regisss/math_qa huggingface dataset:
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 150 meters . they next meet after sally has run 200 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 150 = 300 meters . since second time ( when they run full circumference ) brenda runs 300 meters and sally runs 200 meters , thus the circumference is 300 + 200 = 500 meters . answer : e .
Answer: e
Problem: a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 400 bolts ?
Options: a ) 36 , b ) 72 , c ) 96 , d ) 144 , e ) 180
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 400 bolts 400 * 6 / 25 = 96 mins ans c"
Answer: c
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 110
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 40 . thus , 3434 ( 90 + x ) = 40 + x or 270 + 3 x = 160 + 4 x or x = 110 answer : e"
Answer: e
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 600 m , b ) 300 m , c ) 400 m , d ) 700 m , e ) 500 m
Rationale: "a 600 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1600 ) = 600 m"
Answer: a
Problem: a train passes a station platform in 50 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 240 m , c ) 168 m , d ) 300 m , e ) 691 m
Rationale: speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 50 = 15 = > x = 300 m answer : d
Answer: d
Problem: the lowest number which should be added to 8247 so that the sum is exactly divisible by 5 , 6 , 7 , 8 and 9 is :
Options: a ) 1833 , b ) 1853 , c ) 1733 , d ) 1233 , e ) 1832
Rationale: "l . c . m . of 5 , 6 , 7 , 8 and 9 = 2520 . on dividing 8247 by 2520 , the remainder is 687 . number to be added = ( 2520 - 687 ) = 1833 . answer : option ' a '"
Answer: a
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 3 cm , and the point of contact is 5 cm above the ground , what is the radius of the other ball ?
Options: a ) 3 cm , b ) 9 cm , c ) 12 cm , d ) 15 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 3 = 3 / r - 3 giving r = 15 . answer : d"
Answer: d
Problem: in a class there are a total of 8 rows of desks and each desk can seat one student . there are 10 desks in the first row . in each subsequent row there are 2 more desks than in the previous row . find the maximum number of students seated in the class ?
Options: a ) 112 , b ) 144 , c ) 136 , d ) 132 , e ) 118
Rationale: the 8 rows form an arithmetic progression with first term 10 and last 24 . avg is 17 . so 17 * 8 = 136 answer is c .
Answer: c
Problem: what is the smallest positive integer nn such that 6,480 ∗ n √ 6,480 ∗ n is a perfect cube ?
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
Rationale: "sol : let ' s factorize 6480 and we get 6480 = 3 ^ 4 * 2 ^ 4 * 5 now we need to see for what minimum value of n √ n * 6480 = a ^ 3 where a is an integer so from 6480 we already have 2 ^ 4 * 3 ^ 4 * 5 * n √ n = ( 2 ^ 2 ) ^ 3 * ( 3 ^ 2 ) ^ 3 * ( 5 ) ^ 3 why cause a is an integer which will need to be have the same factors which are in lhs solving for n √ n = ( 2 ^ 6 * 3 ^ 6 * 5 ^ 3 ) / 2 ^ 4 * 3 ^ 4 * 5 and we get n √ n = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 or n = 2 ^ 4 * 3 ^ 4 * 5 ^ 4 or 30 ^ 4 ans is e"
Answer: e
Problem: a candidate who gets 20 % of the marks fails by 40 marks . but another candidate who gets 30 % marks gets 20 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 160 marks , e ) 827 marks
Rationale: "20 % - - - - - - - - - - - - 40 30 % - - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - - - - - - 60 20 % - - - - - - - - - - - - - - 120 120 + 40 = 160 marks answer : d"
Answer: d
Problem: 10 women can complete a work in 8 days and 10 children take 12 days to complete the work . how many days will 6 women and 3 children together take to complete the work ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 9 , e ) 11
Rationale: "explanation : 1 women ’ s 1 day ’ s work = 1 / 8 / 10 = 1 / 80 1 child ’ s 1 day ’ s work = 1 / 12 / 10 = 1 / 120 6 women ’ s 1 day ’ s work = 1 / 80 × 6 = 3 / 40 3 children ’ s 1 day ’ s work = 1 / 120 × 3 = 1 / 40 6 women ’ s + 3 children ’ s 1 day ’ s work = 3 / 40 + 1 / 40 = 1 / 10 therefore , they will finish the whole work in 10 days . answer : option b"
Answer: b
Problem: solve for x and check : - 200 x = 1600
Options: a ) 2000 , b ) 2573 , c ) 1600 , d ) 2950 , e ) none of these
Rationale: "solution : dividing each side by - 200 , we obtain ( - 200 x / - 200 ) = ( 1600 / - 200 ) therefore : x = - 8 check : - 200 x = 1600 ( - 200 * - 8 ) = 1600 1600 = 1600 answer : c"
Answer: c
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 140 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 17.5 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 140 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 140 units is ' 7 times ' 20 , we need ' 7 times ' more time . ( 2.5 hours ) ( 7 times ) = 17.5 hours final answer : [ reveal ] spoiler : c"
Answer: c
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 1 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.8 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.10 i ( last year ) = 1.1 i ( last year ) 1 = 1.1 x i ( last year ) i ( last year ) = 1 / 1.1 = 10 / 11 = 0.90909 . . . or i ( last year ) = 0.91 % answer : c"
Answer: c
Problem: there are 450 birds at a small zoo . the number of birds is 5 times the number of all the other animals combined . how many more birds are there than non bird animals at the zoo ?
Options: a ) 400 , b ) 360 , c ) 270 , d ) 180 , e ) 90
Rationale: total birds = 450 = 5 * other animals ( x ) or x = 90 . so , difference in birds and x = 450 - 90 = 360 . answer is b .
Answer: b
Problem: a man can row downstream at 20 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 15,2 , b ) 15 , 4 , c ) 15 , 8 , d ) 15 , 5 , e ) 15,7
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 30 = > x = 15 , y = 5 . answer : d"
Answer: d
Problem: an seller earns an income of re 1 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 20 th day of business , he earns an income of :
Options: a ) 29 , b ) 57 , c ) 35 , d ) 20 , e ) 30
Rationale: "2 nd day he earns = 3 ( 2 – 1 ) 3 rd day he earns = 3 ( 3 – 1 ) on 20 th day he earns 3 ( 20 - 1 ) = 57 rupees answer : b"
Answer: b
Problem: if 16 ^ y = 4 ^ 16 , what is y ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 16
Rationale: "16 ^ y = 4 ^ 2 y = 4 ^ 16 2 y = 16 y = 8 the answer is c ."
Answer: c
Problem: the sum of the ages of 4 children born at the intervals of 3 years each is 38 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 3 years , c ) 4 years , d ) 5 years , e ) 6 years
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) = 38 4 x = 20 = > x = 5 . age of youngest child = x = 5 years . answer : d"
Answer: d
Problem: if the selling price of 8 articles is same as the cost price of 10 articles . find the gain or loss percentage ?
Options: a ) 25 % , b ) 45 % , c ) 35 % , d ) 65 % , e ) 55 %
Rationale: "let the c . p of each article be re 1 . then , s . p of 8 articles = c . p of 10 articles = rs . 10 now , c . p of 8 articles = rs . 8 , s . p of 8 articles = rs 10 gain = rs ( 10 - 8 ) = rs 2 . gain % = ( 2 / 8 × 100 ) % = 25 % answer : a"
Answer: a
Problem: a cricket player whose bowling average was 24.85 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.85 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 85 , d ) 96 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 24.85 w + 52 total wickets after last match = w + 5 ( 24.85 w + 52 ) / ( w + 5 ) = 24.85 - 0.85 = 24 w = 80 so total wickets aftr last match = w + 5 = 85 answer : c"
Answer: c
Problem: what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 3
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 , e ) none of these
Rationale: "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 3 = 1.66 so biggest is 5 / 3 and smallest is 2 / 3 their difference is 5 / 3 - 2 / 3 = 3 / 3 = 1 option d"
Answer: d
Problem: 10 ^ 222 ÷ 10 ^ 220 = ?
Options: a ) 10 , b ) 1000 , c ) 100 , d ) 10000 , e ) 100000
Rationale: 10 ^ 222 ÷ 10 ^ 220 = 10 ^ ( 222 - 220 ) = 10 ^ 2 = 100 answer is c
Answer: c
Problem: a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is
Options: a ) 285 , b ) 337 , c ) 878 , d ) 227 , e ) 291
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : 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 50 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 70 kg , d ) 80 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 8 ã — 2.5 = 20 if x is the weight of the new person , total increase in weight = x â ˆ ’ 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : option c"
Answer: c
Problem: the average of 10 numbers is calculated as 15 . 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 ) 12.4 , b ) 14 , c ) 16 , d ) 18.6 , e ) none of these
Rationale: explanation : sum of numbers = ( 10 × × 15 - 26 + 36 ) = 160 correct average = 160 / 10 = 16 correct option : c
Answer: c
Problem: if z is not equal to zero , and z = 6 zs − 9 s 2 − − − − − − − − √ z = 6 zs − 9 s 2 , then z equals :
Options: a ) s , b ) 3 s , c ) 4 s , d ) - 3 s , e ) - 4 s
Rationale: squaring on both the sides gives z ^ 2 = 6 zs - 9 s ^ 2 = z ^ 2 - 6 zs + 9 s ^ 2 = z ( z - 3 s ) - 3 s ( z - 3 s ) = ( z - 3 s ) ( z - 3 s ) = z = 3 s answer = b
Answer: b
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 115 . if the ratio of his marks in english and maths is 5 : 1 , find his marks in science ?
Options: a ) 18 , b ) 77 , c ) 25 , d ) 55 , e ) 31
Rationale: "s : e = 1 : 3 e : m = 5 : 1 - - - - - - - - - - - - s : e : m = 5 : 15 : 3 5 / 23 * 115 = 25 answer : c"
Answer: c
Problem: two boats are heading towards each other at constant speeds of 5 miles / hr and 23 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 7 / 12 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 5
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 23 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 28 * 1 / 60 = 7 / 15 miles apart . answer : b ."
Answer: b
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum e of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . e = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Problem: there are cats got together and decided to kill the mice of 999936 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 992,1008 , e ) 931,1009
Rationale: "999936 can be written as 1000000 â € “ 64 = 10002 â € “ 82 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 8 ) * ( 1000 - 8 ) = ( 1008 ) * ( 992 ) given that number of cats is less than number if mice . so number of cats is 992 and number of mice were 1008 answer d"
Answer: d
Problem: a man can row 7 â ½ kmph in still water . if in a river running at 1.5 km / hr an hour , it takes him 50 minutes to row to a place and back , how far off is the place ?
Options: a ) 4 km , b ) 2 km , c ) 5 km , d ) 3 km , e ) 1 km
Rationale: speed downstream = ( 7.5 + 1.5 ) km / hr = 9 km / hr ; speed upstream = ( 7.5 - 1.5 ) kmph = 6 kmph . let the required distance be x km . then , x / 9 + x / 6 = 50 / 60 . 2 x + 3 x = ( 5 / 6 * 18 ) 5 x = 15 x = 3 . hence , the required distance is 3 km . answer d
Answer: d
Problem: a chemical supply company has 60 liters of a 30 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: 60 liters of a 30 % hno 3 solution means hno 3 = 18 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 18 + x = 50 % of ( 60 + x ) or x = 24 . hence , d
Answer: d
Problem: what is the sum of all digits for the number 10 ^ 28 - 44 ?
Options: a ) 233 , b ) 245 , c ) 257 , d ) 270 , e ) 285
Rationale: "10 ^ 28 is a 29 - digit number : 1 followed by 28 zeros . 10 ^ 28 - 44 is a 28 - digit number : 26 9 ' s and 56 at the end . the sum of the digits is 26 * 9 + 5 + 6 = 245 . the answer is b ."
Answer: b
Problem: mr and mrs a are opposite to each other . the distance between mr a and mrs a are 120 km . the speed of mr a and mrs a are 30 kmph , 10 kmph respectively . one bee is running between mr a nose to mrs a nose and returning back to mr a nose . the speed of bee is 60 kmph . then how far bee traveled ?
Options: a ) 160 km , b ) 170 km , c ) 180 km , d ) 190 km , e ) 130 km
Rationale: 30 x + 10 x = 120 x = 3 hrs speed of bee = 60 kmph distance traveled by bee = speed * time taken = 60 * 3 = 180 km answer : c
Answer: c
Problem: each machine of type a has 2 steel parts and 3 chrome parts . each machine of type b has 3 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 40 steel parts and 32 chrome parts , how many machines are in the group
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: look at the below representation of the problem : steel chrome total a 2 3 40 > > no . of type a machines = 40 / 5 = 8 b 3 5 32 > > no . of type b machines = 32 / 8 = 4 so the answer is 12 i . e a . hope its clear .
Answer: a
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 32 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 38 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.4 x + 1.2 x = 1.6 x 1.6 x / 5 x = 0.32 the answer is a ."
Answer: a
Problem: find the average of all the numbers between 6 and 34 which are divisible by 5 ?
Options: a ) 32 , b ) 20 , c ) 28 , d ) 11 , e ) 18
Rationale: "average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = 20 . answer : b"
Answer: b
Problem: set # 1 = { a , b , c , d , e } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: so not a vowel in set - 1 : 3 / 5 and not a vowel in ser - 2 : 5 / 6 now , 3 / 5 ∗ 5 / 6 = 12 this is for not a vowel . then for at least one vowel will be = 1 − 1 / 2 = 1 / 2 answer will be c .
Answer: c
Problem: in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 15 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 4 / 5 , e ) 2 / 15
Rationale: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 15 - - video cassette recorder including 1 / 3 ( equiped with cable tv ) i . e . 1 / 3 ( 1 / 5 ) = 1 / 15 therefore only video cassette recorder = 1 / 15 - 1 / 15 = 0 total = 1 / 5 + 0 + neither cable tv nor videocassette recorders 1 = 1 / 5 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 1 / 5 = 4 / 5 hence d ."
Answer: d
Problem: a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is
Options: a ) 600 , b ) 750 , c ) 1000 , d ) 1250 , e ) none of these
Rationale: "explanation : speed = ( 5 × 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 × 15 × 60 ) m = 1250 m . answer : d"
Answer: d
Problem: a student is ranked 17 th from right and 5 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 17 , from left 5 total = 17 + 5 - 1 = 21 answer : d"
Answer: d
Problem: a reduction of 46 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.45 , b ) 8.45 , c ) 7.45 , d ) 3.45 , e ) 1.45
Rationale: "explanation : 40 * ( 46 / 100 ) = 18.4 - - - 64 ? - - - 12 = > rs . 3.45 answer : d"
Answer: d
Problem: what should be the least number to be added to the 11002 number to make it divisible by 11 ?
Options: a ) 12 , b ) 9 , c ) 18 , d ) 77 , e ) 26
Rationale: "answer : 9 option : b"
Answer: b
Problem: in right triangle abc , ac is the hypotenuse . if ac is 50 and ab + bc = 70 , what is the area of the triangle abc ?
Options: a ) 225
b ) 450
c ) 25 √ 2
d ) 200
e ) 600
Rationale: square ab + bc = 70 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 4900 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 50 ^ 2 = 2500 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 2500 + 2 * ab * bc = 4900 . 2500 + 2 * ab * bc = 4900 . ab * bc = 1200 . the area = 1 / 2 * ab * bc = 600 . answer : e .
Answer: e
Problem: the ratio between x and y is 8 / 5 ; x is increased by 10 and y is multiplied by 10 , what is the ratio between the new values of x and y ?
Options: a ) 8 / 5 , b ) 5 / 8 , c ) 1 , d ) 10 , e ) it can not be determined
Rationale: "ratio = 8 k / 5 k = 8 / 5 , 16 / 10 , etc . x and y are decreased by 5 - - > ( 8 k + 10 ) / ( 5 k * 10 ) new ratio can be 18 / 50 , 26 / 100 , etc . answer : e"
Answer: e
Problem: the sum of three consecutive multiples of 3 is 72 . what is the largest number ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) 39
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 9 x = 63 x = 7 largest number = 3 x + 6 = 27 . 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 . 22 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 ) 103
Rationale: "use the options . the options which after getting added to 27 shows a cube of a number could be right . here 64 + 22 = 86 72 + 22 = 94 86 + 22 = 108 98 + 22 = 120 103 + 22 = 125 - - - ( 5 * 5 * 5 ) so we have 103 as the answer ! e"
Answer: e
Problem: the average age of an adult class is 40 years . 12 new students with an avg age of 34 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 20 , e ) 22
Rationale: "let original strength = y then , 40 y + 12 x 34 = ( y + 12 ) x 36 â ‡ ’ 40 y + 408 = 36 y + 432 â ‡ ’ 4 y = 48 â ˆ ´ y = 6 a"
Answer: a
Problem: the ratio of the volumes of two cubes is 2197 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 169 : 121 , b ) 169 : 127 , c ) 169 : 191 , d ) 121 : 169 , e ) 121 : 182
Rationale: "explanation : ratio of the sides = ³ √ 2197 : ³ √ 1331 = 13 : 11 ratio of surface areas = 13 ^ 2 : 11 ^ 2 = 169 : 121 answer : option a"
Answer: a
Problem: a train 150 m long crosses a platform 120 m long in 10 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 65 kmph , c ) 97 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 150 + 120 = 270 t = 10 s = 270 / 10 * 18 / 5 = 97 kmph answer : c"
Answer: c
Problem: there were totally 100 men . 85 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 85 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 15 - 25 - 15 - 30 = 100 - 85 = 15 answer : e"
Answer: e
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 10 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 1 : 5 , b ) 9 : 25 , c ) 5 : 1 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 / speed b since the times are same , 50 pi / speed a = 10 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 1 correct option : c"
Answer: c
Problem: a trader sells 45 meters of cloth for rs . 4500 at the profit of rs . 14 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 86 , c ) rs . 90 , d ) rs . 95 , e ) none of these
Rationale: "sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 14 = rs . 86 . answer : b"
Answer: b
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 20 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 2.75 , b ) 3.25 , c ) 3.75 , d ) 4.25 , e ) 4.75
Rationale: "time = 10 / 4 + 10 / 8 = 30 / 8 = 3.75 hours the answer is c ."
Answer: c
Problem: 12 times a number gives 156 . the number is
Options: a ) 11 , b ) 12 , c ) 13 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 12 × n = 156 ⇒ n = 13 correct option : c"
Answer: c
Problem: if the sides of a triangle are 30 cm , 28 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
Rationale: "the triangle with sides 30 cm , 28 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 10 = 140 cm 2 answer : option d"
Answer: d
Problem: if the side length of square b is sqrt ( 3 ) times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 9
b ) 6
c ) 4
d ) 3
e ) 2
Rationale: let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 3 ) x ) ^ 2 = 3 x ^ 2 . the answer is d .
Answer: d
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 15 percent , and on day 3 , it is discounted an additional 20 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 68 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 15 % discount = 765 price in day 3 after 20 % discount = 612 so , price in day 3 as percentage of the sale price on day 1 will be = 612 / 900 * 100 = > 68 % answer will definitely be ( c )"
Answer: c
Problem: an author received $ 0.80 in royalties for each of the first 100000 copies of her book sold , and $ 0.30 in royalties for each additional copy sold . if she received a total of $ 260000 in royalties , how many copies of her book were sold ?
Options: a ) 700,000 , b ) 300,000 , c ) 380,000 , d ) 400,000 , e ) 420,000
Rationale: total royalties for first 100.000 books = . 8 * 100,000 = 80,000 total royalties for the rest of the books = 260,000 - 80,000 = 180,000 remaining books = 180,000 / 0.3 = 600,000 total books = 600,000 + 100,000 = 700,000 answer a
Answer: a
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 6 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 7 , e ) 7 / 8
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 6 of the garden is green , so , since all the flowers must be either green or yellow , we know that 5 / 6 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 5 / 6 * 1 / 2 = 3 / 7 , or d ."
Answer: d
Problem: virginia , adrienne , and dennis have taught history for a combined total of 102 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 35 , d ) 43 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 102 = > 3 d = 102 + 27 = 129 = > d = 43 answer d"
Answer: d
Problem: the age of father 10 years ago was thirce the age of his son . 10 years hence , father ’ s age will be twice that of his son . the ration of their present ages is :
Options: a ) 5 : 2 , b ) 7 : 3 , c ) 9 : 2 , d ) 13 : 4 , e ) none of these
Rationale: solution let the ages of father and son 10 year ago be 3 x and x years respectively . then , ( 3 x + 10 ) + 10 = 2 [ ( x + 10 ) + 10 ⇔ 3 x + 20 = 2 x + 40 ⇔ x = 20 . ∴ required ratio = ( 3 x + 10 ) : ( x + 10 ) = 70 : 30 : 7 : 3 . answer b
Answer: b
Problem: a one - foot stick is marked in 1 / 2 and 1 / 4 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "lcm of 8 = 4 1 / 2 marking are ( table of 2 ) 0 . . . . . . 2 . . . . . . . . . . . 4 ( total = 3 ) 1 / 4 marking are ( table of 1 ) 0 . . . . . . . 1 . . . . . . 2 . . . . . . 3 . . . . . . . . 4 ( total = 5 ) overlapping markings are 0 . . . . . . . . 2 . . . . . . . . . 4 ( total = 3 ) total markings = 3 + 5 - 3 = 5 answer = c"
Answer: c
Problem: if integer k is equal to the sum of all even multiples of 25 between 200 and 600 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 50 between 200 and 600 . using arithmetic progression to find n : 600 = 200 + ( n - 1 ) 50 400 + 50 = 50 n 450 = 50 n = > n = 9 the sum would be : 9 * mean mean = [ 600 + 200 ] / 2 = 400 9 * 400 = 3600 d"
Answer: d
Problem: how many integers between 324,700 and 448,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 8,030 , c ) 1,253 , d ) 1,252 , e ) 1,239
Rationale: "the integers are : 324,713 324,813 etc . . . 448,513 the number of integers is 4486 - 3247 = 1239 the answer is e ."
Answer: e
Problem: g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( r ) is divisible by 4 ^ 11 , what is the smallest possible value for r ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: "g ( r ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
Answer: b
Problem: if 1 / 12 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 3 are from africa , 1 / 6 are from asia and the remaining 35 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 110 , b ) 115 , c ) 120 , d ) 125 , e ) 130
Rationale: 1 / 12 + 1 / 8 + 1 / 3 + 1 / 6 = ( 2 + 3 + 8 + 4 ) / 24 = 17 / 24 let x be the number of passengers on the ship . 35 = ( 7 / 24 ) x x = 120 the answer is c .
Answer: c
Problem: 54671 - 14456 - 33466 = ?
Options: a ) 2449 , b ) 5449 , c ) 6749 , d ) 6449 , e ) 6468
Rationale: "c if we calculate we will get 6749"
Answer: c
Problem: one side of a rectangular field is 15 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 100
b ) 120
c ) 150
d ) 180
e ) none
Rationale: solution other side = √ ( 17 ) 2 - ( 15 ) 2 = √ 289 - 225 = √ 64 = 8 m . ∴ area = ( 15 x 8 ) m 2 = 120 m 2 . answer b
Answer: b
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 13 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 3 more or 3 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 2,240 , d ) $ 1,920 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 13 : x + x - 3 = 13 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : c ."
Answer: c
Problem: the ages of two person differ by 20 years . if 7 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 32 , 12 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 7 ) = ( x + 20 - 7 ) = > 4 x = 48 = > x = 12 their present ages are 32 years and 12 year . answer : b"
Answer: b
Problem: how many integers between 1 and 10 ^ 18 are such that the sum of their digits is 2 ?
Options: a ) 161 , b ) 171 , c ) 181 , d ) 191 , e ) 201
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 17 and there are 18 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 17 thus , the total number of integers is 1 + 2 + . . . + 17 + 18 = 18 * 19 / 2 = 171 the answer is b ."
Answer: b
Problem: how many positive integers less than 27 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 ) 20 , e ) 22
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 11 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 , 26 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 11 - 1 = 22 . answer : e ."
Answer: e
Problem: in a corporation , 50 percent of the male employees and 40 percent of the female employees are at least 35 years old . if 42 percent of all the employees are at least 35 years old , what fraction of the employees in the corporation are females ?
Options: a ) 3 / 5 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: you can use the weighted averages formula for a 10 sec solution . no of females / no of males = ( 50 - 42 ) / ( 42 - 40 ) = 4 / 1 no of females as a fraction of total employees = 4 / ( 4 + 1 ) = 4 / 5 ; answer : d
Answer: d
Problem: if 4 men working 10 hours a day earn rs . 1400 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 1890 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1400 : x hence 4 * 10 * x = 9 * 6 * 1400 or x = 9 * 6 * 1400 / 4 * 10 = 1890 answer : d"
Answer: d
Problem: if a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 120 and a perimeter of 46 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 120 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 120 , let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 120 . . . . 120 / 8 = 15 = the longer side perimeter = 8 + 8 + 15 + 15 = 46 c"
Answer: c
Problem: a car gets 33 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 16 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 168 , b ) 172 , c ) 176 , d ) 180 , e ) 184
Rationale: "originally , the distance the car could go on a full tank was 16 * 33 = 528 miles . after it has been modified , the car can go 33 / 0.75 = 44 miles per gallon . on a full tank , the car can go 16 * 44 = 704 miles , thus 176 miles more . the answer is c ."
Answer: c
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 2 / 7 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 2 / 7 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 2 / 7 = 5 / 7 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 5 / 7 = 1 / 3 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 5 / 7 * 2 / 3 = 1 / 2 ans c"
Answer: c
Problem: shekar scored 76 , 65 , 82 , 67 and 55 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 55 ) / 5 = 375 / 5 = 69 hence average = 69 answer : b"
Answer: b
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 2500 resolutions ?
Options: a ) 1187 m , b ) 1704 m , c ) 2179 m , d ) 3520 m , e ) 4297 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 2500 resolutions . = 2500 * 2 * 22 / 7 * 22.4 = 352000 cm = 3520 m answer : d"
Answer: d
Problem: the average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?
Options: a ) 20 , b ) 27 , c ) 72 , d ) 28 , e ) 82
Rationale: "sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b"
Answer: b
Problem: if a person has two rectangular fields . the larger field has thrice the length and 4 times the width of the smaller field . if the smaller field has a length 50 % more than the width . if a person takes 20 minutes to complete one round of a smaller field then what is the time required to complete one round of a larger field ?
Options: a ) 69 minutes , b ) 68 minutes , c ) 58 minutes , d ) 48 minutes , e ) 67 minutes
Rationale: let the width of the smaller rectangle is 4 units then , the length of the smaller rectangle is 6 units ( that is 50 % more than the width ) now the perimeter of the rectangle is 2 ( 6 + 4 ) = 20 units so , 20 units is covered in 20 units , implies covers one unit in one minute so now coming to the larger rectangle the width = 16 units , length = 18 units , perimeter = 2 ( 16 + 18 ) 68 units thus , to cover the larger field , 68 minutes required to cover the rectangle . answer : b
Answer: b
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 7 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 7 miles / gallon . additional 5 miles / gallon is required to match the actual mileage . imo option c ."
Answer: c
Problem: some of 40 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 20 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 1
Rationale: "let total paint = 1 let amount replaced = x 40 ( 1 - x ) + 20 x = 20 x = 1 / 1 answer : e"
Answer: e
Problem: there are two concentric circles with radii 10 and 6 . if the radius of the outer circle is increased by 20 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ?
Options: a ) 11 , b ) 111 , c ) 211 , d ) 311 , e ) 411
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 100 pi . the area of the small circle is 36 pi . the area a 1 between the circles is 64 pi . when the big circle ' s radius increases , the new area is 144 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 135 pi . the ratio of a 2 / a 1 is 135 / 64 = 2.11 which is an increase of 111 % . the answer is b ."
Answer: b
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 3.2 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 20 , c ) 50 , d ) 8.6 , e ) 40
Rationale: "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 3.2 km / hr hence , speed of the man = 15 - 3.2 = 11.8 km / hr man ' s speed against the current = speed of the man - speed of the current = 11.8 - 3.2 = 8.6 km / hr answer is d ."
Answer: d
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 46,875 , how much profit did the business make ?
Options: a ) $ 55,000 , b ) $ 75,000 , c ) $ 95,000 , d ) $ 115,000 , e ) $ 125,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 46875 p = $ 75,000 the answer is b ."
Answer: b
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 24 days . how long will y take to complete the work ?
Options: a ) 30 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 24 days whole work will be done by y in 24 * 5 / 4 = 30 days answer is a"
Answer: a
Problem: linda bought 3 notebooks at $ 1.20 each ; a box of pencils at $ 1.50 and a box of pens at $ 1.70 . how much did linda spend ?
Options: a ) $ 6.80 , b ) $ 8.40 , c ) $ 7.70 , d ) $ 4.70 , e ) $ 3.90
Rationale: linda spent 1.20 ? 3 = $ 3.60 on notebooks the total amount of money that linda spent is equal to 3.60 + 1.50 + 1.70 = $ 6.80 correct answer a
Answer: a
Problem: a park square in shape has a 3 metre wide road inside it running along its sides . the area occupied by the road is 1764 square metres . what is the perimeter along the outer edge of the road ?
Options: a ) 576 metres
b ) 589 metres
c ) 600 metres
d ) 700 metres
e ) none
Rationale: solution let the length of the outer edges be x metres . then , length of the inner edge = ( x - 6 ) m . ∴ x 2 - ( x - 6 ) 2 = 1764 ‹ = › x 2 - ( x 2 - 12 x + 36 ) = 1764 ‹ = › 12 x = 1800 ‹ = › x = 150 . ∴ required perimeter = ( 4 x ) m ‹ = › ( 4 x 150 ) m = 600 m . answer c
Answer: c
Problem: two numbers are respectively 20 % and 50 % more than a third number . the percentage that is first of the second is ?
Options: a ) 45 % , b ) 80 % , c ) 78 % , d ) 94 % , e ) 68 %
Rationale: "i ii iii 120 150 100 150 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 80 % answer : b"
Answer: b
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22932 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 30 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22932 / - - 17640 / - = rs . 5292 / - rate of interest = ( 5292 / 22932 ) × ( 100 / 1 ) = > 30 % answer : option e"
Answer: e
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 60 ?
Options: a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 60 4 n < 53 n < 13 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 13 ) combining the two - 1.5 < n < 13.25 n = 1 to 13 ( 48 integers ) and n = - 1 and 0 so 15 integers . b"
Answer: b
Problem: the average of first 25 natural numbers is ?
Options: a ) 14 , b ) 13 , c ) 15 , d ) 18 , e ) 12
Rationale: "sum of 25 natural no . = 650 / 2 = 325 average = 325 / 25 = 13 answer : b"
Answer: b
Problem: r = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set r and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs r , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Problem: a $ 79.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: "listed selling price of chair = 79.95 $ discounted selling price of chair = 59.95 $ discount = 79.95 - 59.95 = 20 $ % decrease in price of chair = ( 20 / 79.95 ) * 100 % = 25 % approx answer c"
Answer: c
Problem: 5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 16 days . how many additional pipes , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: this is an inverse proportional problem . . . . . . 5 pipes in 16 days ; so for 4 days , it will be = 16 x 5 / 4 = 20 so , 20 - 5 = 15 answer e
Answer: e
Problem: a heap of grapes is divided into groups of 3 , 5 and 7 and each time one coconut is left over . the least number of grapes in the heap is ? a . 31 b . 41 c . 51 d . 61
Options: a ) a ) 31 , b ) b ) 41 , c ) c ) 106 , d ) d ) 61 , e ) e ) 71
Rationale: lcm = 105 = > 105 + 1 = 106 answer : c
Answer: c
Problem: the diagonals of a rhombus are 12 cm and 10 cm . find its area ?
Options: a ) 158 , b ) 129 , c ) 150 , d ) 123 , e ) 60
Rationale: "1 / 2 * 12 * 10 = 60 answer : e"
Answer: e
Problem: three 6 faced dice are thrown together . the probability that no two dice show the same number on them is
Options: a ) 5 / 0 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 6
Rationale: "explanation : no two dice show same number would mean all the three faces should show different numbers . the first can fall in any one of the six ways . the second die can show a different number in five ways . the third should show a number that is different from the first and second . this can happen in four ways . thus 6 * 5 * 4 = 120 favourable cases . the total cases are 6 * 6 * 6 = 216 . the probability = 120 / 216 = 5 / 9 . answer : b"
Answer: b
Problem: find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively .
Options: a ) 121 , b ) 124 , c ) 127 , d ) 122 , e ) 129
Rationale: "required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 _______ 1651 ) 2032 ( 1 1651 1651 _______ 381 ) 1651 ( 4 1524 _________ 127 ) 381 ( 3 381 0 required number = 127 . answer is c ."
Answer: c