regisss/math_qa huggingface dataset:
Problem: the price of a tv was increased by 30 percent . the new price was then increased by 20 percent . a single increase of what percent is equivalent to these two successive increases ?
Options: a ) 50 % , b ) 60 % , c ) 65 % , d ) 56 % , e ) 45 %
Rationale: consider base price - $ 100 25 % increase = 1.30 * 100 = $ 130 another 20 % increase on new price = 1.2 * 130 = $ 156 so final price of radio - $ 156 therefore a 56 % increase correct option - d
Answer: d
Problem: simplify : 500 x 500 - 200 x 200
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 210000 , e ) none of them
Rationale: "( 500 ) ^ 2 - ( 200 ) ^ 2 = ( 500 + 200 ) ( 500 - 200 ) = 700 x 300 = 210000 . answer is d ."
Answer: d
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 4320 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 12000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 4320 â ˆ — 100 / 12 â ˆ — 3 = rs 12000 option c"
Answer: c
Problem: a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 10 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 27 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 10 % are male i . e 10 / 100 * 20 = 2 geese ( males ) and now we know out of the total 20 geese , 2 are male , then 18 have to be female . now the ratio part , male geese ratios = 2 / 30 = 1 / 15 . - a female geese ratios = 18 / 70 = 9 / 35 - b cross multiply equations a and b and you get = 7 / 27 . ans d"
Answer: d
Problem: of 64 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 64 thrower = 37 rest = 64 - 37 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 37 + 18 = 55 so b . 55 is the right answer"
Answer: b
Problem: pipe a can fill a tank in 30 minutes . pipe b can fill the same tank 6 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 15 / 4 minutes , c ) 192 / 7 minutes , d ) 224 / 7 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 30 minutes - - > the rate of a = 1 / 30 tank / minute ; pipe b can fill the same tank 6 times fasterthan pipe a - - > the rate of b = 1 / 30 + 6 / 30 = 7 / 30 tank / minute . their combined rate = 1 / 30 + 7 / 30 = 4 / 15 tank / minute ; therefore , a and b can fill the tank in 15 / 4 minutes . answer : b"
Answer: b
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 9 days , then c alone can do it in ?
Options: a ) 11 , b ) 17 , c ) 18 , d ) 19 , e ) 16
Rationale: "c = 1 / 4 - 1 / 12 – 1 / 9 = 1 / 18 = > 18 days ' answer : c"
Answer: c
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6.4 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: since michelle earns 6.4 % interest compounded semiannually , then she earns 3.2 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3.2 % * 5 = 16 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 16 % , only answer choice a fits . answer : a
Answer: a
Problem: a certain maroon paint contains 50 percent blue pigment and 50 percent red pigment by weight . a certain green paint contains 30 percent blue pigment and 70 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 ) 3 , b ) 3.5 , c ) 2.5 , d ) 4 , e ) 4.5
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 * . 5 = 2.5 grams of red pigment
Answer: c
Problem: chris age after 15 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) 20 , b ) 25 , c ) 15 , d ) 22 , e ) 10
Rationale: "chris present age = x after 15 years = x + 15 5 years back = x - 5 x + 15 = 5 ( x - 5 ) x = 10 answer is e"
Answer: e
Problem: a can do a work in 14 days and working together a and b can do the same work in 10 days . in what time can b alone do the work ?
Options: a ) 25 days , b ) 30 days , c ) 23 days , d ) 35 days , e ) 45 days
Rationale: work done by b in 1 day = 1 / 10 - 1 / 14 = ( 7 - 5 ) / 70 = 1 / 35 so , b alone can do the work in 35 days . answer : d
Answer: d
Problem: if the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 53 , c ) 49 , d ) 48 , e ) 44
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 45 = 225 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 225 i . e . 5 a = 215 i . e . a = 43 i . e . largest e = 43 + 10 = 53 answer : option b"
Answer: b
Problem: find the lowest common multiple of 24 , 30 and 40 .
Options: a ) 360 , b ) 420 , c ) 120 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 5 = 120 . answer is c"
Answer: c
Problem: a certain number when divided by 39 leaves a remainder 15 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 2
Rationale: "explanation : 39 + 15 = 54 / 13 = 2 ( remainder ) answer : e"
Answer: e
Problem: a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 13.3 hrs , c ) 1.9 hrs , d ) 7.2 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 5 - 1 / 8 ) = 3 / 40 the cistern will be filled in 40 / 3 hrs i . e . , 13.3 hrs . answer : b"
Answer: b
Problem: a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 4 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 2 / 5 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 4 / 8 * c : ( b + c ) / 2 = ( 4 / 8 ) * c b = 0 for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 0 ) / 2 = 0 median = ( a + c ) / 2 = ( 0 + c ) / 2 = c / 2 = ( 1 / 2 ) * c ( answer b )"
Answer: b
Problem: a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 360 less than the sum lent . what was the sum lent ?
Options: a ) 540 , b ) 560 , c ) 580 , d ) 600 , e ) 680
Rationale: "p - 360 = ( p * 5 * 8 ) / 100 p = 600 the answer is d ."
Answer: d
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 19 days more ?
Options: a ) 11 , b ) 40 , c ) 66 , d ) 55 , e ) 44
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 19 x * 19 = 760 * 20 x = 800 760 - - - - - - - 40 answer : b"
Answer: b
Problem: if p represents the product of the first 14 positive integers , then p is not a multiple of
Options: a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 85
Rationale: "answer is e . since prime factor of 85 is 5 x 17 . 17 is a prime number and not part of the first 14 positive integers . a ) 9 x 11 b ) 12 x 7 c ) 12 x 6 d ) 13 x 5 e ) 5 x 17"
Answer: e
Problem: how many pieces of 0.36 meteres can be cut from a rod 26.5 meteres long
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 73
Rationale: "explanation : we need so simple divide 26.5 / 0.36 , = ( 2650 / 36 ) = 73 option d"
Answer: d
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 25 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 36 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.4 x + 1.0 x = 1.4 x 1.4 x / 5 x = 0.28 the answer is a ."
Answer: a
Problem: the temperature of a certain cup of coffee 5 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 61.875 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 5 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 5 a ) + 60 60 = 120 * ( 2 ^ - 5 a ) 60 / 120 = 2 ^ - 5 a 1 / 2 = 2 ^ - 5 a 2 ^ - 1 = 2 ^ - 5 a - 1 = - 5 a 1 / 5 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 5 * 30 ) + 60 f = 120 * ( 2 ^ - 6 ) + 60 f = 120 * ( 1 / 2 ^ 6 ) + 60 f = 120 * 1 / 64 + 60 f = 1.875 + 60 = 61.875 answer b !"
Answer: b
Problem: 5 n + 2 > 12 and 7 n - 12 < 44 ; n must be between which numbers ?
Options: a ) 2 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9
Rationale: "5 n + 2 > 12 5 n > 10 n > 2 7 n - 12 < 44 7 n < 56 n < 8 so n must be between 2 and 8 2 < n < 8 correct answer a"
Answer: a
Problem: a pupil ' s marks were wrongly entered as 73 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 56 , b ) 80 , c ) 20 , d ) 25 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 73 - 45 ) = > x / 2 = 28 = > x = 56 . answer : a"
Answer: a
Problem: a cube of edge 8 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25 , b ) 1 : 22 , c ) 1 : 52 , d ) 1 : 64 , e ) none
Rationale: "sol . required ratio = 6 * 1 * 1 / 6 * 8 * 8 = 1 / 64 = 1 : 64 . answer d"
Answer: d
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 6 ] ] ?
Options: a ) 3 , b ) 52 , c ) 15 , d ) 19 , e ) 25
Rationale: "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 6 ] ] = 6 ^ 2 + 2 * 6 + 4 = 52 . option b"
Answer: b
Problem: 2015.98 + 1275.087 – 175.98 × 0.95 + 988.09 = ?
Options: a ) 4004 , b ) 4725 , c ) 4404 , d ) 4044 , e ) 4055
Rationale: "explanation : = 2016 + 1275 – 275.98 × 1 + 988 = 2016 + 1275 - 275 + 988 = 4004 answer : option a"
Answer: a
Problem: the sum of ages of 5 children born 3 years different each is 50 yrs . what is the age of the elder child ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 19 , e ) 20
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . x + 12 = 4 + 12 = 16 c"
Answer: c
Problem: the average of 6 no . ' s is 5.40 . the average of 2 of them is 5.2 , while the average of the other 2 is 5.80 . what is the average of the remaining 2 no ' s ?
Options: a ) 5.2 , b ) 2.6 , c ) 3.6 , d ) 4.5 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 5.40 * 6 ) - [ ( 5.2 * 2 ) + ( 5.8 * 2 ) ] = 32.40 - ( 10.4 + 11.6 ) = 32.40 - 22.0 = 10.40 . required average = ( 10.4 / 2 ) = 5.2 answer : a"
Answer: a
Problem: a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 5 tons ?
Options: a ) 12 , b ) 24 , c ) 36 , d ) 48 , e ) 60
Rationale: the weight of one car and one truck is 5.75 tons . 70 / 5.75 = 12 plus a remainder the ferry could carry 12 cars and 12 trucks for a total of 24 vehicles . the answer is b .
Answer: b
Problem: x , a , z , and b are single digit positive integers . x = 1 / 8 a . z = 1 / 8 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 28 , b ) 35 , c ) 49 , d ) 63 , e ) 55
Rationale: "a = 8 x , b = 8 z therefore ( 8 x . 10 + 8 z ) - ( 10 x + z ) = ( 8 - 1 ) ( 10 x + z ) = 7 . ( 10 x + z ) number should be divisible by 7 e"
Answer: e
Problem: two positive integers differ by 4 , and sum of their reciprocals is 4 . then one of the numbers is
Options: a ) a ) 3 , b ) b ) 1 , c ) 2 , d ) d ) 21 , e ) e ) 28
Rationale: "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 4 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 4 or ( n ^ 2 + 4 n ) * 4 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , c"
Answer: c
Problem: if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 110 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 71 , b ) 72 , c ) 73 , d ) 74 , e ) 75
Rationale: let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 110 3 x = 105 x = 35 kg then the student ' s weight is 75 kg . the answer is e .
Answer: e
Problem: what annual installment will discharge a debt of rs . 1428 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 345 , c ) 425 , d ) 335 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1428 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1428 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1428 * 25 ) x = ( 1428 * 25 ) / 84 = rs . 425 . therefore , each installment = rs . 425 . answer is c ."
Answer: c
Problem: in a group of ducks and cows , the total number of legs are 16 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 8 , d ) 12 , e ) 14
Rationale: let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 16 = > 2 x = 16 = > x = 8 c
Answer: c
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 4 . if x invested rs . 40,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 40000 / y = 2 / 4 â € ¹ = â € º y = ( 40000 ã — 4 / 2 ) . â € ¹ = â € º y = 80000 . answer d"
Answer: d
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 110 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 55 , c ) 56 , d ) 16 , e ) 14
Rationale: 10 x = 110 = > x = 11 therefore the secretary who worked the longest spent 11 x 5 = 55 hours on the project option ( b )
Answer: b
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 155 kg then find the average weight of all the 7 rounds ?
Options: a ) 98.5 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 155 / 7 = 88.5 kgs answer : b"
Answer: b
Problem: set j consists of 18 consecutive even numbers . if the smallest term in the set is - 12 , what is the range of the positive integers in set j ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "since there are only 18 integers , another approach is the just list all 18 . we get : - 12 , - 10 , - 8 , - 6 , - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 range of positive integers = 22 - 2 = 20 answer : c"
Answer: c
Problem: what is the remainder when 1201 × 1202 × 1203 × 1207 is divided by 6 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the remainders when dividing each number by six are : 1 , 2 , 3 , and 1 . the product is 1 * 2 * 3 * 1 = 6 the remainder when dividing 6 by 6 is 0 . the answer is a ."
Answer: a
Problem: find the area of circle whose diameter is 8 m .
Options: a ) 50.00 square meter
b ) 50.04 square meter
c ) 50.28 square meter
d ) 50.24 square meter
e ) 50.43 square meter
Rationale: diameter = 8 meter . radius = diameter / 2 . = 8 / 2 . = 4 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 4 . area of a circle = 3.14 ã — 4 ã — 4 . . = 3.14 ã — 16 . = 50.28 square meter answer : c
Answer: c
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many s hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in s = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 56 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 450,000 , e ) $ 640,000
Rationale: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 56 years , the investment will get doubled 56 / 14 = 4 times . so the amount invested will get doubled thrice . so , 40000 * 2 ^ 4 = 640000 hence , the answer is e .
Answer: e
Problem: having received his weekly allowance , a student spent 2 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.20 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 2.00 , b ) $ 2.25 , c ) $ 2.50 , d ) $ 2.75 , e ) $ 3.00
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 3 / 5 ) x = 120 cents ( 2 / 5 ) x = 120 x = $ 3.00 the answer is e ."
Answer: e
Problem: ashley paid 5 dollars for 1 notebook and 1 pencil . if both prices were integers , how many pencils did ashley buy if she paid 93 dollars for the pencils and for 15 notebooks ?
Options: a ) 6 . , b ) 16 . , c ) 18 , d ) 21 , e ) 26
Rationale: 5 = 1 p + 1 n 93 = xp + 15 n , where x is the number of pencils possible prices for 1 p & 1 n ( integers ) : n = 1 p = 4 then 15 n = 15 , 4 x = 93 - 15 = 78 , x = 19.5 ( not an integer ) n = 2 p = 3 then 15 n = 30 , 3 x = 93 - 30 = 63 , x = 21 ( the answer we were looking for , no need to continue calculations ) n = 3 p = 2 n = 4 p = 1 answer : d
Answer: d
Problem: what is 2 2 / 3 - 1 1 / 4 divided by 1 / 5 - 1 / 6 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 85 / 2 , e ) 51 / 4
Rationale: "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 5 - 1 / 6 = ( 6 - 5 ) / 30 = 1 / 30 so 17 / 12 / 1 / 30 = 17 / 12 * 30 = 85 / 2 answer - d"
Answer: d
Problem: a train running at the speed of 142 km / hr crosses a pole in 12 seconds . find the length of the train .
Options: a ) 540 , b ) 288 , c ) 200 , d ) 340 , e ) 712
Rationale: "speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time 45 * 12 = 540 meter answer : a"
Answer: a
Problem: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 10 inches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 10 , b ) 20 , c ) 17.5 , d ) 43 , e ) 50
Rationale: "his height was = 5 feet 5 inch = 10 + 60 = 70 inch . required % correction = 70 * ( 1.25 - 1 ) = 17.5 c"
Answer: c
Problem: at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint . how many liters of blue paint must be added to 16 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "in 16 liters , red = 5 / 8 * 16 = 10 and blue = 6 so , 10 / ( 6 + x ) = 3 / 6 or , x = 14 ( answer c )"
Answer: c
Problem: the difference between c . i . and s . i . on an amount of $ 20,000 for 2 years is $ 98 . what is the rate of interest per annum ?
Options: a ) 9 % , b ) 8 % , c ) 7 % , d ) 6 % , e ) 5 %
Rationale: "$ 98 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 20000 * x . the interest on the first year ' s interest is 20000 * x * x 20000 * x ^ 2 = 98 x = 0.07 the answer is c ."
Answer: c
Problem: in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 3 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.01
Rationale: "number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 3 = ~ 4.14 passengers using logan airport = 4.14 / 4 = ~ 1.01 so e"
Answer: e
Problem: ( 4300431 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764813 , d ) 1675123 , e ) none of them
Rationale: "let 4300431 - x = 2535618 then x = 4300431 - 2535618 = 1764813 answer is c"
Answer: c
Problem: by selling 18 pencils for a rupee a man loses 15 % . how many for a rupee should he sell in order to gain 15 % ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 89 , e ) 81
Rationale: "85 % - - - 18 115 % - - - ? 85 / 115 * 18 = 13 answer : b"
Answer: b
Problem: a contractor undertakes to do a piece of work in 40 days . he engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time . if he had not engaged the additional men , how many days behind schedule would it be finished ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 2
Rationale: explanation : \ inline \ fn _ jvn [ ( 100 \ times 35 ) + ( 200 \ times 5 ) ] men can finish the work in 1 day \ inline \ fn _ jvn \ therefore 4500 men can finish the work in 1 day . 100 men can finish it in \ inline \ fn _ jvn \ frac { 4500 } { 100 } = 45 days . this is 5 days behind schedule answer : b
Answer: b
Problem: how many integers are between 4 and 88 / 9 , inclusive ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "88 / 9 = 9 . xx we are not concerned about the exact value of 88 / 9 as we just need the integers . the different integers between 4 and 88 / 9 would be 4 , 5 , 6 , 7 , 8 , 9 total number of integers = 6 option d"
Answer: d
Problem: how many integers from 1 to 100 ( both inclusive ) have odd number of factors ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) greater than 10
Rationale: all perfect squares have odd # of factors . squaring integers 1 - 10 produces 1 , 4 , 9 , 16 , . . . 100 which all have odd # of factors . answer is d
Answer: d
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 278 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: "consider sister weight now as x jakes weight ( 2 times + 8 ) = 2 x + 8 ( 2 x + 8 ) + ( x ) = 278 x = 90 jake ' s weight is . . . . 188 correct answer is e"
Answer: e
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 12000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 14520
Rationale: "the required population is = 12000 ( 1 + 10 / 100 ) ^ 2 = 12000 * 11 / 10 * 11 / 10 = 14520 answer is e"
Answer: e
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 65.50 , his capital is ?
Options: a ) 24,602 , b ) 26,200 , c ) 24,600 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 65.50 32 x - 31 x = 6550 * 4 x = 26,200 . answer : b"
Answer: b
Problem: a monkey start climbing up a tree 19 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 16 hrs it wil be 16 ft . bt since the height of the tree is 19 ft , so if the monkey hops up the tree in the next hr i . e 17 th hr then it reaches at the top of the tree . hence it takes 17 hrs for monkey to reach at the top answer : d"
Answer: d
Problem: find the value of y from ( 12 ) ^ 2 x 6 ^ 3 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 72
Rationale: "72 e"
Answer: e
Problem: before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 6.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 10 , d ) 1 / 78 , e ) 30
Rationale: "pete covered 6.5 * 60 = 390 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 390 = 1 / 78 . answer : d ."
Answer: d
Problem: a cistern 12 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 64 , b ) 72 , c ) 80 , d ) 88 , e ) 96
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 12 x 1.25 ) + 12 x 4 ] = 88 the answer is d ."
Answer: d
Problem: the instructions state that cheryl needs 2 / 9 square yards of one type of material and 1 / 8 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 4 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 1 / 8 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: total bought = 2 / 9 + 1 / 8 left part 4 / 18 - - - > 2 / 9 so used part 2 / 9 + 1 / 8 - 2 / 9 = 1 / 8 answer : c
Answer: c
Problem: the average age of 17 students of a class is 17 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 17 th student is
Options: a ) 62 , b ) 66 , c ) 18 , d ) 75 , e ) 12
Rationale: "explanation : age of the 17 th student = [ 17 * 17 - ( 14 * 5 + 16 * 9 ) ] = ( 289 - 214 ) = 75 years . answer : d"
Answer: d
Problem: right triangle abc is the base of the prism in the figure above . if ab = ac = √ 2 and the height of the prism is 3 , what is the volume of the prism ?
Options: a ) 1
b ) 3 / 2
c ) 2
d ) 3
e ) 6
Rationale: volume of prism = area of base * height = 1 / 2 * ( square root of 2 ) * ( square root of 2 ) * 3 = 3 answer : d
Answer: d
Problem: in a dairy farm , 20 cows eat 20 bags of husk in 20 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 20 cows per day ⇒ 20 × 1 × 20 = 1 × 20 × x for one cow = 20 days answer : c"
Answer: c
Problem: the average ( arithmetic mean ) of 4 different integers is 68 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 5 , b ) 19 , c ) 29 , d ) 30 , e ) 33
Rationale: "total of integers = 68 * 4 = 272 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 = 272 - ( 90 + 89 + 88 ) = 272 - 267 = 5 answer : a"
Answer: a
Problem: how much more would rs . 60000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 482 , b ) 725 , c ) 992 , d ) 1446 , e ) 923
Rationale: "60000 ( 11 / 10 ) 4 - 60000 ( 6 / 5 ) 2 = 1446 answer : d"
Answer: d
Problem: ramu bought an old car for rs . 45000 . he spent rs . 12000 on repairs and sold it for rs . 80000 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 40 % , d ) 58 % , e ) 13 %
Rationale: "total cp = rs . 45000 + rs . 12000 = rs . 57000 and sp = rs . 80000 profit ( % ) = ( 80000 - 57000 ) / 57000 * 100 = 40 % answer : c"
Answer: c
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 15 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 6
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 15 / 2.5 ) = 6 hrs answer : e"
Answer: e
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 198 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 13
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 198 - $ 120 = $ 78 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 78 / $ 6 = 13 ans is e"
Answer: e
Problem: a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 10 : 30 am in the same direction at the rate of 84 km / h . at what time will the second train catch the first train ?
Options: a ) 4 : 30 , b ) 5 : 00 , c ) 5 : 30 , d ) 6 : 00 , e ) 6 : 30
Rationale: "in one hour and thirty minutes the first train travels 105 km . the second train catches the first train at a rate of 84 km / h - 70 km / h = 14 km / h . the second train will catch the first train in 105 / 14 = 7.5 hours , so at 6 : 00 pm . the answer is d ."
Answer: d
Problem: a grocery store bought some apples at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples ?
Options: a ) 1 : 7 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 2 , e ) 2 : 5
Rationale: to avoid fractions , assume there were 45 apples . so the store bought them for 45 / 5 = 9 dollars . to break even , the selling price should be $ 9 too . 45 mangoes can be split into 1 : 4 , 2 : 3 or 1 : 2 . so let ' s try these . 45 split in the ratio 1 : 4 gives 9 and 36 . 9 apples split into 3 apples each will give $ 3 . 36 apples split into 6 apples each will give $ 6 . they add up to $ 9 so we have hit the right answer . answer ( c )
Answer: c
Problem: if 11 lions can kill 11 deers in 11 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 11 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 11 ( lions ) * 11 ( min ) / 11 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 11 answer : b"
Answer: b
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 6 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 19 : 2 , b ) 18 : 3 , c ) 29 : 11 , d ) 29 : 5 , e ) 29 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 6 = 15 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 4 + 7 / 2 = 29 / 4 = 7.25 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 7.25 : 2.75 = 29 : 11 . answer : c"
Answer: c
Problem: what is 1 percent of 12,356 ?
Options: a ) 123.56 , b ) 1.2356 , c ) 12.356 , d ) 0.012356 , e ) 0.0012356
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 1 ( 1 / 100 ) 12,356 . the answer is 123.56 . hence , the correct answer is a .
Answer: a
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 3 . answer : b .
Answer: b
Problem: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 35 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 48.3 % , b ) 52.8 % , c ) 55.5 % , d ) 58.3 % , e ) 61.4 %
Rationale: "35 % is 5 % - points above 30 % and 25 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 5 : 1 . 5 / 6 * 70 % = 58.3 % the answer is d ."
Answer: d
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 70 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 7 / 48,000 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 70 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 70 / 800 * 1 / 600 = 7 / 48,000 . answer : c ."
Answer: c
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 9 , b ) 5 , c ) 7 , d ) 6 , e ) 10
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 24 / 60 ) ) km = 10 km . answer : e"
Answer: e
Problem: the instructions state that cheryl needs 4 / 9 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: "total bought = 4 / 9 + 2 / 3 left part 8 / 18 - - - > 4 / 9 so used part 4 / 9 + 2 / 3 - 4 / 9 = 2 / 3 answer : c"
Answer: c
Problem: a sells a bicycle to b at a profit of 30 % and b sells it to c at a loss of 20 % . find the resultant profit or loss .
Options: a ) 5 % , b ) 4 % , c ) - 4 % , d ) - 12 % , e ) 2 %
Rationale: the resultant profit or loss = 30 - 20 - ( 30 * 20 ) / 100 = 4 % profit = 4 % answer is b
Answer: b
Problem: a man can row at 6 kmph in still water . if the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back , how far is the place ?
Options: a ) 5.33 km , b ) 6.33 km , c ) 5.63 km , d ) 7.33 km , e ) 5.93 km
Rationale: "speed in still water = 6 kmph speed of the current = 2 kmph speed downstream = ( 6 + 2 ) = 8 kmph speed upstream = ( 6 - 2 ) = 4 kmph let the required distance be x km total time taken = 2 hour x / 8 + x / 4 = 2 x + 2 x / 8 = 2 3 x / 8 = 2 3 x = 16 x = 5.33 km answer : a"
Answer: a
Problem: in a survey of 335 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 38 / 67 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 91
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 281 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 335 we have to find not part time and not uninsured . in other words not part time and insured = x / 335 = ( 281 - 104 + 13 ) / 335 = 38 / 67 answer is a ."
Answer: a
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1 , 500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 10 5 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the ratio of investments is 500 : 1,500 = 1 : 3 . the deviation from the average return from $ 500 investment and $ 1,500 investment must be in the ration 3 : 1 . $ 500 investment return has the deviation from the mean of 8.5 - 7 = 1.5 % , thus $ 1,500 investment return must have the deviation from the mean equal to 0.5 % , which means that $ 1 , 500 investment has 8.5 + 0.5 = 9 % yearly return . answer : a ."
Answer: a
Problem: 8 : 4 seconds : : ? : 4 minutes
Options: a ) 10 , b ) 8 , c ) 20 , d ) 25 , e ) 30
Rationale: "8 * 4 = 4 * x x = 8 answer : b"
Answer: b
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 7 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 m 3 , b ) 4580 m 3 , c ) 10500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 7000 * 2 * 45 ) / 60 = 10500 m 3 answer : option c"
Answer: c
Problem: what is the area of square field whose side of length 10 m ?
Options: a ) 100 , b ) 662 , c ) 772 , d ) 882 , e ) 21
Rationale: "10 * 10 = 100 sq m answer : a"
Answer: a
Problem: at a local appliance manufacturing facility , the workers received a 25 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 125 = 1250 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 125 = 8 so he can reduce his work by 2 hours . which is 20 % . answer c"
Answer: c
Problem: if 625 ^ ( - x ) + 5 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . a"
Answer: a
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4529 , b ) s . 4586 , c ) s . 4597 , d ) s . 4530 , e ) s . 5436
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 6 = rs . 5436 answer : e"
Answer: e
Problem: a car dealership has 40 cars on the lot , 10 % of which are silver . if the dealership receives a new shipment of 80 cars , 25 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 21 % , e ) 22 %
Rationale: the number of silver cars is 0.1 * 40 + 0.25 * 80 = 24 the percentage of cars which are silver is 24 / 120 = 20 % the answer is c .
Answer: c
Problem: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 333 and for 36 kgs of apples is 366 then the cost of first 15 kgs of apples is
Options: a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 150 , e ) 3.61
Rationale: "ans : by framing equations we get 30 l + 3 q = 333 30 l + 6 q = 366 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 60 l + 6 q = 666 30 l + 6 q = 366 30 l = 300 = > l = 10 then we get l = 10 cost of 15 kgs of apples = 15 x 10 = 150 answer : d"
Answer: d
Problem: the sub - duplicate ratio of 16 : 36 is
Options: a ) 4 : 6 , b ) 1 : 2 , c ) 1 : 3 , d ) 1 : 4 , e ) 2 : 3
Rationale: "root ( 16 ) : root ( 36 ) = 4 : 6 answer : a"
Answer: a
Problem: there are 2 red chips and 4 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 50 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ b _ b _ b _ b so . . 6 ! / number of repeated letters ( 2 ! ) ( 4 ! ) = 10 ans : e"
Answer: e
Problem: a can give b 70 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 139.78 , b ) 139.13 , c ) 139.22 , d ) 111.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 930 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 930 = 860.21 m . b can give c = 1000 - 860.21 = 139.78 m . answer : a"
Answer: a
Problem: find the area of trapezium whose parallel sides are 10 cm and 18 cm long , and the distance between them is 10.00001 cm .
Options: a ) 140 cm 2 , b ) 185 cm 2 , c ) 185 cm 2 , d ) 185 cm 2 , e ) 195 cm 2
Rationale: "explanation : area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 10 + 18 ) * ( 10 ) = 140 cm 2 answer : option a"
Answer: a
Problem: a car drives 40 miles on local roads at 20 mph , and 180 miles on the highway at 60 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 52 mph , e ) 58 mph
Rationale: "explanations 1 ) in phase # 1 of the trip , the car traveled 40 mi at 20 mph . that time of this phase was : time = distance / rate = ( 40 mi ) / ( 20 mph ) = 2 hr in phase # 2 of the trip , the car traveled 180 mi at 60 mph . that time of this phase was : time = distance / rate = ( 180 mi ) / ( 60 mph ) = 3 hr the total distance of the trip = 40 mi + 180 mi = 220 mi the total time of the trip = 2 hr + 3 hr = 5 hr the average speed of trip is given by speed = distance / time = ( 220 mi ) / ( 5 hr ) = 44 mph answer : c ."
Answer: c
Problem: a man sold 18 toys for rs . 16800 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) rs . 600 , b ) rs . 800 , c ) rs . 500 , d ) rs . 900 , e ) rs . 970
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 16800 . gain = sp – cp 3 x = 16800 – 18 x 21 x = 16800 x = rs . 800 . answer : b"
Answer: b
Problem: in the coordinate plane , points ( x , 1 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x + y =
Options: a ) 6.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 1 ) = ( 4 , 1 ) and ( 10 , y ) = ( 10 , 2.5 ) - - > x + y = 4 + 2.5 = 6.5 answer : a ."
Answer: a
Problem: a doctor prescribed 20 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 25 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 20 c . c % prescribed dosage greater than the typical dosage = ( 20 - 16 / 16 ) * 100 % = ( 2 / 16 ) * 100 % = 25 % answer a"
Answer: a
Problem: the ratio between the present age of p and q is 6 : 7 . if q is 4 years old then p , what will be the ratio of the ages of p and q after 4 year ?
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 7 : 8 , d ) 4 : 3 , e ) none of these
Rationale: "solution let p ' s age and q ' s age be 6 x years and 7 x years respectively . then , 7 x - 6 x = 4 ⇔ x = 4 . ∴ required ratio = ( 6 x + 4 ) : ( 7 x + 4 ) = 28 : 32 = 7 : 8 . answer c"
Answer: c
Problem: 3 people have $ 28 , $ 72 , and $ 98 , respectively . if they pool their money then redistribute it among them , what is the maximum value for the median amount of money ?
Options: a ) $ 72 , b ) $ 85 , c ) $ 99 , d ) $ 101 , e ) $ 202
Rationale: solution - total money distributed is $ 198 . in order to maximize median , one person has to accept $ 0 and remaining two people share $ 99 each . hence median is $ 99 . ans c
Answer: c