regisss/math_qa huggingface dataset:
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 25,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 60000 , c ) 50000 , d ) 75000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 125000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 125000 - x ) = x / 3 + x / 2 = 62500 = 5 x / 6 = 62500 = x = 62500 x 6 / 5 = 75000 savings in public provident fund = rs . ( 125000 - 75000 ) = rs . 50000 answer is c ."
Answer: c
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 25 metres of cloth ?
Options: a ) 488 , b ) 204 , c ) 195 , d ) 178 , e ) 133
Rationale: let the required time be x seconds . more metres , more time ( direct proportion ) 0.128 : 25 : : 1 : x 0.128 x = 25 x 1 x = 25 / 0.128 = ( 25 x 1000 ) / 128 x = 195.31 . required time = 195 sec ( approximately ) . answer is c .
Answer: c
Problem: the sum of two numbers is 45 . the sum of their quotient and is reciprocal is 2.05 , the product of the numbers is ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: a + b = 45 a / b + b / a = 2.05 = > ( a ^ 2 + b ^ 2 ) / ab = 2.05 = > ( ( a + b ) ^ 2 − 2 ab ) / ab = 2.05 = > ( a + b ) ^ 2 = 2.05 ab + 2 ab = 4.05 ab = > ab = 45 ^ 2 / 4.05 = 500 answer : c
Answer: c
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 15 % of the money for taxi fare and buys 15 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 17.5 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 15 % of 200 = 30 for taxi fare , so he is left with 170 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 70 ( 170 - 100 ) no of oranges he can buy = 70 / 4 = > 17,5 so , george can buy 15 oranges . b"
Answer: b
Problem: daal is now being sold at rate rs . 20 a kg . during last month its rate was rs 16 per kg . by how reduce percent should a family its consumption so as to keep the expenditure fixed ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: last month rate = 16 per kg this month rate = 20 per kg if 20 = 100 % then 16 = ? therefore % = ( 16 * 100 ) / 20 = 80 % to reduce consumption 100 - 80 = 20 % answer : b
Answer: b
Problem: a certain maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight . a certain green paint contains 10 percent blue pigment and 90 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 1.5 , b ) 2 , c ) 2.5 , d ) 3 , e ) 3.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 3 = 1.5 grams of red pigment
Answer: a
Problem: before 4 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 52 , d ) 60 , e ) 64
Rationale: "a - 4 = 4 ( b - 4 ) - - > a - 4 b = - 12 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 20 - - > a = 3 ( 24 ) = 72 a - b = 72 - 20 = 52 answer : c"
Answer: c
Problem: a cricket bat is sold for $ 850 , making a profit of $ 225 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "225 / ( 850 - 225 ) = 225 / 625 = 9 / 25 bit more than 33 % . answer : d"
Answer: d
Problem: what is the least number to be added to 661 to make it a perfect square ?
Options: a ) 13 , b ) 15 , c ) 20 , d ) 16 , e ) 45
Rationale: "the numbers greater than 661 and are square of number is 676 . the least number that should be added 661 to make it perfect square = 676 - 661 = 15 . answer : b"
Answer: b
Problem: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 40 . he was allowed to drop his lowest score . after doing so , his average test score improved to 45 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 40 . so what we can assume is that we have 4 test scores , each 40 . he dropped his lowest score and the avg went to 45 . this means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 40 . so the lowest score = 40 - 15 = 25 answer ( b )"
Answer: b
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 49 , e ) 52
Rationale: "let their ages are 9 x , 15 x and 25 x respectively . difference between the ages of patrick and monica = 25 x - 9 x = 16 x where 49 x = 147 or x = 3 so diff in ages = 16 x = 16 * 3 = 48 yrs answer : a"
Answer: a
Problem: if the price of a certain bond on may 1 st was 2 / 3 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 2 / 3 * 12 = 8 ; the price on july 1 st = 8 * 1.50 = 12 . the average price of the bond on may 1 st and july 1 st = ( 8 + 12 ) / 2 = 10 . the price of the bond on june 1 st ( 12 ) is 6 / 5 times ( 120 % ) the average price of the bond on may 1 st and july 1 st . answer : c ."
Answer: c
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 252 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 5.5 , e ) 8
Rationale: "required run rate = 252 - ( 3.2 x 10 ) = 220 = 5.5 40 40 d"
Answer: d
Problem: the area of a square is equal to nine times the area of a rectangle of dimensions 121 cm * 144 cm . what is the perimeter of the square ?
Options: a ) 1500 cm , b ) 1800 cm , c ) 1584 cm , d ) 1718 cm , e ) 1086 cm
Rationale: "area of the square = s * s = 9 ( 121 * 144 ) = > s = 3 * 11 * 12 = 396 cm perimeter of the square = 4 * 396 = 1584 cm . answer : c"
Answer: c
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 48 = 21 $ ( 21 / 69 ) * 100 = 30.434 % answer : b"
Answer: b
Problem: a and b started a business investing rs . 90,000 and rs 30,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 1 , c ) 18 : 20 , d ) 18 : 4 , e ) 17 : 4
Rationale: "a : b = 90000 : 30000 = 9 : 3 = 3 : 1 answer : b"
Answer: b
Problem: what is the time required for a bike to cover a distance of 450 km with a speed of 90 kmh ?
Options: a ) 5 hours , b ) 3 hours , c ) 8 hours , d ) 6 hours , e ) 4 hours
Rationale: time = distance / speed time = 450 / 90 = 5 answer : a
Answer: a
Problem: how many even multiples of 25 are there between 249 and 501 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "250 = 10 * 25 500 = 20 * 25 the even multiples are 25 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 8 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 64 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 8 = 128 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 128 pi / 200 pi = 0.64 a"
Answer: a
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors c ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have c = 2 * 3 * 5 * 7 = 840 thus , answer b"
Answer: b
Problem: if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 150 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) − 80 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 150 = = = > b + c = 300 ( a + b ) - ( b + c ) = 220 - 300 = = = > a + b - b - c = - 80 = = = > a - c = - 80 answer : d"
Answer: d
Problem: the average of marks obtained by 120 boys was 40 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 125 , d ) 130 , e ) 145
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 40 24 x = 4800 - 1800 = > x = 3000 / 24 x = 125 hence , the number of boys passed = 125 . answer : c"
Answer: c
Problem: in a group of 27 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 6
Rationale: "a 7 add 7 + 10 + 4 to get 21 . then subtract 21 from the total students ⇒ 27 – 21 = 6 . answer is e"
Answer: e
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 4,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 11,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 4,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 4,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 320 = 0.10 x combine terms and subtract 0.08 x from both sides : 230 = 0.02 x divide both sides by 0.02 : 11,500 = x your answer is a ."
Answer: a
Problem: the points a ( 0 , 0 ) , b ( 0 , 4 a - 4 ) and c ( 2 a + 1 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 88 , b ) 98 , c ) 108 , d ) 78 , e ) 90
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 6 ) now 4 a - 4 = 2 a + 6 2 a = 10 , a = 5 therefore , a ( 0,0 ) ; b ( 0,16 ) ; c ( 11,16 ) 1 / 2 * 11 * 16 = 88 answer : a"
Answer: a
Problem: machine a takes 100 hours to complete a certain job and starts that job at 7 am . after two hour of working alone , machine a is joined by machine b and together they complete the job at 6 pm . how long would it have taken machine b to complete the jobif it had worked alone for the entire job ?
Options: a ) 10.11 , b ) 9.99 , c ) 11.1 , d ) 44.11 , e ) 1.01
Rationale: "let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 2 hr ( so 2 units done ) then a and b finish total work in 15 hours . hence a and b finish 98 units in 9 hours . of these 1 x 9 = 9 units were done by a . hence b did 89 units in 9 hours . hence b ( working rate ) = 89 / 9 units / hr hence b takes 100 x 9 / 89 = 10.11 hours to complete the job . answer a ."
Answer: a
Problem: average age of students of an adult school is 46 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 120 , c ) 360 , d ) 168 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 46 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 48 so , required no . of students after joining the new students = x + 120 = 168 . answer : d"
Answer: d
Problem: on a map , 3.5 inches represent 35 miles . how many miles approximately is the distance if you measured 127 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 515 , b ) 500 , c ) 525 , d ) 530 , e ) 535
Rationale: "1 inch = 2.54 cm 3.5 inch = 2.54 * 3.5 cm 8.89 cm = 35 miles 127 cms = 35 / 8.89 * 127 = 500 miles answer : b"
Answer: b
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length ?
Options: a ) 16.5 , b ) 16.0 , c ) 15 , d ) 16.8 , e ) 16.1
Rationale: "d = 110 + 140 = 250 m s = 60 * 5 / 18 = 50 / 3 t = 250 * 3 / 50 = 15 sec answer : c"
Answer: c
Problem: if the product of two numbers is 51216 and their h . c . f . is 33 , find their l . c . m .
Options: a ) 600 , b ) 680 , c ) 582 , d ) 560 , e ) none of these
Rationale: "explanation : hcf * lcm = 51216 , because we know product of two numbers = product of hcf and lcm lcm = 51216 / 88 = 582 option c"
Answer: c
Problem: at an elementary school , 70 % of the faculty members are women and 40 % of the faculty members are married . if 1 ⁄ 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 2 / 7 , d ) 7 ⁄ 30 , e ) 5 ⁄ 70
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 20 - - - - - 20 - - - - - - - - - 40 not married - - - - - 10 - - - - - 50 - - - - - - - - - 60 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married woman / total woman , so 20 / 70 = 2 / 7 c"
Answer: c
Problem: a train which has 300 m long , is running 80 kmph . in what time will it cross a person moving at 16 kmph in same direction ?
Options: a ) 25 sec , b ) 35 sec , c ) 15 sec , d ) 45 sec , e ) 20 sec
Rationale: time taken to cross a moving person = length of train / relative speed time taken = 300 / ( ( 80 - 16 ) ( 5 / 18 ) = 300 / 64 * ( 5 / 18 ) = 300 / 20 = 15 sec answer : c
Answer: c
Problem: what is the number of integers from 1 to 500 ( inclusive ) that are divisible by neither 10 nor by 15 ?
Options: a ) 170 , b ) 250 , c ) 300 , d ) 560 , e ) 420
Rationale: in 500 consecutive numbers , number of multiples of 10 = 500 / 10 = 50 ( ignore decimals ) in 500 consecutive numbers , number of multiples of 15 = 500 / 15 = 33 number of multiples of 10 * 15 i . e . 150 = 500 / 150 = 3 number of integers from 1 to 500 that are divisible by neither 10 nor by 15 = 500 - ( 50 + 33 - 3 ) { using the concept of sets here ) = 420 answer is e
Answer: e
Problem: 495 x 495 = ?
Options: a ) 250000 , b ) 250025 , c ) 5000 , d ) 245025 , e ) 240000
Rationale: "495 x 495 = ( 495 ) 2 = ( 500 - 5 ) 2 = ( 500 ) 2 + ( 5 ) 2 - ( 2 x 500 x 5 ) = 250000 + 25 - 5000 = 250025 - 5000 = 245025 . d )"
Answer: d
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 33 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 ) 4 , b ) 5 , c ) 2 , d ) 7 , e ) 8
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 33 kg joins the group , total weight of boys = 30 x + 33 so 30 x + 33 = 31 ( x + 1 ) = > x = 2 . answer : c"
Answer: c
Problem: what is the number of integers from 11 to 1010 ( inclusive ) that are divisible by neither 12 nor by 15 ?
Options: a ) 565 , b ) 856 , c ) 783 , d ) 590 , e ) 300
Rationale: "in 1000 consecutive numbers , number of multiples of 12 = 1000 / 12 = 83 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 15 = 1000 / 15 = 66 number of multiples of 12 * 15 i . e . 180 = 1000 / 180 = 5 number of integers from 11 to 1010 that are divisible by neither 12 nor by 15 = 1000 - ( 83 + 66 - 5 ) { using the concept of sets here ) = 856 answer is b"
Answer: b
Problem: the ages of ashley and mary are in the ratio 4 : 7 . the sum of their ages is 22 . find the age of mary .
Options: a ) 11 yrs , b ) 12 yrs , c ) 13 yrs , d ) 14 yrs , e ) 15 yrs
Rationale: "a : m = 4 : 7 let the ages of a & m be x & 22 - x x / 22 - x = 4 / 7 x = 8 a = 8 yrs m = 14 yrs answer : d"
Answer: d
Problem: a rectangular field has a length 10 meters more than it is width . if the area of the field is 171 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 17
b ) 19
c ) 21
d ) 23
e ) 25
Rationale: area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 the length is 19 meters . the answer is b .
Answer: b
Problem: a man is 26 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 24 , e ) 10
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 26 ) years . ( x + 26 ) + 2 = 2 ( x + 2 ) x + 28 = 2 x + 4 = > x = 24 . answer : d"
Answer: d
Problem: if a 2 + b 2 + c 2 = 250 and ab + bc + ca = 3 , then a + b + c is
Options: a ) 4 , b ) 8 , c ) 16 , d ) 32 , e ) 64
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 250 and ab + bc + ca = 3 , ( a + b + c ) ^ 2 = 250 + 2 ( 3 ) = 256 = 16 ^ 2 therefore : a + b + c = 16 answer : c"
Answer: c
Problem: if x is a positive number and 5 the square root of x is equal to x / 25 , then x =
Options: a ) 10 , b ) 25 , c ) 5 , d ) 2 , e ) 1
Rationale: "5 of sqrt ( x ) = x / 25 , which means that sqrt ( x ) = x / 5 or x = x ^ 2 / 25 - > divide by x 1 = x / 25 x = 25 b ."
Answer: b
Problem: if sales tax is reduced from 5 % to 4 % , then what difference it will make if you purchase an item of rs . 1000
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: explanation : clue : answer will be 5 % of 1000 - 4 % of 1000 answer : option a
Answer: a
Problem: of all the homes on gotham street , 1 / 3 are termite - ridden , and 1 / 4 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 1 / 6 , e ) 3 / 4
Rationale: "the fraction of homes which are termite - infested but not collapsing is 3 / 4 * 1 / 3 = 1 / 4 the answer is c ."
Answer: c
Problem: convert 100 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 176000 yards
Rationale: "1 mile = 1760 yards 100 miles = 100 * 1760 = 176000 yards answer is e"
Answer: e
Problem: take number 1000 and then add 20 to it . now add 1000 one more time . now add 30 . now add 1000 one more time . now add 40 . now add 1000 one more time . now add 10 . what is the total ?
Options: a ) 4100 , b ) 3590 , c ) 2800 , d ) 3700 , e ) 3600
Rationale: a 4100
Answer: a
Problem: elena ’ s bread recipe calls for 2 ounces of butter for each 5 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 20
Rationale: "solving through algebra route : 2 b + 5 f = x amount if we multiply this equation with 4 we get : 8 b + 20 f = 4 x therefore , we got 8 ounces of butter and 4 x amount of quantity when we use 20 ounces of floor . ans : e"
Answer: e
Problem: three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 38 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters
b ) 36 square meters
c ) 42 square meters
d ) 83.3 square meters
e ) 41 square meters
Rationale: 300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 38 = 82 sq m of the wallpaper overlaps in three layers . 82 sq m makes two extra layers hence the area over which it makes two extra layers is 41 sq m . answer ( e ) .
Answer: e
Problem: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord l in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . l = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Problem: all factors of a positive integer x are multiplied and the product obtained is x ^ 3 . if x is greater than 1 , how many factors does x have ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: the question can be done in seconds if you understand the properties of factors of a number . note that every distinct factor of a number which is not a perfect square has a complementary factor . for example , factors of 6 : 1 , 2 , 3 , 6 1 has a complementary factor 6 such that 1 * 6 = 6 ( the original number ) 2 has a complementary factor 3 such that 2 * 3 = 6 ( the original number ) so if you have a number , n , which is not a perfect square , and start multiplying its factors , you will get n to a certain power . the power will half of the number of factors . for example , 6 has 4 factors and when you multiply all 4 factors , you get 6 ^ 2 ( 2 is half of 4 ) . so if you know that the product of all factors is x ^ 3 , it means there must have been twice the number of factors i . e . 3 * 2 = 6 factors . e )
Answer: e
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 19 marks , what was the maximum marks he could have got ?
Options: a ) 543 , b ) 677 , c ) 770 , d ) 867 , e ) 832
Rationale: "if mike had scored 19 marks more , he could have scored 30 % therefore , mike required 212 + 19 = 231 marks let the maximum marks be m . then 30 % of m = 231 ( 30 / 100 ) × m = 231 m = ( 231 × 100 ) / 30 m = 23100 / 30 m = 770 answer : c"
Answer: c
Problem: mary works in a restaurant a maximum of 40 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 360 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 20 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 20 ) = $ 200 . the total amount is $ 160 + $ 200 = $ 360 answer c 360 ."
Answer: c
Problem: sonika deposited rs . 13000 which amounted to rs . 10200 after 4 years at simple interest . had the interest been 5 % more . she would get how much ?
Options: a ) 18990 , b ) 13002 , c ) 12800 , d ) 12300 , e ) 14500
Rationale: "( 13000 * 4 * 5 ) / 100 = 2600 10200 - - - - - - - - 12800 answer : c"
Answer: c
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , the how old is b ?
Options: a ) 10 years , b ) 12 years , c ) 14 years , d ) 18 years , e ) 16 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 x = 9 . hence , b ' s age = 2 x = 19 years . d )"
Answer: d
Problem: a shopkeeper sells 400 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) rs . 59 , b ) rs . 58 , c ) rs . 09 , d ) rs . 50 , e ) rs . 13
Rationale: "sp per metre = 18000 / 400 = rs . 45 loss per metre = rs . 5 cp per metre = 45 + 5 = rs . 50 answer : d"
Answer: d
Problem: the positive integers m and n leave remainders of 2 and 3 , respectively , when divided by 6 . m > n . what is the remainder when m – n is divided by 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: m is 2 more than a multiple of 6 ; n is 3 more than a multiple of 6 . m - n will be 1 less than a multiple of 6 ( 5 , 11 , 17 , . . . ) , therefore m - n will yield a remainder of 5 when divided by 6 . answer : e .
Answer: e
Problem: the mean of 50 observations was 36 . it was found later that an observation 44 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.22 , b ) 36.12 , c ) 36.22 , d ) 36.42 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 44 - 23 ) = 1821 . â ˆ ´ correct mean = 1821 / 50 = 36.42 . answer d"
Answer: d
Problem: the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5292 sq cm . what is the ratio of the width and the area of the rectangle ?
Options: a ) 1 : 72 , b ) 1 : 76 , c ) 1 : 80 , d ) 1 : 84 , e ) 1 : 88
Rationale: "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 5292 12 x ^ 2 = 5292 x ^ 2 = 441 x = 21 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 84 the answer is d ."
Answer: d
Problem: is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 = > x = 5 hence , b ' s age = 2 x = 10 years . answer : d"
Answer: d
Problem: if a * b = 2 a – 3 b + ab , then 5 * 7 + 7 * 5 is equal to :
Options: a ) 34 , b ) 18 , c ) 72 , d ) 78 , e ) 82
Rationale: 5 * 7 + 7 * 5 = ( 2 * 5 – 5 * 7 + 5 * 7 ) + ( 2 * 7 – 5 * 5 + 7 * 5 ) = ( 10 + 14 – 25 + 35 ) = 34 . answer : a
Answer: a
Problem: two family reunions are happening at the park avenue hotel , the oates reunion and the hall reunion . all 100 guests at the hotel attend at least one of the reunions . if 40 people attend the oates reunion and 70 people attend the hall reunion , how many people attend both reunions
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 22
Rationale: no of people in oates reunion = 40 no of people in hall reunion = 70 attending both = x all guests attend at least one . therefore , 100 = 40 + 70 - ( both ) both = 10 answer c
Answer: c
Problem: a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 4 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 54
Rationale: if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 4 each hour . in any equally spaced list , the median equals the mean . here , the mean is 450 / 9 = 50 , so the median is also 50 , and that is the amount eaten in the 5 th hour . we need to add 4 to find the total eaten in the next hour , so the answer is 54 option e .
Answer: e
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 9 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 9 / 13 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 9 / 4 = s * 13 / 4 tips = s * 9 / 4 fraction of his income came from tips = ( s * 9 / 4 ) / ( s * 13 / 4 ) = 9 / 13 answer : c"
Answer: c
Problem: the largest 5 digit number exactly divisible by 91 is :
Options: a ) 25698 , b ) 581396 , c ) 369741 , d ) 99918 , e ) 1258
Rationale: "explanation : largest 5 - digit number = 99999 91 ) 99999 ( 1098 91 - - - 899 819 - - - - 809 728 - - - 81 - - - required number = ( 99999 - 81 ) = 99918 . answer : d"
Answer: d
Problem: the average age of a husband and his wife was 23 years at the time of their marriage . after 5 years they have a one - year old child . the average age of the family now is :
Options: a ) 25 , b ) 23 , c ) 19 , d ) 18 , e ) 17
Rationale: explanation : sum of the present ages of husband , wife and child = ( 23 * 2 + 5 * 2 ) + 1 = 57 years . required average = ( 57 / 3 ) = 19 years . answer : c
Answer: c
Problem: what sum of money put at c . i amounts in 2 years to rs . 8820 and in 3 years to rs . 9261 ?
Options: a ) rs . 8000 , b ) rs . 8400 , c ) rs . 7500 , d ) rs . 7800 , e ) none of these
Rationale: "explanation : 8820 - - - - 441 100 - - - - ? = > 5 % x * 105 / 100 * 105 / 100 = 8820 x * 1.1025 = 8820 x = 8820 / 1.1025 = > 8000 answer is a"
Answer: a
Problem: if the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres , what is the area of the field in square metres ?
Options: a ) 18000
b ) 40000
c ) 31000
d ) 19000
e ) 16000
Rationale: let breadth is x then length is 30 + x now the perimeter = 2 ( x + 30 + x ) = 540 solving this we get x = 120 now the area is 120 * 150 = 18000 answer : a
Answer: a
Problem: what is the greater of the two numbers whose product is 2560 , given that the sum of the two numbers exceeds their difference by 32 ?
Options: a ) a ) 90 , b ) b ) 100 , c ) c ) 160 , d ) d ) 70 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 32 i . e . , g + s - ( g - s ) = 32 i . e . , 2 s = 32 = > s = 16 g = 2560 / s = 160 . answer : c"
Answer: c
Problem: the profits of qrs company rose 10 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 %
Rationale: "we need multipliers . multiplier for a 10 % increases = 1 + 0.10 = 1.1 multiplier for a 20 % decreases = 1 – 0.20 = 0.8 multiplier for a 50 % increases = 1 + 0.50 = 1.5 now , multiply these . first , multiply ( 0.8 ) and ( 1.5 ) , using the doubling & halving trick . half of 0.80 is 0.40 , and twice 1.5 is 3 ( 0.8 ) * ( 1.5 ) = ( 0.4 ) * ( 3 ) = 1.2 now , multiply this by 1.1 1.2 * 1.1 = 1.32 thus , the three percent changes combined produce a 32 % increase . answer = ( b ) ."
Answer: b
Problem: what will be the cost of building a fence around a circular plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) a ) rs . 3944
b ) b ) rs . 3495.28
c ) c ) rs . 3988
d ) d ) rs . 3949
e ) e ) rs . 3923
Rationale: let the side of the circular plot be a ft . pi * ( r ) ^ 2 = 289 = > r = 9.59 length of the fence = perimeter of the plot = 2 * pi * r = 60.26 ft . cost of building the fence = 60.26 * 58 = rs . 3495.28 answer : b
Answer: b
Problem: the amount of principal rs . 4000 at compound interest at the ratio of 10 % p . a . for 3 years is
Options: a ) rs . 5342 , b ) rs . 4325 , c ) rs . 5324 , d ) rs . 3425 , e ) rs . 3525
Rationale: 5324 answer : c
Answer: c
Problem: twenty eight meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 2 √ 2
b ) 2 √ 5
c ) 5
d ) 7
e ) none of these
Rationale: area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 28 = > x / 360 * 2 * pi * r + 2 r = 28 = > 2 a / r + 2 r = 28 = > a = r 14 - r ^ 2 = r 14 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 14 - 2 r = 0 r = 7 d
Answer: d
Problem: if 2 x = 3 y = 20 , then 12 xy = ?
Options: a ) 1,200 , b ) 800 , c ) 120 , d ) 40 , e ) 20
Rationale: "2 x = 20 ; x = 10 3 y = 20 ; y = 20 / 3 multiply : 12 xy = 12 * 10 * 20 / 3 = 800 . answer : b ."
Answer: b
Problem: when a number is divided by 6 & then multiply by 12 the answer is 12 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 12 = > 2 x = 12 = > x = 6 e"
Answer: e
Problem: divide $ 1162 among a , b , c in the ratio 35 : 28 : 20 .
Options: a ) 490 , 490,490 , b ) 360 , 392,460 , c ) 490 , 392,280 , d ) 260 , 160,60 , e ) 492 , 390,280
Rationale: "sum of ratio terms = ( 35 + 28 + 20 ) = 83 . a ' s share = $ ( 1162 x ( 35 / 83 ) ) = $ 490 ; b ' s share = $ ( 1162 x ( 28 / 83 ) ) = $ . 392 ; c ' s share = $ ( 1162 x ( 20 / 83 ) ) = $ 280 . answer c 490 , 392,280"
Answer: c
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 2 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "rx * ( t + 2 ) = w ry * ( t ) = w . also , w / ( t + 2 ) + w / t = ( 5 w / 4 ) * ( 1 / 3 ) or 1 / t + 1 / ( t + 2 ) = 5 / 12 - - > ( 3 + 2 ) / 12 = 1 / 4 + 1 / 6 thus , t = 4 . replacing , rx = w / 6 , w / 6 * t = 2 w or t = 12 days . answer : e"
Answer: e
Problem: how long will a boy take to run round a square field of side 60 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 96 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 60 * 4 = 240 m time taken = 240 * 2 / 5 = 96 sec answer is a"
Answer: a
Problem: a 60 cm long wire is to be cut into two pieces so that one piece will be 2 / 4 th of the other , how many centimeters will the shorter piece be ?
Options: a ) a ) 73 , b ) b ) 20 , c ) c ) 83 , d ) d ) 21 , e ) e ) 52
Rationale: "explanation : 1 : 2 / 4 = 4 : 2 2 / 6 * 60 = 20 answer : option b"
Answer: b
Problem: a boat running up stram takes 6 hours to cover a certain distance , while it takes 8 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 7 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 8 ( x - y ) 6 x + 6 y = 8 x - 8 y 14 y = 2 x 7 y = x x / y = 7 / 1 7 : 1 answer : option d"
Answer: d
Problem: if a book is sold at 9 % profit instead of 9 % loss , it would have brought rs 9 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 50 , d ) 70 , e ) 80
Rationale: let c . p . of the book be rs . ’ x ’ given , 1.09 x - 0.91 x = 9 = > 0.18 x = 9 = 9 / 0.18 = rs 50 answer : c
Answer: c
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m cube ) is :
Options: a ) 4120 m cube , b ) 4140 m cube , c ) 5140 m cube , d ) 5120 m cube , e ) none of these
Rationale: "explanation : l = ( 48 - 16 ) m = 32 m , [ because 8 + 8 = 16 ] b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m cube = 5120 m cube . option d"
Answer: d
Problem: aarti can do a piece of work in 6 days . in how many days will she complete three time of work of same type ?
Options: a ) 6 days , b ) 18 days , c ) 21 days , d ) 3 days , e ) 13 days
Rationale: "we have the important relation , more work , more time ( days ) a piece of work can be done in 6 days . three times of work of same type can be done in 6 x 3 = 18 days answer b"
Answer: b
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 3 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 218 , c ) 200 , d ) 600 , e ) 211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 3 = > x = 600 answer : d ) rs 600"
Answer: d
Problem: the average ( arithmetic mean ) of 4 positive integers is 45 . if the average of 2 of these integers is 45 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 65 , c ) 100 , d ) 89 , e ) 115
Rationale: "a + b + c + d = 180 a + b = 90 c + d = 90 greatest possible = 89 ( just less than 1 ) answer = d"
Answer: d
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 20 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 30 , d ) 40 , e ) 5
Rationale: arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 40 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 20 hence , the correct answer is a
Answer: a
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,052 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1052 / 1000 ) - 1 = 0.052 = 5.2 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.052 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.052 - 0.01 x = - 0.008 x = - 0.008 / - 0.01 = 8 / 10 = 80 % so x = 80 % of the 1000 which is 800 answer : d"
Answer: d
Problem: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 260 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 104 cm , d ) 120 cm , e ) 130 cm
Rationale: when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 260 2.5 h = 260 h = 104 . c is the answer .
Answer: c
Problem: 16.02 ã — 0.00001 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.00001 = 0.0001602 the answer is e ."
Answer: e
Problem: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 17 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) $ 22.50 , b ) $ 23.50 , c ) $ 24.50 , d ) $ 25.50 , e ) $ 26.50
Rationale: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 17 ) = 0.8 x x = 1.2 ( 17 ) / 0.8 = 1.5 ( 17 ) = $ 25.50 the answer is d ."
Answer: d
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in a hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of a ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * a = 1 = > x = 1 / a when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / a = 4 / 3 = > 1 / a = ( 8 - 3 ) / 6 = 5 / 6 = > a = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Problem: the total age of a and b is 10 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 10 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 10 â € ¹ = â € º a - c = 10 . answer b"
Answer: b
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 5 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 43 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "i think b - 43 / 60 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 5 x so old = x , new = 4 x now 1 / 3 of x are occupied and 1 / 5 of 4 x are occupied which simplifies to ( 4 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 4 / 5 of x occupied in the new ward . add them up to get 17 / 15 of x there are 4 x beds in new tower so ratio is : ( 17 / 15 ) x / 4 x = 17 / 60 of x subtract that from 60 / 60 of x and you get the number of un - occupied beds to total capacity of new tower = 43 / 60 . b"
Answer: b
Problem: what is the probability of having 53 fridays in an ordinary year
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) 1 / 9
Rationale: "1 / 7 because 53 friday in ordinary year then 53 * 7 = 371 ( 53 / 371 = 1 / 7 ) answer : c"
Answer: c
Problem: how many integerskgreater than 100 and less than 900 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be seven pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 7 * 10 = 70 hence c ."
Answer: c
Problem: how many halves are there in 9 - fourth ?
Options: a ) 8 , b ) 4.5 , c ) 3.2 , d ) 7 , e ) 3
Rationale: divide 9 / 4 by 1 / 2 = 9 / 4 ÷ 1 / 2 = 9 / 4 * 2 / 1 = 18 / 4 = 4.5 . answer is b .
Answer: b
Problem: what is the population standard deviation for the numbers : 75 , 83 , 96 , 100 , 121 and 125 ?
Options: a ) 18.2 , b ) 20 , c ) 25 , d ) 26 , e ) 28
Rationale: 1 . firstly find the mean : mean = ( 75 + 83 + 96 + 100 + 121 + 125 ) ÷ 6 = 600 ÷ 6 = 100 2 . next find the variance . to calculate the variance , take each difference , square it , and then average the result : ( 75 - 100 ) 2 + ( 83 - 100 ) 2 + ( 96 - 100 ) 2 + ( 100 - 100 ) 2 + ( 121 - 100 ) 2 + ( 125 - 100 ) 2 = ( - 25 ) 2 + ( - 17 ) 2 + ( - 4 ) 2 + ( 0 ) 2 + ( 21 ) 2 + ( 25 ) 2 = 625 + 289 + 16 + 0 + 441 + 625 = 1996 so the variance = 1996 ÷ 6 = 332.66 . . . 3 . the standard deviation is just the square root of the variance = √ ( 332.66 . . . ) = 18.2 correct to 1 decimal places answer is a
Answer: a
Problem: 63 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 128 , c ) 152 , d ) 216 , e ) 153
Rationale: "63 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 63 = 153 hence , e is the answer ."
Answer: e
Problem: there are two tanks a & b with same capacity of 20 litres . if the water inflow rate ( speed ) in tank a is 2 litres per hour & in tank b is 4 litres per hour . how much longer tank a takes to fill than tank b ?
Options: a ) 4 hours , b ) 5 hours , c ) 3 hours , d ) 2 hours , e ) 1 hour
Rationale: time taken for tank a to fill = 20 / 2 = 10 hours time taken for tank b to fill = 20 / 4 = 5 hours so tank a takes 5 more hours to fill answer : b
Answer: b
Problem: while calculating the edge of a square , a worker makes an error of 2 % in excess . what % error does he make in calculating area ? ( % )
Options: a ) 4.09
b ) 4.0
c ) 4.04
d ) 4.02
e ) 4.01
Rationale: explanation : given error = 2 % while measuring the side of a square . if the correct value of the side of square is 100 , the measured value : = > 100 + 2 % * 100 = 100 + 2 = 102 the area of square with edge 100 = side * side = > 100 * 100 = > 10000 the area of square with side 102 = 102 * 102 = 10404 error in area calculation = 10404 - 1000 = 404 % error = ( 404 / 10000 ) * 100 = 4.04 % answer : c
Answer: c
Problem: how many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "total multiples of 13 : 15 ( first multiple : 13 , last multiple : 195 ) total multiples of 12 : 16 ( first multiple : 12 , last multiple : 192 ) multiple of 12 and 13 : 1 ( 156 ) 15 + 16 - 1 = 30 answer : c"
Answer: c
Problem: if a / b = 1 / 2 , b / c = 5 , c / d = 2 / 3 , d / e = 1 / 6 and e / f = 2 / 3 , then what is the value of abc / def ?
Options: a ) 50 / 729 , b ) 20 / 456 , c ) 45 / 752 , d ) 13 / 452 , e ) 45 / 741
Rationale: "say a = 2 . then : a / b = 1 / 2 - - > b = 4 ; b / c = 5 - - > c = 4 / 5 ; c / d = 2 / 3 - - > d = 6 / 5 ; d / e = 1 / 6 - - > e = 36 / 5 ; e / f = 2 / 3 - - > f = 54 / 2 . abc / def = ( 2 * 4 * 4 / 5 ) / ( 6 / 5 * 36 / 5 * 54 / 5 ) = 50 / 729 . answer : a ."
Answer: a
Problem: a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 40,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 103 , c ) 105 , d ) 115 , e ) 125
Rationale: "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 40000 - 30000 = 10000 so 25 more machines . . total = 125 machines imo e . . ."
Answer: e
Problem: find the average of all the numbers between 6 and 30 which are divisible by 4 .
Options: a ) 15 , b ) 18 , c ) 20 , d ) 22 , e ) none
Rationale: "sol . average = ( 8 + 12 + 16 + 20 + 24 + 28 / 6 ) = 108 / 6 = 18 answer b"
Answer: b