regisss/math_qa huggingface dataset:
Problem: average between 2 sets of numbers is closer to the set with more no ' s ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 92 , e ) 94
Rationale: "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"
Answer: b
Problem: a merchant marks his goods up by 30 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 17 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %
Rationale: "let the price be 100 . the price becomes 130 after a 30 % markup . now a discount of 10 % on 130 . profit = 117 - 100 17 % answer a"
Answer: a
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 46 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 16 , e ) $ 28
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 46 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 46 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 46 i . e . x = 30 i . e . fixed monthly charge , y = 16 answer : option d"
Answer: d
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 70 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 42 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 70 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 70 / 10 = 7 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 7 = 42 kms . . . answer - a"
Answer: a
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 18 days , then c alone can do it in ?
Options: a ) 7 days , b ) 3 days , c ) 9 days , d ) 8 days , e ) 2 days
Rationale: "c 9 days c = 1 / 4 - 1 / 12 – 1 / 18 = 1 / 9 = > 9 days"
Answer: c
Problem: machine a and machine b are each used to manufacture 440 sprockets . it takes machine a 10 hours longer to produce 440 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 4.4 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 440 qt = 400 for a : ( t + 10 ) ( q ) = 440 qt + 10 q = 440 400 + 10 q = 440 q = 4 so a can produce 4 / hour . then b can produce = 4 ( 1.1 ) = 4.4 / hour . d"
Answer: d
Problem: on a certain day , tim invested $ 600 at 10 percent annual interest , compounded annually , and lana invested 800 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 15 , c ) $ 44 , d ) $ 100 , e ) $ 105
Rationale: compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 600 ( 1.10 ) ^ 2 = 600 ( 1.21 ) = 726 and lana would have 800 ( 1.05 ) ^ 2 = 800 ( 1.1025 ) = 882 thus , tim earned 126 dollars , while lana earned 82 dollars the difference is $ 44 and the answer is c .
Answer: c
Problem: if y is the smallest positive integer such that 630 multiplied by y is the square of an integer , then y must be
Options: a ) 20 , b ) 50 , c ) 60 , d ) 70 , e ) 140
Rationale: "630 = 2 * 3 ^ 2 * 5 * 7 to be perfect square , we need to multiply by at least 2 * 5 * 7 = 70 . the answer is d ."
Answer: d
Problem: today mary ’ s father is 4 times as old as mary . 3 years ago , he was 5 times as old . how old is mary today ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: dad ' s age = 4 m 5 * ( m - 3 ) = 4 m - 3 m = 12 the answer is d .
Answer: d
Problem: a horse is tethered to one corner of a rectangular grassy field 42 m by 26 m with a rope 16 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 308 m 2 , c ) 201 m 2 , d ) 205 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 16 ) 2 = 201 m 2 answer c"
Answer: c
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line perpendicular to x = 2 y + 5 , then k = ?
Options: a ) - 5 , b ) - 8 , c ) 2 , d ) - 4 , e ) 1
Rationale: "the slope = k / 2 the line perpendicular to x = 2 y + 5 or y = 1 / 2 x - 5 / 2 has a slope = - 1 / ( 1 / 2 ) = - 2 - - - > k / 2 = - 2 - - > k = - 4 answer is d"
Answer: d
Problem: a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 thinnings ?
Options: a ) 22 , b ) 77 , c ) 26 , d ) 37 , e ) 88
Rationale: "16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d"
Answer: d
Problem: the average ( arithmetic mean ) of 4 different integers is 76 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 37
Rationale: "total of integers = 76 * 4 = 3004 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 304 - ( 90 + 89 + 88 ) = 304 - 267 = 37 answer : e"
Answer: e
Problem: a certain elevator has a safe weight limit of 2,000 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2000 so 200 * x + 230 * x = 2000 = > 430 x = 2000 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 we are not taking 10 as answer because say 10 th person has minimum of 200 weight then 200 * 5 + 230 * 5 = 2150 ( which is more than 2000 ) answer c .
Answer: c
Problem: the average salary of all the workers in a workshop is $ 8000 . the average salary of 7 technicians is $ 12000 and the average salary of the rest is $ 6000 . the total number of workers in the shop is ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 25 , e ) 31
Rationale: let the total number of workers be x 8000 x = 12000 * 7 + 6000 ( x - 7 ) x = 21 answer is c
Answer: c
Problem: a farmer grows broccoli in his farm that is in the shape of a square . each broccoli takes 1 square foot of area in his garden . this year , he has increased his output by 101 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did he produce this year ?
Options: a ) 2400
b ) 2601
c ) 1987
d ) 2000
e ) can not be determined
Rationale: explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 101 , the area would have increased by 101 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 101 ( x + y ) ( x - y ) = 101 . 101 is a prime number and hence it will have only two factors . i . e . , 101 and 1 . therefore , 101 can be expressed as product of 2 numbers in only way = 101 * 1 i . e . , ( x + y ) ( x - y ) = 101 * 1 so , ( x + y ) should be 101 and ( x - y ) should be 1 . solving the two equations we get x = 51 and y = 50 . therefore , number of broccoli produced this year = x 2 = 512 = 2601 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , c and d . as 2400,1987 and 2000 are not the square of any number . check choice b : if this year ' s produce is 2601 , last year ' s produce would have been 2601 - 101 = 2500 2500 is the square of 50 . so , 2601 is the answer . choice b
Answer: b
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds . the ratio of their speeds i
Options: a ) 1 : 3 , b ) 3 : 2 , c ) 3 : 4 , d ) 4 : 2 , e ) none of these
Rationale: "explanation : let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x metres , and length of the second train = 17 y metres . 27 x + 17 y / x + y = 23 27 x + 17 y = 23 x + 23 y 4 x = 6 y x / y = 3 / 2 answer is b"
Answer: b
Problem: a person can swim in still water at 10 km / h . if the speed of water 8 km / h , how many hours will the man take to swim back against the current for 16 km ?
Options: a ) 3 , b ) 7 , c ) 5 , d ) 8 , e ) 6
Rationale: "m = 10 s = 8 us = 10 - 8 = 2 d = 16 t = 16 / 2 = 8 answer : d"
Answer: d
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 60 % of the total school population of x students , what is x ?
Options: a ) 122 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = x / 100 * 60 / 100 * x = > x ^ 2 = 9 * 10000 / 6 = > x = 122 a"
Answer: a
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 65 kilometers , maxwell ' s walking speed is 2 km / h , and brad ' s running speed is 3 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 25 , b ) 23 , c ) 22 , d ) 24 , e ) 26
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 2 xt = 65 - 3 xt ( i . e distance = speed x time ) = > 5 t = 65 hence t = 13 oa = 2 x 13 = 26 km answer : e"
Answer: e
Problem: what is the smallest integer that is multiple of 5 , 7,9
Options: a ) a ) 70 , b ) b ) 315 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 5 , 7 and 9 which is 315 . the answer is b ."
Answer: b
Problem: the odds in favour of an events are 3 : 5 . the probability of occurrence of the event is
Options: a ) 3 / 8 , b ) 2 / 7 , c ) 1 / 3 , d ) 2 / 5 , e ) 6 / 7
Rationale: number of cases favourable to e = 3 total number of cases = 3 + 5 = 8 p ( e ) = 3 / 8 answer is a
Answer: a
Problem: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 3 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 100 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 3 people . so $ 75 . but , he also has to put in the average for himself ( the fourth person ) , so add $ 75 . so $ 150 is your answer . answer b"
Answer: b
Problem: in a class of 40 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 14
Rationale: 26 + 20 - 17 = 29 40 - 29 = 11 play neither answer is d
Answer: d
Problem: seller selling an apple for rs . 18 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 19 , d ) 18 , e ) 20
Rationale: "sp = 18 loss = cp 19 loss = cp − sp = cp − 18 ⇒ cp 19 = cp − 18 ⇒ 18 cp 19 = 18 ⇒ cp 19 = 1 ⇒ cp = 19 c"
Answer: c
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 8 , what is the least possible value of n ?
Options: a ) 7 , b ) 4 , c ) 5 , d ) 3 , e ) 6
Rationale: we need 3 factors of 2 , so n must be at least 4 . therefore , the answer is b .
Answer: b
Problem: 1.5 , 2.5 , 4.5 , 7.5 , 11.5 , ( . . . . )
Options: a ) 16.5 , b ) 15.5 , c ) 14.5 , d ) 17.5 , e ) 17
Rationale: "explanation : 1 , 2 , 3 , 4 , 5 , etc . hence 5 = 16.5 answer : a"
Answer: a
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 4 seconds to pass a telegraph post , then the length of the train is
Options: a ) 80 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 4 ) m = 80 m answer : option a"
Answer: a
Problem: what positive number , when squared , is equal to the cube of the positive square root of 14 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 16 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 4 = > x = 4 answer d"
Answer: d
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 250 per month . what is his monthly salary ?
Options: a ) 5000 , b ) 2999 , c ) 2878 , d ) 6250 , e ) 2771
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 250 = > 6250 answer : d"
Answer: d
Problem: if 15 students in a class average 75 % on an exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 80 % , b ) 81 % , c ) 82 % , d ) 83 % , e ) 84 %
Rationale: "( 15 * 75 + 10 * 90 ) / 25 = 81 % the answer is b ."
Answer: b
Problem: in a 100 m race a beats b by 25 m b beats c by 4 then a beats c by
Options: a ) 24 m , b ) 25 m , c ) 26 m , d ) 27 m , e ) 28 m
Rationale: a : b = 100 : 75 b : c = 100 : 96 . a : c = ( a / b x b / c ) = ( 100 / 75 x 100 / 96 ) = 100 / 72 = 100 : 72 . a beats c by ( 100 - 72 ) m = 28 m . answer : e
Answer: e
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 50 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 31 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 50 / 100 ) * 300 = 100 + 150 = 250 % comission = ( 250 / 800 ) * 100 = 31.3 ~ 31 % answer is e"
Answer: e
Problem: the number of singles that a baseball player hit increased 10 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 1 percent . if the total number of singles and doubles that she hit increased 3 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 2 : 3 , b ) 3 : 5 , c ) 4 : 7 , d ) 5 : 8 , e ) 7 : 9
Rationale: "soln : - 1.10 s + 0.99 d = 1.03 [ s + d ] 0.07 s = 0.04 d s / d = 4 / 7 answer : c"
Answer: c
Problem: a man swims downstream 60 km and upstream 100 km taking 10 hours each time , what is the speed of the man in still water ?
Options: a ) 24 , b ) 42 , c ) 6 , d ) 8 , e ) 12
Rationale: "60 - - - 10 ds = 6 ? - - - - 1 100 - - - - 10 us = 10 ? - - - - 1 m = ? m = ( 10 + 6 ) / 2 = 8 answer : d"
Answer: d
Problem: a light flashes every 30 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 650 , d ) 700 , e ) 120
Rationale: 1 flash = 30 sec for 1 min = 2 flashes so for 1 hour = 2 * 60 = 120 flashes . answer : e
Answer: e
Problem: the difference between the place values of two sixes in the numerical 81369206 is
Options: a ) 0 , b ) 599 , c ) 5994 , d ) 59994 , e ) none of them
Rationale: "required difference = ( 60000 - 6 ) = 59994 . answer is d"
Answer: d
Problem: if the area of a circle is 81 pi square feet , find its circumference .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "the area is given by pi * r * r . hence pi * r * r = 81 pi r * r = 81 * hence r = 81 feet the circumference is given by 2 * pi * r = 2 * pi * 9 = 18 pi feet correct answer d"
Answer: d
Problem: tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 100 ?
Options: a ) 4 , b ) 12 , c ) 15 , d ) 20 , e ) 24
Rationale: "you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is e"
Answer: e
Problem: at an election 2 candidates are participated and a candidate got 20 % of votes and defeated by 500 . and 10 votes are invalid . find the total polled votes ?
Options: a ) 843 , b ) 1023 , c ) 965 , d ) 413 , e ) 1245
Rationale: "winner votes = 100 - 20 = 80 polled votes = [ ( 100 * 500 ) / 2 * 80 - 100 ] + 10 = 843 ( approximately ) answer is a"
Answer: a
Problem: a cat chases a rat 6 hours after the rat runs . cat takes 4 hours to reach the rat . if the average speed of the cat is 90 kmph , what s the average speed of the rat ?
Options: a ) 32 kmph , b ) 26 kmph , c ) 35 kmph , d ) 36 kmph , e ) 32 kmph
Rationale: cat take 10 hours and rat take 4 hours . . . then distance chased by them is 90 * 4 . so speed of rat is ( 90 * 4 ) / 10 = 36 kmph . answer is d
Answer: d
Problem: average of 5 consecutive even numbers is 35 . find the greatest number in these 5 numbers ?
Options: a ) 26 , b ) 29 , c ) 39 , d ) 42 , e ) 43
Rationale: 39 option ' c '
Answer: c
Problem: a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . what is the area of the wall photo , in square inches ?
Options: a ) 96
b ) 86
c ) 108
d ) 144
e ) 118
Rationale: this question is an example of a ' punch out ' question - we have to find the area of everything , then ' punch out ' the part that we do n ' t want . we ' re told that a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . we ' re asked for the area of the wall photo , in square inches . area of a rectangle = ( length ) ( width ) so the area of the wall photo is . . . ( 8 ) ( 12 ) = 96 the wall photo ' adds ' 2 inches to the top , bottom , left and right ' sides ' of the picture , so the area of everything is . . . ( 8 + 2 + 2 ) ( 12 + 2 + 2 ) = ( 12 ) ( 16 ) = 196 when we ' punch out ' the area of the paper , we ' ll be left with the area of the wall photo : 192 - 96 = 96 final answer : a
Answer: a
Problem: the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 45 , c ) c ) 729 , d ) d ) 34 , e ) e ) 35
Rationale: "explanation : 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 * 36 / 2 = 45 cm 2 answer : option b"
Answer: b
Problem: john found that the average of 15 no . ' s is 40 . if 10 is added to each number then the mean of number is ?
Options: a ) 50 , b ) 55 , c ) 65 , d ) 72 , e ) 78
Rationale: ( x + x 1 + . . . x 14 ) / 15 = 40 50 option a
Answer: a
Problem: a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 2000 in march , how many cars does he need to sell in april in order to double his march earnings ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: 1000 + 200 x = 4000 x = 15 cars . the answer is b .
Answer: b
Problem: barbata invests $ 2200 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1100 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2200 + 0.05 * 2200 + x + 0.08 x = 2200 + x + 0.06 ( 2200 + x ) 0.05 * 2200 + 0.08 x = 0.06 x + 0.06 * 2200 0.02 x = 2200 ( 0.06 - 0.05 ) x = 2200 * 0.01 / 0.02 = 1100 ans : ` ` a ' '"
Answer: a
Problem: 24 lbs of coffee p and 25 lbs of coffee v are mixed to make coffee x and y . the ratio of p to v in coffee x is 4 to 1 , in y is 1 to 5 . how much of p is contained in the mixture x ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: let there be 4 x lbs of p in x and x lbs of v in x let there be y lbs of p in y and 5 y lbs of v in y now total p is 4 x + y = 24 and total q is x + 5 y = 25 solving the two equations , we get x = 5 and y = 4 mixture x has 4 x lbs of p = 4 x = 4 * 5 = 20 lbs answer : b
Answer: b
Problem: the average of 10 numbers is 0 . in those 10 , at the least , how many may be greater than or equal to zero ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: explanation : average of 10 numbers = 0 sum of 10 numbers = ( 0 x 10 ) = 0 . it is quite possible that 9 of these numbers may be negative and if there sum is - a , then 10 th number is ( a ) . answer : b
Answer: b
Problem: a movie buff buys movies on dvd and on blu - ray in a ratio of 13 : 4 . if she returns 2 blu - ray movies , that ratio would change to 7 : 2 . if she buys movies on no other medium , what was the original number of movies purchased ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 119
Rationale: "now coming to the process m ( d ) = 13 x and b ( d ) = 4 x now from the next line the new eqn becomes 13 x / ( 4 x - 2 ) = 7 / 2 solving it 26 x = 28 x - 14 x = 7 which means m ( d ) = 91 and b ( d ) = 28 so total initially is m ( d ) + b ( d ) = 119 e"
Answer: e
Problem: arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 80 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 9 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 20000 * 12 = 80000 * ( 12 – x ) = > x = 9 . answer : b"
Answer: b
Problem: if x + y = 260 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 230 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 260 x - y = 200 2 x = 60 x = 30 y = 230 answer is b"
Answer: b
Problem: a man can row 24 kmph in still water . it takes him thrice as long to row up as to row down the river . find the rate of the stream ?
Options: a ) 6 , b ) 12 , c ) 18 , d ) 15 , e ) 20
Rationale: "let man ' s rate upsteam be x kmph then his rate of downstream = 3 x kmph rate still water = 1 / 2 ( 3 x + x ) = 2 x 2 x = 24 x = 12 rate of upstream = 12 rate of downstream = 36 rate of stream 1 / 2 ( 36 - 12 ) = 12 kmph answer is b ."
Answer: b
Problem: a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 36.00 , how much did he pay for it ?
Options: a ) $ 34.40 , b ) $ 34.00 , c ) $ 32.00 , d ) $ 30.00 , e ) $ 35.00
Rationale: "let the cost price of book = x selling price of book = 36 $ markup % = 20 ( 120 / 100 ) x = 36 = > x = 30 answer d"
Answer: d
Problem: the hcf of two numbers is 42 and the other two factors of their lcm are 10 and 20 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 840 , d ) 504 , e ) 555
Rationale: "explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 10 & 20 then the numbers are ( 42 * 10 ) and ( 42 x 20 ) = 420 and 840 answer : option c"
Answer: c
Problem: suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 92 runs thereby increasing his average by 4 runs . what is his average after the 17 th innings ?
Options: a ) 48 , b ) 64 , c ) 28 , d ) 72 , e ) 27
Rationale: to improve his average by 4 runs per innings he has to contribute 16 x 4 = 64 runs for the previous 16 innings . thus , the average after the 17 th innings = 92 - 64 = 28 . answer : c
Answer: c
Problem: the wages earned by robin is 38 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 27.53 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 138 and $ 160 respectively . charles earns $ 38 more than robin who earns $ 138 . therefore , charles ' wage is 38 / 138 * 100 = 27.53 % . the correct choice is ( b )"
Answer: b
Problem: a dog have birth to 12 puppies , 2 female and 10 male . what is the ratio of the female puppies to the male ?
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 10 , d ) 2 / 12 , e ) 1 / 8
Rationale: if female is 2 and male is 10 , then 1 / 5 . so ratio of female to male is = 2 / 10 = 1 / 5 answer : a
Answer: a
Problem: a box contains 6 black , 8 red and 4 green marbles . 2 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 49 / 153 , b ) 18 / 153 , c ) 49 / 153 , d ) 40 / 153 , e ) 24 / 72
Rationale: "explanation : total marbles in a box = 6 black + 8 red + 4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random . therefore , n ( s ) = 18 c 2 = 153 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 6 c 2 + 8 c 2 + 4 c 2 = 15 + 28 + 6 = 49 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 49 / 153 answer : a"
Answer: a
Problem: if x / 2 = y / 5 = z / 6 , then ( x + y + z ) / x is equal to :
Options: a ) 13 , b ) 12 , c ) 15 / 2 , d ) 13 / 2 , e ) none of these
Rationale: "explanation : solution : let x / 2 = y / 5 = z / 6 = k = > x = 2 k , y = 5 k , z = 6 k . . ' . ( x + y + z ) / x = ( 2 k + 5 k + 6 k ) / 2 k = > 13 k / 2 k = 13 / 2 answer : d"
Answer: d
Problem: a man has some hens and cows . if the number of heads be 48 and the number of feet equals 136 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 48 = > h + c = 48 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 48 = > c = 20 substituting the value of c in equation 1 , we get h + 20 = 48 = > h = 48 - 20 = 28 i . e . , number of hens = 28 answer : e"
Answer: e
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 12 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 8 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 12 = 88 km / hr time taken = 100 / 88 = 1 hr 8 min answer is b"
Answer: b
Problem: the average of 25 results is 20 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 128 , b ) 75 , c ) 69 , d ) 78 , e ) 45
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 20 or , x = 128 . answer : option a"
Answer: a
Problem: if d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer , then d must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e .
Answer: e
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 14190 ?
Options: a ) 3200 , b ) 4000 , c ) 3250 , d ) 4128 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 14190 ã — 16 / 55 = rs . 4128 . share of z in the profit is rs . 4128 . option d"
Answer: d
Problem: there are 250 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?
Options: a ) 134 , b ) 138 , c ) 142 , d ) 146 , e ) 150
Rationale: "the number of nurses at the hospital is ( 3 / 5 ) * 250 = 150 . the answer is e ."
Answer: e
Problem: in an examination , 300 students appeared . out of these students ; 26 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 37 , c ) 54 , d ) 60 , e ) 01
Rationale: "the number of students with first division = 26 % of 300 = 26 / 100 × 300 = 7800 / 100 = 78 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 78 + 162 ) = 60 answer : d"
Answer: d
Problem: on a certain transatlantic crossing , 30 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "0.30 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.30 p = 0.40 ( rt ) rt / p = 3 / 4 = 75 % answer - e"
Answer: e
Problem: p and q invested in a shop . the profits were divided in the ratio of 4 : 6 respectively . if p invested rs . 55,000 , the amount invested by q is :
Options: a ) 48000 , b ) 40000 , c ) 35000 , d ) 60000 , e ) none
Rationale: "suppose q invested rs . y . then , 50000 / y = 4 / 6 or y = [ 50000 x 6 / 4 ] = 75000 . answer e"
Answer: e
Problem: evaluate ( 12 + 22 + 32 + . . . + 102 )
Options: a ) 430 , b ) 720 , c ) 385 , d ) 265 , e ) 295
Rationale: "we know that ( 12 + 22 + 32 + . . . + n 2 ) = 1 / 6 n ( n + 1 ) ( 2 n + 1 ) putting n = 10 , required sum = 1 / 6 x 10 x 11 x 21 = 385 option c"
Answer: c
Problem: divide rs . 32000 in the ratio 3 : 3 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 16000 , 16000 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "3 / 6 * 32000 = 16000 5 / 6 * 32000 = 16000 answer : c"
Answer: c
Problem: find value for x from below equation ? x + 1 = - 4
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = - 4 - 1 2 . simplify both sides : x = - 5 a"
Answer: a
Problem: what is the remainder when 1201 × 1202 × 1204 × 1205 is divided by 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the remainders when dividing each number by six are : 1 , 2 , 4 , and 5 . the product is 1 * 2 * 4 * 5 = 40 the remainder when dividing 40 by 6 is 4 . the answer is d ."
Answer: d
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio d of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) d = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Problem: at what rate of compound interest per annum will a sum of $ 1200 becomes 1348.32 in 2 years ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 10 %
Rationale: "let the rate be r % p . a . 1200 * ( 1 + r / 100 ) ^ 2 = 1348.32 ( 1 + r / 100 ) ^ 2 = 134832 / 120000 = 11236 / 10000 ( 1 + r / 100 ) ^ 2 = ( 106 / 100 ) ^ 2 1 + r / 100 = 106 / 100 r = 6 % answer is b"
Answer: b
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 45 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 45 kg joins the group , total weight of boys = 30 x + 45 so 30 x + 45 = 31 ( x + 1 ) = > x = 14 . answer : a"
Answer: a
Problem: the food in a camp lasts for 10 men for 50 days . if 10 more men join , how many days will the food last ?
Options: a ) 22 days , b ) 25 days , c ) 50 days , d ) 16 days , e ) 17 days
Rationale: "one man can consume the same food in 10 * 50 = 500 days . 10 more men join , the total number of men = 20 the number of days the food will last = 500 / 20 = 25 days . answer : b"
Answer: b
Problem: a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 6 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "on the way down , the rate is 1.5 * 6 = 9 miles per day . the distance of the route down the mountain is 2 * 9 = 18 miles . the answer is c ."
Answer: c
Problem: if a ^ 2 + b ^ 2 = 15 and ab = 25 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 50
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 15 - 25 = - 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 15 + 25 = 40 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 40 - 10 = 50 e"
Answer: e
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 3 full and other jar 1 / 2 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 2 / 3 , b ) 2 / 7 , c ) 1 / 2 , d ) 7 / 12 , e ) 1 / 7
Rationale: same amount of water made bigger jar 1 / 3 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 3 + 1 / 3 = 2 / 3 full . answer : a .
Answer: a
Problem: a certain candy manufacturer reduced the weight of candy bar m by 5 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ?
Options: a ) 5.5 , b ) 5.4 , c ) 5.3 , d ) 5.2 , e ) 5.1
Rationale: assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.95 oz new price of candy = 1 / 0.95 = 1.052 price increase 5.2 % d
Answer: d
Problem: if | x - 9 | = 3 x , then x = ?
Options: a ) 1.5 , b ) 3.1 , c ) 4.5 , d ) - 2.25 , e ) - 4.5
Rationale: "| x - 9 | = 3 x . . . ( given ) x ^ 2 - 18 x + 81 = 9 x ^ 2 8 * x ^ 2 + 18 * x - 81 = 0 . . . . ( by solving above eq . we get ) , x = - 4.5 or 2.25 = = = > ans - e"
Answer: e
Problem: mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 60 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 64 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 40 ( 60 percent less than juan ' s income ) ; mary ' s income = 64 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 64 ) is 64 % of juan ' s income ( 100 ) . answer : a ."
Answer: a
Problem: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 7 .
Options: a ) 150 , b ) 152 , c ) 154 , d ) 158 , e ) 160
Rationale: d = d * q + r d = 17 * 9 + 7 d = 153 + 7 d = 160 answer e
Answer: e
Problem: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs 1920 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2507 , d ) 3200 , e ) 2400
Rationale: "p - 1920 = ( p * 5 * 4 ) / 100 p = 2400 answer : e"
Answer: e
Problem: the diagonals of a rhombus are 15 cm and 20 cm . find its area ?
Options: a ) 158 , b ) 129 , c ) 150 , d ) 123 , e ) 117
Rationale: "1 / 2 * 15 * 20 = 150 answer : c"
Answer: c
Problem: how many different positive integers exist between 10 ^ 3 and 10 ^ 4 , the sum of whose digits is equal to 2 ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 4 , e ) 18
Rationale: "so , the numbers should be from 1,000 to 10,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 1,001 1,010 1,100 3 numbers . 2 . one 2 and the rest are 0 ' s : 2,000 1 number . total = 4 numbers . answer : d"
Answer: d
Problem: if 1 / ( x + 4 ) + 1 / ( x - 4 ) = 1 / ( x - 4 ) , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 1 , d ) 2 , e ) 3
Rationale: "if we solve the question , we get x = 4 . option : b"
Answer: b
Problem: 8 : 18 : : 24 : ?
Options: a ) 38 , b ) 32 , c ) 44 , d ) 43 , e ) 42
Rationale: "3 ^ 2 - 1 = 8 4 ^ 2 + 2 = 18 5 ^ 2 - 1 = 24 there for 6 ^ 2 + 2 = 38 answer : a"
Answer: a
Problem: in n is a positive integer less than 200 , and 2 n / 108 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( b ) . 2 n / 108 must be an integer . = > n / 54 must be an integer . hence n must be a multiple of 2 * 3 * 9 . = > n has 3 different prime integers ."
Answer: b
Problem: what percent is 100 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 10 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 100 / 1000 × 100 = 10000 / 1000 = 10 % answer is c"
Answer: c
Problem: the average of 9 observations was 8 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 18 , b ) 12 , c ) 15 , d ) 17 , e ) 19
Rationale: explanation : 1 to 9 = 8 * 9 = 72 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 72 = 18 option a
Answer: a
Problem: sophia finished 2 / 3 of a book . she calculated that she finished 30 more pages than she has yet to read . how long is her book ?
Options: a ) a ) 90 , b ) b ) 150 , c ) c ) 130 , d ) d ) 190 , e ) e ) 210
Rationale: "let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x − 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x − 1 / 3 * x = 30 1 / 3 * x = 30 x = 90 so the book is 90 pages long . answer is a ."
Answer: a
Problem: in a recent election , geoff received 0.5 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,571 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 54 , c ) 56 , d ) 60 , e ) 63
Rationale: "we are told that a candidate needs to receive more than x % of the vote . we got that a candidate needs to receive more than 3,600 votes ( 3,601 ) . 3,600 is 60 % of total votes . thus x = 60 % . answer : d"
Answer: d
Problem: which expression is the greatest ?
Options: a ) 3252 / 3257 , b ) 3456 / 3461 , c ) 3591 / 3596 , d ) 3346 / 3351 , e ) 3453 / 3458
Rationale: let 3252 / 3257 be the original fraction . notice that it is a positive proper fraction . hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one . hence we just have to pick the number that adds the greatest value to both the numerator and the denominator . options can be re - written as ( x - 5 ) x = > 1 - ( 5 / x ) a ) 1 - ( 5 / 3257 ) b ) 1 - ( 5 / 3461 ) c ) 1 - ( 5 / 3596 ) d ) 1 - ( 5 / 3351 ) e ) 1 - ( 5 / 3458 ) answer : c
Answer: c
Problem: the end of a blade on an airplane propeller is 10 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 300 π , d ) 480 π , e ) 1,200 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 10 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 10 / 5280 = 300 π c is the answer"
Answer: c
Problem: if there are 200 questions in a 3 hr examination . among these questions are 100 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 72 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 120 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 100 x + 100 * 2 x = 180 x = 180 / 300 x = 0.6 time taken for type a problem = 100 * 2 * 0.6 = 120 min answer : e"
Answer: e
Problem: a and b are 90 km apart they start to move each other simultaneously a at speed 10 and b at 5 km / hr if every hour they double their speed what is distance that a pass until he meet b ?
Options: a ) 30 km , b ) 40 km , c ) 50 km , d ) 60 km , e ) 70 km
Rationale: in 2 hours a covers ( 10 + 20 ) = 30 km b covers ( 5 + 10 ) = 15 km , total covered = 45 in the next hour they have to cover ( 90 - 45 ) km with the speeds 40 km / hr and 20 km / hr respectively let them take another t hrs to meet so sum of the distance to be covered by both is 45 km ( 40 * t ) + ( 20 * t ) = 45 km gives t = ( 3 / 4 ) hrs we need to fid out the distance covered by a which equals to = 30 + ( 40 * ( 3 / 4 ) ) = 60 km answer : d
Answer: d
Problem: a card board of size 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the card box . find the total number of pins used .
Options: a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139
Rationale: total 35 pins are there and 4 sides of card board . . . so 35 x 4 = 140 now in the rectangle 4 vertices have 4 pins which is common to the sides . . . . so 140 - 4 = 136 answer : b
Answer: b
Problem: a cistern can be filled by a tap in 2 hours while it can be emptied by another tap in 4 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?
Options: a ) 2 hr , b ) 5 hr , c ) 7 hr , d ) 1 hr , e ) 4 hr
Rationale: "net part filled in 1 hour 1 / 2 - 1 / 4 = 1 / 4 the cistern will be filled in 4 hr answer is e"
Answer: e
Problem: evaluate combination 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) !
Options: a ) 1617 , b ) 4753 , c ) 1417 , d ) 4353 , e ) none of these
Rationale: explanation : ncr = n ! / ( r ) ! ( n − r ) ! 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) ! = 98 ∗ 97 * 96 ! / ( 96 ) ! ( 2 ) ! = 98 * 97 / 2 ∗ 1 = 4753 option b
Answer: b
Problem: a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 116 , b ) 132 , c ) 148 , d ) 164 , e ) 180
Rationale: 3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 4 = 84 . the minimum number of horses and ponies is 164 . the answer is d .
Answer: d
Problem: there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 8 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120
Rationale: "method 2 : each person is one participant of 4 games . so there are in all 8 * 5 = 40 instances of one participant games . but each game has 2 participants so total number of games = 40 / 2 = 20 b"
Answer: b
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 12 minutes ?
Options: a ) 15 , b ) 18 , c ) 77 , d ) 52 , e ) 42
Rationale: 90 * 12 / 60 = 18 kmph answer : b
Answer: b
Problem: in a chess competition involving some men and women , every player needs to play exactly one game with every other player . it was found that in 45 games , both the players were women and in 190 games , both players were men . what is the number of games in which one person was a man and other person was a woman ?
Options: a ) 40 , b ) 120 , c ) 180 , d ) 200 , e ) 220
Rationale: this is similar to handshake problem , if there are nn people , then number of handshakes = 1 + 2 + . . . n = n ∗ ( n − 1 ) / 2 no . of women be xx and given x ∗ ( x − 1 ) / 2 = 45 this gives x = 10 | | | y no . of men : solve y ∗ ( y − 1 ) / 2 = 190 . this gives y = 20 so total men vs . women = 10 * 20 = 200 . answer is d
Answer: d
Problem: 11 is subtracted from 40 % of a number and results is 23 . what is the number ?
Options: a ) 160 , b ) 92 , c ) 88 , d ) 85 , e ) 34
Rationale: "( 40 / 100 ) * x â € “ 11 = 23 4 x = 340 x = 85 answer : d"
Answer: d
Problem: 0.1 + 0.1 ^ 2 + 0.1 ^ 3 =
Options: a ) 0.1 , b ) 0.111 , c ) 0.1221 , d ) 0.2341 , e ) 0.3
Rationale: "you have a mistake in your question . choice b should be ( . 111 ) and not ( . 11 ) . the equation in the solution can be simplified to ( . 1 + . 01 + . 001 ) . adding those together you get : . 100 . 010 . 001 - - - - - - . 111 - which is answer choice ( b )"
Answer: b
Problem: an article is bought for rs . 675 and sold for rs . 900 , find the gain percent ?
Options: a ) 33 1 / 8 % , b ) 33 9 / 3 % , c ) 33 1 / 3 % , d ) 93 1 / 3 % , e ) 33 2 / 3 %
Rationale: "675 - - - - 225 100 - - - - ? = > 33 1 / 3 % answer : c"
Answer: c
Problem: in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 15 : 8 : : 12 : x = > 8 x 15 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 15 ) = > x = 8 answer : d"
Answer: d
Problem: what is the maximum number of pieces of birthday cake of size 4 ” by 4 ” that can be cut from a cake 20 ” by 20 ” ?
Options: a ) 5 , b ) 10 , c ) 16 , d ) 20 , e ) 25
Rationale: "each length = 20 ' ' each piece = 4 ' ' cake could be divided to maximum of 25 pieces answer : e"
Answer: e