regisss/math_qa huggingface dataset:
Problem: what is the value of â ˆ š 36 % ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 60 % , e ) 40 %
Rationale: "explanation : br > â ˆ š 16 % = â ˆ š 36 / â ˆ š 100 = 6 / 10 = 60 / 100 = 60 % correct answer is d ) 60 %"
Answer: d
Problem: there are two concentric circles with radii 8 and 4 . if the radius of the outer circle is increased by 25 % and the radius of the inner circle decreased by 25 % , by what percent does the area between the circles increase ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 64 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 48 pi . when the big circle ' s radius increases , the new area is 100 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 91 pi . the ratio of a 2 / a 1 is 91 / 48 = 1.9 which is an increase of 90 % . the answer is d ."
Answer: d
Problem: alice can bake a pie in 5 minutes . bob can bake a pie in 6 minutes . compute how many more pies alice can bake than bob in 60 minutes .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: alice can bake 60 / 5 = 12 pies in 60 minutes . bob can bake 60 / 6 = 10 pies in 60 minutes . alice can therefore bake 12 - 10 = 2 more pies than bob . correct answer b
Answer: b
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6100 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6470 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6100 * 6 ) – 30,130 ] = rs . ( 36600 – 30,130 ) = rs . 6470 answer c"
Answer: c
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 6 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 17 / 216 , b ) 19 / 216 , c ) 23 / 216 , d ) 25 / 216 , e ) 35 / 216
Rationale: "one case is : 1 / 6 * 1 / 6 * 5 / 6 * 5 / 6 = 25 / 1296 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 25 / 1296 ) = 25 / 216 the answer is d ."
Answer: d
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , c receives :
Options: a ) s . 14,000 , b ) s . 14,200 , c ) s . 4,400 , d ) s . 8,400 , e ) s . 4,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 x 12 / 50 ) = rs . 8,400 . d"
Answer: d
Problem: a building contractor employs 20 male , 15 female and 5 child workers . to a male worker he pays rs . 35 per day , to a female worker rs . 20 per day and a child worker rs . 8 per day . the average wage per day paid by the contractor is ?
Options: a ) 22 , b ) 23 , c ) 28 , d ) 29 , e ) 26
Rationale: "20 15 5 35 20 8 500 + 300 + 40 = 1040 / 40 = 26 answer : e"
Answer: e
Problem: ( ( 1 ^ 5 m ) / ( 5 ^ 5 m ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ?
Options: a ) 7 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: ( ( 1 ^ 5 m ) / ( 5 ^ 5 m ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ 5 m ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ 5 m = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ 5 m ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 7 answer a
Answer: a
Problem: eggs are sold in packages of 6 or 11 only . if doris bought 79 eggs exactly , what could be the number of large packs doris bought ?
Options: a ) 6 . , b ) 2 . , c ) 3 . , d ) 5 . , e ) 4 .
Rationale: no strategy involved . simple question demanding fast calculation . 11 x 5 = 55 = > 79 - 55 = 24 = > 24 / 6 is an integer ans d . 5 . good luck
Answer: d
Problem: how long does a train 200 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 82.1 sec , b ) 12.1 sec , c ) 16.1 sec , d ) 13.1 sec , e ) 16.6 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 200 + 132 = 332 m . required time = 332 / 20 = 16.6 sec . answer : e"
Answer: e
Problem: two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 125 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 6 , b ) 14 , c ) 16 , d ) 20 , e ) 18
Rationale: "sol . speed of the first train = [ 150 / 10 ] m / sec = 15 m / sec . speed of the second train = [ 150 / 15 ] m / sec = 10 m / sec . relative speed = ( 15 + 10 ) = m / sec = 25 m / sec . ∴ required time = ( 125 + 125 ) / 25 secc = 6 sec . answer a"
Answer: a
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 6 , 0 ) , ( 0 , - 3.5 ) , ( - 6 , 0 ) ?
Options: a ) 42 , b ) 56 , c ) 88 , d ) 112 , e ) 116
Rationale: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 6 + 6 = 12 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 12 * 7 = 42 a is the answer"
Answer: a
Problem: the perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 30
b ) 31
c ) 32
d ) 34
e ) 35
Rationale: area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 28 / 2 = 35 cm 2 answer : option e
Answer: e
Problem: find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 year ?
Options: a ) 306.06 , b ) 306.02 , c ) 306.04 , d ) 306.09 , e ) 306.12
Rationale: "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"
Answer: c
Problem: micheal and adam can do together a piece of work in 20 days . after they have worked together for 14 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 50 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 14 = 7 / 10 left work = 1 - 7 / 10 = 3 / 10 adam completes 3 / 10 work in 10 day so he took 10 * 10 / 3 = 100 / 3 days to complete the left work alone . thus the rate of adam is 3 / 100 rate of micheal = 1 / 20 - 3 / 100 = 1 / 50 thus micheal takes 50 days to complete the whole work . ans . a"
Answer: a
Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 3 or 17 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
Rationale: "number of multiples of 3 from 1 through 30 = 30 / 3 = 10 number of multiples of 17 from 1 through 30 = 30 / 17 = 1 number of multiples of 3 and 17 both from 1 through 30 = number of multiples of 17 * 3 ( = 51 ) = 0 total favourable cases = 10 + 1 - 0 = 11 probability = 11 / 30 answer : option e"
Answer: e
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 35 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 416 , b ) s . 480 , c ) s . 429 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 35 % = 35 % of 640 = rs . 224 sp = cp - loss = 640 - 224 = rs . 416 answer : a"
Answer: a
Problem: a present value of a machine is $ 900 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 729
Rationale: "p = $ 900 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 900 * 9 / 10 * 9 / 10 = $ 729 answer is e"
Answer: e
Problem: a motorist knows 6 different routes from bristol to birmingham . from birmingham to sheffield he knows 3 different routes and from sheffield to carlisle he knows two different routes . how many routes does he know from bristol to carlisle ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 24 , e ) 36
Rationale: explanation : total number of routes from bristol to carlisle = ( 6 x 3 x 2 ) = 36 . answer : e
Answer: e
Problem: the grade point average of one third of the classroom is 54 ; the grade point average of the rest is 45 . what is the grade point average of the whole class ?
Options: a ) 52 , b ) 54 , c ) 48 , d ) 58 , e ) 60
Rationale: "let n = total students in class total points for 1 / 3 class = 54 n / 3 = 18 n total points for 2 / 3 class = 45 * 2 n / 3 = 30 n total points for whole class = 18 n + 30 n = 48 n 48 n total class points / n total students = 48 grade point average for total class answer : c"
Answer: c
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 72 km / hr ?
Options: a ) 2.5 , b ) 5 , c ) 2.4 , d ) 2.8 , e ) 2.1
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 100 / 20 = 5 sec . answer : b"
Answer: b
Problem: if x is an integer that has exactly 3 positive divisors ( these include 1 and x ) , how many positive divisors does x ^ 3 have ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: since factors of ' 4 ' are { 1 , 2,4 } 4 ^ 3 = 64 number of factors / divisors of 64 = 2 ^ 6 we know that when a number is expressed as a product of the prime factors as below : n = a ^ x * b ^ y * c ^ z then no . of divisors = ( x + 1 ) * ( y + 1 ) * ( z + 1 ) then here ( 6 + 1 ) = 7 answer : d
Answer: d
Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is -
Options: a ) 1 / 39 , b ) 1 / 36 , c ) 1 / 32 , d ) 1 / 31 , e ) 1 / 30
Rationale: "explanation : it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 and 666 . those are six in number . further the three dice can fall in 6 * 6 * 6 = 216 ways . hence the probability is 6 / 216 = 1 / 36 answer : b"
Answer: b
Problem: how many bricks , each measuring 5 cm x 11 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 2 cm ?
Options: a ) 5600 , b ) 6000 , c ) 2909 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 2 ) / ( 5 x 11 x 6 ) = 2909 . answer : option c"
Answer: c
Problem: a can do a piece of work in 7 days and b can do it in 6 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 8 / 13 , c ) 3 / 13 , d ) 9 / 11 , e ) 10 / 13
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 6 ( a + b ) ’ s one day work = 1 / 7 + 1 / 6 = 13 / 42 = > time = 42 / 13 = 3 3 / 13 days answer : option c"
Answer: c
Problem: 60 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 38400 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none
Rationale: answer ∵ 60 % of p = 23040 ∴ p = ( 23040 x 100 ) / 60 = 38400 correct option : a
Answer: a
Problem: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.25 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 36 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.25 and remainder is 9 so . 25 x y = 9 hence y = 36 ans c"
Answer: c
Problem: what least number should be subtracted from 13605 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 33
Rationale: 13605 ÷ 87 = 156 , remainder = 33 hence 33 is the least number which can be subtracted from 13605 such that the remainder is divisible by 87 answer is e
Answer: e
Problem: 378 × ? = 252
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 / 2 , d ) 2 / 8 , e ) none of these
Rationale: "explanation : 378 × ? = 252 ? = 252 / 378 = 126 / 189 = 14 / 21 = 2 / 3 answer is a"
Answer: a
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 20 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 40 , e ) 80
Rationale: total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 20 = > 20 = x - 20 = > x = 20 + 20 = 40 answer is d .
Answer: d
Problem: liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 20 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 40 mph
Rationale: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 20 where s is the speed and 20 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 20 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 40 mph therefore answer is e"
Answer: e
Problem: rs . 1690 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 780 , d ) s . 540 , e ) s . 549
Rationale: "a + b + c = 1690 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1690 = rs . 780 answer : c"
Answer: c
Problem: if 41 / 88 = 0.46590 , what is the 77 th digit to the right of the decimal point of the fraction ?
Options: a ) 6 , b ) 2 , c ) 5 , d ) 0 , e ) 9
Rationale: "we are not concerned what 41 / 88 means . . we have to look at the decimal . . 0.6590 means 0.465909090 . . . . so leaving girst , second and third digit to the right of decimal , all odd numbered are 0 and all even numbered are 9 . . here 77 is odd , so ans is 0 answer is d"
Answer: d
Problem: a train running at the speed of 100 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: speed = ( 100 * 5 / 18 ) m / sec = ( 250 / 9 ) m / sec length of the train = ( speed x time ) = ( 250 / 9 * 18 ) m = 500 m . answer : c
Answer: c
Problem: there has been successive increases of 15 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 12 % , b ) 15 % , c ) 18 % , d ) 21 % , e ) 24 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.15 * p = x * p y = x / ( 1.1 * 1.15 ) which is about 0.79 x which is a decrease of about 21 % . the answer is d ."
Answer: d
Problem: two numbers are less than a third number by 30 % and 37 % . how much percent is the second number is less than the first ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: let the third number be x first number = 70 % of x = 7 x / 10 ; second number = 63 % of x = 63 x / 100 ; difference = 7 x / 10 - 63 x / 100 = 7 x / 100 ; required percentage = 7 x / 100 * 10 / 7 x * 100 = 10 % answer is a
Answer: a
Problem: there are 300 seniors at morse high school , and 40 % of them have cars . of the remaining grades ( freshmen , sophomores , and juniors ) , only 10 % of them have cars . if 15 % of all the students at morse have cars , how many students are in those other 3 lower grades ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1350 , e ) 1500
Rationale: let the total no of students be n . the no of seniors having cars is 40 % of 300 i . e . 120 . the rest of the students with other three grades who have cars is 10 % of ( n - 300 ) . the total no of students with cars is 15 % of n . thus , 0.15 n = 120 + 0.1 ( n - 300 ) on solving this , we get n = 1800 . hence , the no of students with other three grades is 1800 - 300 , i . e . 1500 ( e ) .
Answer: e
Problem: in an examination , a student scores 6 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 280 marks , the no of questions he attempts correctly is :
Options: a ) a ) 20 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 37
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 6 x – ( 60 – x ) = 280 = > 7 x = 340 = > x = 20 answer : a"
Answer: a
Problem: a box measuring 90 inches long by 45 inches wide by 9 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 50 , d ) 108 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 9 is the biggest number that could divide all three , 90 , 45 and 9 . thus side of cube must be 9 , and total number of cubes = 90 / 9 * 45 / 9 * 9 / 9 = 50 ans c it is ."
Answer: c
Problem: you collect baseball cards . suppose you start out with 11 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 12 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "solution start with 11 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 11 + 1 which is 6 , so you ' re left with 11 - 6 = 5 . peter takes 1 baseball card from you : 5 - 1 = 4 baseball cards . paul triples the number of baseball cards you have : 4 ã — 3 = 12 baseball cards . so you have 12 at the end . correct answer : a"
Answer: a
Problem: a bullet train 130 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 10 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 13 sec , c ) 12 sec , d ) 11 sec , e ) 16 sec
Rationale: "b 13 sec speed of the bullet train relative to man = ( 50 + 10 ) kmph = 60 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 130 m at ( 30 / 3 ) m / sec = ( 130 * 3 / 30 ) sec = 13 sec"
Answer: b
Problem: find the smallest number of five digits exactly divisible by 22 , 33,66 and 44 .
Options: a ) 10101 , b ) 11000 , c ) 10110 , d ) 10111 , e ) 10100
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 22,33 , 66,44 i . e 132 , on dividing 10000 by 132 , we get 32 as remainder . therefore , required number = 10000 + ( 132 â € “ 32 ) = 10100 . answer is e ."
Answer: e
Problem: a man walking at a constant rate of 5 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 25 miles per hour . the woman stops to wait for the man 5 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 25 , e ) 28
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 5 * 25 / 60 = 25 / 12 miles and the man walks the distance mm , which is 5 * 5 / 60 = 5 / 12 mile . the difference of 25 / 12 - 5 / 12 = 1 / 3 miles ( mw ) will be covered by the man in ( 4 / 3 ) / 4 = 1 / 3 of an hour , which is 20 minutes . answer b ."
Answer: b
Problem: the ages of two persons differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,10 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: explanation : let their ages be x and ( x + 20 ) years . 5 ( x - 5 ) = ( x + 20 - 5 ) or 4 x = 40 or x = 10 . their present ages are 30 years and 10 years option d
Answer: d
Problem: p and q are the only two applicants qualified for a short - term research project that pays 300 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 15 , d ) $ 20 , e ) $ 25
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 300 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 300 / 30 = $ 10 p ' s hourly wage is 300 / ( t - 10 ) = $ 15 which is $ 5 per hour more . the answer is a ."
Answer: a
Problem: the average length of the sides of triangle abc is 12 . what is the perimeter of triangle abc ?
Options: a ) 4
b ) 6
c ) 12
d ) 24
e ) 36
Rationale: ( average ) = ( perimeter ) / 3 ; 12 = ( perimeter ) / 3 ; ( perimeter ) = 36 . answer : e .
Answer: e
Problem: a retailer buys 140 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 105 , b ) 155 , c ) 125 , d ) 185 , e ) 285
Rationale: "let the market price of each pen be $ 1 then , cost price of 140 pens = $ 36 selling price of 140 pens = 99 % of $ 140 = $ 138.60 profit % = ( ( 102.60 * 100 ) / 36 ) % = 285 % answer e"
Answer: e
Problem: if 3 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "3 ( log 2 ^ 2 * 5 ^ 2 ) = x 3 log ( 5 * 2 ) ^ 2 = x 3 * 2 log ( 5 * 2 ) = x 6 log 10 = x log 10 base 10 = 1 so 6 * 1 = x x = 6 answer : b"
Answer: b
Problem: two trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 11 , b ) 9 , c ) 13 , d ) 14 , e ) 12.8
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 18 = 6.7 m / sec . relative speed = 12 + 6.7 = 18.7 m / sec . required time = ( 120 + 120 ) / 18.7 = 12.8 sec . answer : option e"
Answer: e
Problem: if one - third of one fourth of a number is 15 , then 3 - tenth of that number is :
Options: a ) 35 , b ) 25 , c ) 45 , d ) 54 , e ) 52
Rationale: let the number be x . then , 1 / 3 of 1 / 4 of x = 15 x = 15 * 12 = 180 so , required number = ( 3 / 10 * 180 ) = 54 . answer : d
Answer: d
Problem: r is the set of positive even integers less than 201 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 201 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , 36 , 64 , 100 , 144 , and 196 are even integers ( less than 201 ) that are in both sets . solution : seven answer : e"
Answer: e
Problem: on dividing a number by 7 , we get 3 as quotient and 0 as remainder . on dividing the same number by 3 , what will be the remainder ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 0 , e ) 4
Rationale: "number = 7 * 3 + 0 = 21 3 ) 21 ( 7 21 - - - - - - - - 0 required number = 0 . answer : d"
Answer: d
Problem: the unit digit in the product ( 722 * 774 * 889 * 223 ) is :
Options: a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 2 * 4 * 9 * 3 ) = 6 answer : c"
Answer: c
Problem: a and b invests rs . 3000 and rs . 7000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 14 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 7 * 12 ) 54 : 84 = > 9 : 14 . answer : c"
Answer: c
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 23 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64
b ) 72
c ) 86
d ) 98
e ) 102
Rationale: use the options . the options which after getting added to 23 shows a cube of a number could be right . here 64 + 23 = 87 72 + 23 = 95 86 + 23 = 109 98 + 23 = 121 102 + 23 = 125 - - - ( 5 * 5 * 5 ) so we have 102 as the answer ! e
Answer: e
Problem: what is the % change in the area of a rectangle when its length increases by 25 % and its width decreases by 25 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 6 % decrease , e ) insufficient data
Rationale: "( 125 / 10 ) * ( 75 / 10 ) = 9375 / 100 ~ 94 of original area 0.94 is a 6 % decrease from 100 / 100 - > d"
Answer: d
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 70 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 14
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 70 = 6 k + 4 k = > k = 7 total red ' s in bag a will be 2 k = 14 e"
Answer: e
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 60 marks . how many sums did sandy get correct ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 60 5 x = 120 x = 24 the answer is d ."
Answer: d
Problem: a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 35 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of silver cars is 0.2 * 40 + 0.35 * 80 = 36 the percentage of cars which are silver is 36 / 120 = 30 % the answer is a ."
Answer: a
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 2 ?
Options: a ) $ 0.50 , b ) $ 0.75 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 5 is p ( 5 ) = 9.50 + 0.25 ( 5 – 1 ) = 9.50 + 0.25 * 4 ; salary grade of 2 is p ( 2 ) = 9.50 + 0.25 ( 2 – 1 ) = 9.50 + 0.25 ; p ( 5 ) - p ( 2 ) = 9.50 + 0.25 * 4 - 9.50 - 0.25 = 0.75 . answer : b ."
Answer: b
Problem: what is the product of all the possible values of x if x ^ 2 - 2 x - 8 ?
Options: a ) – 29 , b ) – 12 , c ) - 8 , d ) 29 , e ) 168
Rationale: "explanation : = > y = x ^ 2 - 2 x - 8 = > y = ( x + 2 ) ( x - 4 ) = > x = - 2 , y = 4 product x = ( - 2 ) ( 4 ) = - 8 answer option - 8 answer : c"
Answer: c
Problem: in a class of 30 students , 5 students did not borrow any books from the library , 10 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 4 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 5 , b ) 8 , c ) 16 , d ) 18 , e ) 20
Rationale: "the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 4 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 4 books per student , so total number of books they could have borrowed is 4 * 4 = 16 books . so the 5 th student could have borrowed is 32 - 16 = 16 books . answer : c ."
Answer: c
Problem: in a office work is distribute between p persons . if 1 / 4 members are absent then work increased for each person is ?
Options: a ) 33.33 % , b ) 24.33 % , c ) 15.33 % , d ) 16.33 % , e ) 17.33 %
Rationale: "let total % of work is 100 % total person = p 1 / 4 person are absent of total person . so absent person is 1 / 4 p ie p / 4 . left person is , p - p / 4 = 3 p / 4 . p person do the work 100 % 1 person do the work 100 * p % 3 p / 4 person do the work ( 100 * p * 4 ) / 3 p % = 133.33 % work increased for each person is = ( 133.33 - 100 ) % = 33.33 % answer : a"
Answer: a
Problem: john has $ 1,200 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1200 x = 1000 money not spend = 1000 - 800 = 200 answer : a"
Answer: a
Problem: if a , b and c together can finish a piece of work in 2 days . a alone in 12 days and b in 18 days , then c alone can do it in ?
Options: a ) 5 days , b ) 4 days , c ) 3 days , d ) 2 days , e ) 7 days
Rationale: "c = 1 / 2 - 1 / 12 – 1 / 18 = 1 / 3 = > 3 days answer : c"
Answer: c
Problem: a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 2110 , b ) 3210 , c ) 4320 , d ) 5430 , e ) 6540
Rationale: "the tank is emptied at this rate : 9 + 6 - 3 = 12 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 12 = 4320 minutes . the answer is c ."
Answer: c
Problem: a cistern is normally filled in 12 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 84 , c ) 40 , d ) 99 , e ) 11
Rationale: "1 / 12 - 1 / x = 1 / 14 x = 84 answer : b"
Answer: b
Problem: when positive integer n is divided by positive integer j , the remainder is 28 . if n / j = 154.04 , what is value of j ?
Options: a ) 400 , b ) 350 , c ) 700 , d ) 750 , e ) 800
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 154.04 here 154 is the quotient . given that remainder = 28 so , 154.04 = 154 + 28 / j so , j = 700 answer : c"
Answer: c
Problem: what least number should be subtracted from 13602 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13602 ÷ 87 = 156 , remainder = 30 hence 30 is the least number which can be subtracted from 13602 such that the remainder is divisible by 87 answer is d"
Answer: d
Problem: 45 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 45 = 60 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 60 = 90 litres . answer b"
Answer: b
Problem: christine and siri have 21 rs between them . christine has 20 rs more than siri . how much does christine have .
Options: a ) 16.5 , b ) 17.5 , c ) 18.5 , d ) 19.5 , e ) 20.5
Rationale: let siri has x rs , then christine has 20 + x rs given x + ( 20 + x ) = 21 = > 2 x = 1 or x = 0.5 so christine and siri has 20.5 and 0.5 rs respectively . answer : e
Answer: e
Problem: the ratio between the length and the breadth of a rectangular park is 1 : 3 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 4 min , then the area of the park ( in sq . m ) is ?
Options: a ) 800 m , b ) 12000 m , c ) 36000 m , d ) 80000 m , e ) 30000 m
Rationale: "perimeter = distance covered in 4 min . = ( 12000 x 4 ) / 60 m = 800 m . let length = 1 x metres and breadth = 3 x metres . then , 2 ( 1 x + 3 x ) = 800 or x = 100 . length = 100 m and breadth = 300 m . area = ( 100 x 300 ) m 2 = 30000 m e"
Answer: e
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 4 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 34 , e ) 41
Rationale: let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 4 = > 2 b - b - 4 = 30 b = 34 so the present age of b is 34 years answer : d
Answer: d
Problem: the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 23 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.4 , b ) 984.4 , c ) 877.4 , d ) 637.4 , e ) 667.4
Rationale: let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 23 = 2 r a = 12 / 5 r and r = 69 a = 165.6 required total cost = 4 * 165.6 + 3 * 69 + 5 * 23 = 662.4 + 207 + 115 = $ 984.40 b
Answer: b
Problem: if x is equal to the sum of the integers from 50 to 60 , inclusive , and y is the number of even integers from 50 to 60 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 391 , d ) 491 , e ) 611
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 50 + ( 11 - 1 ) * 1 } = 11 * 55 = 605 = x number of even number = ( 60 - 50 ) / 2 + 1 = 6 = y x + y = 605 + 6 = 611 e"
Answer: e
Problem: a number x is 7 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 85.7 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 7 . then y = 1 is less than x = 7 by ( 7 - 1 ) / 7 * 100 = 6 / 7 * 100 = 85.7 % . answer : b ."
Answer: b
Problem: an alloy weighing 48 ounces is 25 % gold . how many ounces of pure gold must be added to create an alloy that is 40 % gold ?
Options: a ) 15 , b ) 20 , c ) 12 , d ) 14 , e ) 7
Rationale: an alloy of 48 oz which is 25 % gold means there is 12 oz of gold . to get to an alloy that is 40 % gold , let ' s use this expression : ( 12 + x ) / ( 48 + x ) = 0.40 with x representing the amount of pure gold that must be added to get to 40 % . the expression we are using represents the new total weight of pure gold over the new total weight of the alloy and this fraction should represent 40 % or 0.4 . you will see that 12 is the correct answer , as 24 / 60 = 0.4 choose c
Answer: c
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 420 . find the sum ?
Options: a ) s . 5000 , b ) s . 7000 , c ) s . 14000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 420 = > 30 x / 100 - 24 x / 100 = 420 = > 6 x / 100 = 420 = > x = 7000 . answer : b"
Answer: b
Problem: if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is
Options: a ) 343 , b ) 393 , c ) 363 , d ) 391 , e ) 409
Rationale: n = smallest number n + 6 = largest number ( n + n + 6 ) / 2 = 20 = > ( 2 n + 6 ) / 2 = 20 = > n + 3 = 20 = > n = 17 so product of n and n + 6 = ( 17 ) ( 23 ) = 391 answer - d
Answer: d
Problem: a train , 120 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 255 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 120 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 120 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 120 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 120 + x = > 45 ã — 10 ã — 10 / 12 = 120 + x = > 15 ã — 10 ã — 10 / 4 = 120 + x = > 15 ã — 25 = 120 + x = 375 = > x = 375 - 120 = 255 answer : option b"
Answer: b
Problem: find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 6 ) 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 / 6 = 2 / 1 = 2 : 3 answer is e"
Answer: e
Problem: the number 90 can be written as the sum of the squares of 4 different positive integers . what is the sum of these 4 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "4 ^ 2 + 3 ^ 2 + 8 ^ 2 + 1 ^ 2 = 90 - - > 1 + 3 + 8 + 4 = 16 . b"
Answer: b
Problem: a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts overtaking the john ( he is riding on the horse ) before it starts overtaking the mike ( who is also riding on his horse ) coming from the opposite direction in 24 seconds . in how much time ( in secs ) after the train has crossed the mike do the john meets to mike ?
Options: a ) 3576 s , b ) 3589 s , c ) 3596 s , d ) 3598 s , e ) 3576 s
Rationale: "let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - ( i ) and - - - - - - - - - ( ii ) from eq . ( i ) and ( ii ) 3 ( r - a ) = 2 ( r + k ) r = 3 a + 2 k in 30 minutes ( i . e 1800 seconds ) , the train covers 1800 r ( distance ) but the arun also covers 1800 a ( distance ) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 ( r - a ) - 24 ( a + k ) time required = = ( 3600 - 24 ) = 3576 s e"
Answer: e
Problem: two trains 100 m and 60 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 5.76 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 100 + 60 = 160 m . required time = 160 * 9 / 250 = 5.76 = 5.76 sec . answer : b"
Answer: b
Problem: the price of lunch for 15 people was $ 207.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.00 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "if the amount spent excluding the gratuity was x , then x ( 1.15 ) = 207 = > x = 207 / 1.15 = 180 then the average price per person = 180 / 15 = 12 option ( b )"
Answer: b
Problem: find the missing figures : 0.50 % of ? = 0.12
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let 0.50 % of x = 0.12 . then , 0.50 * x / 100 = 0.12 x = [ ( 0.12 * 100 ) / 0.50 ] = 24 . answer is e ."
Answer: e
Problem: a no . when divided by 220 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 15
Rationale: "220 + 43 = 263 / 17 = 8 ( remainder ) b"
Answer: b
Problem: shipment - - - - - - no . of defective chips / shipment - - - total chips in shipment s 2 - - - - - - - - - - - - - - 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - 6 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18000 s 4 - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts s 1 , s 2 , s 3 and s 4 comined as shown in the table above . what is the expected number q of defective chips in a shipment of 60000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 25
Rationale: i agree with your solution = 20 . but the question is : there are different combination to get 60000 chips . for example : 1 * s 3 + 2 * s 4 + 2 * s 2 . in this way , we ship 60000 chips with only 6 + 4 * 2 + 2 * 2 = 18 defective chips , better than the average of 20 . the question is to find the expected number q of defective chips , i guess it assume the minimum # , therefore it might not be 20 .
Answer: b
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 8 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 8 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 8 * 3 * 1 ) / 3 = 24 / 3 = 8 b"
Answer: b
Problem: the maximum number of students among them 640 pens and 520 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "number of pens = 640 number of pencils = 520 required number of students = h . c . f . of 640 and 520 = 40 answer is a"
Answer: a
Problem: a certain airline ' s fleet consisted of 80 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let x be the number of years . 4 x > 80 - 3 x 7 x > 80 x > 11 + 3 / 7 the answer is d ."
Answer: d
Problem: if the numbers 1 to 96 are written on 96 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 96 , d ) 1 , e ) 2
Rationale: there are 25 primes , 70 composite numbers from 1 to 96 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 96 . answer : c
Answer: c
Problem: sandy walked 25 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 25 meters . she then turned to her right and walked 12 meters . what distance is she from the starting point and in which direction ?
Options: a ) 32 meters east , b ) 32 meters north , c ) 32 meters west , d ) 42 meters east , e ) 52 meters west
Rationale: "the net distance is 20 + 12 = 32 meters to the east . the answer is a ."
Answer: a
Problem: the length of the bridge , which a train 120 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 239 , b ) 277 , c ) 255 , d ) 88 , e ) 232
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 = = > 2 ( 120 + x ) = 750 = = > x = 255 m . answer : c"
Answer: c
Problem: how many liters of water must be evaporated from 50 liters of a 1 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 35 , b ) 40 , c ) 42 , d ) 45 , e ) 48
Rationale: 1 % of a 50 liter solution is 0.5 l which is 10 % of the solution at the end . the solution at the end must be 5 l . we need to evaporate 45 liters . the answer is d .
Answer: d
Problem: raman mixed 27 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 ) 190 , d ) 188 , e ) 112
Rationale: "explanation : cp per kg of mixture = [ 27 ( 150 ) + 36 ( 125 ) ] / ( 27 + 36 ) = rs . 135.71 sp = cp [ ( 100 + profit % ) / 100 ] = 135.71 * [ ( 100 + 40 ) / 100 ] = rs . 190 . answer : c"
Answer: c
Problem: the average of 50 numbers id 56 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 51.35 , e ) 56.25
Rationale: explanation : total of 50 numbers = ( 50 × 56 ) = 2800 total of 48 numbers = ( 2800 - ( 45 + 55 ) ] = 2700 required average = 2700 / 48 = 56.25 answer : e
Answer: e
Problem: a set consists of 12 numbers , all are even or multiple of 5 . if 7 numbers are even and 14 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 9
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 12 = 7 + 14 - { both } + 0 ; { both } = 9 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : e ."
Answer: e
Problem: sum of the squares of 3 no . is 149 and the sum of their products taken two at a time is 70 . find the sum ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 13 , e ) 18
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 149 + 2 * 70 a + b + c = â ˆ š 289 = 17 answer a"
Answer: a
Problem: if x and y are positive integers and x = 5 y + 2 , what is the remainder when x is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that x and y are positive integers and x = 5 y + 2 . we ' re asked for the remainder when x is divided by 5 . if . . . . y = 1 x = 7 7 / 5 = 1 remainder 2 final answer : c"
Answer: c
Problem: if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 5 * 7 * 9 = 68 then find , 7 * 9 * 11 = ?
Options: a ) 106 , b ) 49 , c ) 68 , d ) 38 , e ) 55
Rationale: a 106 ( 11 * 9 ) + 7 = 106
Answer: a
Problem: a is twice as good a workman as b and they took 7 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 7 x = 1 / 21 = > 21 days answer : c"
Answer: c
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 4 cm , and bd = 6 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 4 ( ac = 4 ) d - 8 ( bd = 6 ) cd is 8 - 4 = 4 . ans d"
Answer: d
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 844 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 728 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 844 - 815 ) = rs . 29 . s . i . for 3 years = rs . ( 29 x 3 ) = rs . 87 . principal = rs . ( 815 - 87 ) = rs . 728 . answer : option d"
Answer: d