers multiples of 3 is 72 . what is the largest number ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) none
Rationale: "solution let the number be x and x + 2 . then , ( x + 2 ) 2 - x 2 = 84 ⇔ 4 x + 4 = 84 ⇔ 4 x = 80 ⇔ x = 20 . ∴ required sum = x + ( x + 2 ) = 2 x + 2 = 42 . answer c"
Answer: c
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back , how far is the place ?
Options: a ) 144 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 30 2 x + 3 x = 720 x = 144 km answer is a"
Answer: a
Problem: mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate q in miles per hour for the entire trip ?
Options: a ) q = 26.7 , b ) q = 30.0 , c ) q = 40.0 , d ) q = 53.3 , e ) q = 60.0
Rationale: "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ."
Answer: c
Problem: 6 friends went to a hotel and decided to pay the bill amount equally . but 5 of them could pay rs . 100 each as a result 6 th has to pay rs . 100 extra than his share . find the amount paid by him .
Options: a ) 156 , b ) 220 , c ) 130 , d ) 240 , e ) none
Rationale: "explanation : average amount paid by 5 persons = rs . 100 increase in average due to rs . 120 paid extra by the 6 th men = rs . 100 / 5 = rs . 20 therefore , average expenditure of 6 friends = rs . 100 + rs . 20 = rs . 120 therefore , amount paid by the 6 th men = rs . 120 + rs . 100 = rs . 220 correct option : b"
Answer: b
Problem: the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is :
Options: a ) 12 , b ) 24 , c ) 84 , d ) 48 , e ) 42
Rationale: "let the numbers be x and 4 x . then , x * 4 x = 84 * 21 x 2 = ( 84 * 21 ) / 4 = x = 21 . hence , larger number = 4 x = 84 . answer : c"
Answer: c
Problem: 15.06 * 0.00000001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 1.506 e - 07 , e ) none of these
Rationale: "explanation : clearly after decimal 10 digits should be there . option d"
Answer: d
Problem: evaluate 28 % of 450 + 45 % of 240
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 234
Rationale: "explanation : = ( 28 / 100 ) * 450 + ( 45 / 100 ) * 240 = 126 + 108 = 234 answer : option e"
Answer: e
Problem: a straight line in the xy - plane has y - intercept of 12 and a slope of 4 / 7 . given the x - coordinate of the point is 49 , find it ' s y - coordinate .
Options: a ) 27 , b ) 16 , c ) 29.7 , d ) 28 , e ) 18
Rationale: "eq of line = y = mx + c m = 4 / 7 c = 12 x = 49 substitute the givens : y = ( 4 / 7 * 49 ) + 12 , y = 16 + 12 = 28 correct option is d"
Answer: d
Problem: if 50 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 120 , b ) 100 , c ) 75 , d ) 90 , e ) none of these
Rationale: let the number be x . then 50 % of 3 / 5 of x = 36 50 / 100 * 3 / 5 * x = 36 x = ( 36 * 10 / 3 ) = 120 required number = 120 . correct option : a
Answer: a
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability t that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) t = 5 / 6 . answer : c"
Answer: c
Problem: the manufacturing cost of a shoe is rs . 180 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) rs 222 , b ) rs 216 , c ) rs 220 , d ) rs 210 , e ) rs 217
Rationale: explanation : total cost of a watch = 180 + ( 500 / 100 ) = 185 . gain = 20 % = > sp = 1.2 cp = 1.2 x 185 = 222 answer : a
Answer: a
Problem: a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 20 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 64 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 80 then it is marked down by 20 % = 80 - 16 = 64 . hence it is 64 % od the original price . hence answer is d ."
Answer: d
Problem: in a factory , there are 30 % technicians and 70 % non - technicians . if the 30 % of the technicians and 70 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 22 % , e ) 48 %
Rationale: "total = 100 t = 30 nt = 70 30 * ( 70 / 100 ) = 21 70 * ( 30 / 100 ) = 21 21 + 21 = 42 = > 100 - 42 = 58 % answer : e"
Answer: e
Problem: to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 14 hours a day ?
Options: a ) 24 , b ) 23 , c ) 24 , d ) 20.57 , e ) 22
Rationale: man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 14 = 280 therefore number of days = 5760 / 280 = 20.57 days ans = d
Answer: d
Problem: if a * b = 2 a – 3 b + ab , then 3 * 5 + 5 * 3 is equal to :
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 29
Rationale: "solution 3 × 5 + 5 × 3 = ( 2 × 3 - 3 × 5 + 3 × 5 ) + 2 ( 2 × 5 - 3 × 3 + 5 × 3 ) = ( 6 + 10 - 9 + 15 ) = 22 . answer a"
Answer: a
Problem: average temperature of first 4 days of a week is 6 ° c and that of the last 4 days is 40.3 ° c . if the average temperature of the week be 39.1 ° c , the temperature on 4 th day is ?
Options: a ) 36.7 ° c , b ) 38.6 ° c , c ) 39.8 ° c , d ) 41.9 ° c , e ) 51.9 ° c
Rationale: let temperature on 4 th day be x ° c therefore , 4 x 38.6 + 4 x 40.3 - x = 7 x 39.1 = > x = 41.9 therefore , temperature on 4 th day = 41.9 ° c . answer : d
Answer: d
Problem: what annual installment will discharge a debt of rs . 4600 due in 4 years at 10 % simple interest ?
Options: a ) 1000 , b ) 1030 , c ) 1100 , d ) none of these , e ) 1101
Rationale: "let the 1 st installment = 100 / - it is 3 yrs before due iind is 2 yr before due iii 3 rd is 1 yr before due ivth is 0 yrs before due on 1 st installment interest will be paid for 3 yrs 2 nd installment interest will be paid for 2 yrs 3 rd installment interest will be paid for 1 yr 4 th installment interest will be paid for 0 yr interest = p [ ( 100 ( 3 + 2 + 1 + 0 ) x 10 ) / 100 ] = 60 / - total loan discharged = 4 * 100 + 60 / - = 460 / - now installment of 100 / - loan discharged = 460 / - loan discharged 4600 / - ? installment = 1000 / - answer : a ."
Answer: a
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 21,700 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 3000 = $ 21700 correct option : a
Answer: a
Problem: there are 18 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 1370 , b ) 1530 , c ) 1790 , d ) 1950 , e ) 2110
Rationale: "the number of ways to choose two teams is 18 c 2 = 18 * 17 / 2 = 153 the total number of games in the season is 10 * 153 = 1530 . the answer is b ."
Answer: b
Problem: how many multiples of 9 are there between 1 and 50 , exclusive ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 3
Rationale: "5 multiples of 9 between 1 and 50 exclusive . from 9 * 1 upto 9 * 5 , ( 1 , 2,3 , 4,5 ) . hence , 5 multiples ! correct option is a"
Answer: a
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 7 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 840 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 7 / 100 x 12000 ) = rs . 840 . answer b
Answer: b
Problem: the distance between delhi and mathura is 130 kms . a starts from delhi with a speed of 25 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 30 kmph at 9 p . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 77 , c ) 16 , d ) 10 , e ) 98
Rationale: "d = 130 – 25 = 105 rs = 30 + 25 = 55 t = 105 / 55 = 2 hours 8 a . m . + 2 = 11 a . m . . answer : a"
Answer: a
Problem: how is 1 / 2 % expressed as a decimal fraction ?
Options: a ) 0.5 , b ) 0.05 , c ) 0.005 , d ) 0.0005 , e ) 5
Rationale: as 1 / 2 = 0.5 and its percent value will be 0.5 / 100 = 0.005 answer : c
Answer: c
Problem: a hostel had provisions for 250 men for 28 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 35 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: a hostel had provisions for 250 men for 28 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 28 250 × 28 = 200 x 5 × 28 = 4 x x = 5 × 7 = 35 answer a
Answer: a
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 20 percent of b , what is the value of m / x ?
Options: a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2
Rationale: "x equals a increased by 25 percent of a = > x = a + 25 % a = 1.25 a m equals b decreased by 20 percent of b = > m = b - 20 % b = 0.8 b m / x = 0.8 b / 1.25 a putting the value of b / a = 5 / 4 we get m / x = 4 / 5 answer : c"
Answer: c
Problem: if rs . 480 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 570 , e ) s . 585
Rationale: "80 = ( 480 * 4 * r ) / 100 r = 3.125 % i = ( 480 * 6 * 3.125 ) / 100 = 90 480 + 90 = 570 answer : d"
Answer: d
Problem: the perimeter of a square is 48 m . find the area of the square .
Options: a ) 161 m â ² .
b ) 144 m â ² .
c ) 166 m â ² .
d ) 169 m â ² .
e ) 273 m â ² .
Rationale: perimeter of square = 48 m but perimeter of square = 4 ã — side therefore , 4 ã — side = 48 m therefore , side = 48 / 4 m = 12 m now , the area of the square = ( side ã — side ) therefore , area of the square = 12 ã — 12 m â ² = 144 m â ² . answer : option b
Answer: b
Problem: rectangular tile each of size 25 cm by 16 cm must be laid horizontally on a rectangular floor of size 180 cm by 120 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 52 , b ) 54 , c ) 55 , d ) 65 , e ) 48
Rationale: "area of tile = 25 * 16 = 400 area of floor = 180 * 120 = 21600 no of tiles = 21600 / 400 = 54 so , the no of tile = 54 answer : b"
Answer: b
Problem: a house wife saved $ 2.75 in buying an item on sale . if she spent $ 20 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 20 + 2.75 = $ 22.75 saving = 2.75 / 22.75 * 100 = 12 % approximately answer is e"
Answer: e
Problem: the ratio of buses to cars on river road is 1 to 3 . if there are 40 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 60 , b ) 75 , c ) 85 , d ) 95 , e ) 105
Rationale: "b / c = 1 / 3 c - b = 40 . . . . . . . . . > b = c - 40 ( c - 40 ) / c = 1 / 3 testing answers . clearly eliminate bcde put c = 60 . . . . . . . . . > ( 60 - 40 ) / 60 = 20 / 60 = 1 / 3 answer : a"
Answer: a
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 25 . the largest number is :
Options: a ) 28 , b ) 30 , c ) 36 , d ) 42 , e ) 45
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 25 15 x = 75 x = 5 largest number = 6 x = 30 . answer b"
Answer: b
Problem: in a garden , 26 trees are planted at equal distances along a yard 600 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 12 , d ) 24 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 600 / 25 = 24 i . e . , distance between two consecutive trees = 24 answer is d ."
Answer: d
Problem: on a wedding catering service , an experienced chef can prepare a service for a wedding in 6 hours while an novice chef would finish the preparations in 7 hours . if the catering service employs the same number of novice and experienced chefs , then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: experienced chefs work = 1 wedding / 6 hours novice chefs work = 1 wedding / 7 hours since we do n ' t know the number of experienced or novice chefs but know that there is an equal number each , let the number of chefs for each group equalx 1 hr and 36 mins = 8 / 5 an hour x / 6 + x / 7 = 1 wedding / ( 8 / 5 ) x / 6 + x / 7 = 5 / 8 x = 2 so there are 2 novice chefs and 2 experienced chefs . in total there are 4 . the answer is c .
Answer: c
Problem: there is a 20 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ?
Options: a ) 40 % , b ) 48 % , c ) 56 % , d ) 64 % , e ) 72 %
Rationale: "p ( china and not malaysia ) = 0.2 * 0.4 = 0.08 p ( malaysia and not china ) = 0.6 * 0.8 = 0.48 total probability = 0.08 + 0.48 = 0.56 = 56 % the answer is c ."
Answer: c
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quality of alcohol in the given mixture .
Options: a ) 10 , b ) 8 , c ) 7.5 , d ) 6 , e ) 3.5
Rationale: "let the quantity of alcohol and water be 4 x and 3 x 4 x / ( 3 x + 5 ) = 4 / 5 20 x = 4 ( 3 x + 5 ) x = 2.5 quantity of alcohol = 4 * 2.5 = 10 liters . answer is a"
Answer: a
Problem: a 150 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 230 meter , d ) 350 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 150 / 9 = 500 / 9 = > x + 150 = 500 = > x = 350 so the length of the train is 350 meters option d"
Answer: d
Problem: the average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ?
Options: a ) 30.5 , b ) 26 , c ) 30 , d ) 18 , e ) 11
Rationale: "explanation : 18 + 22 + 7 * 3 = 61 / 2 = 30.5 answer : a"
Answer: a