Cheukting/mathqa huggingface dataset:
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): ( 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (general): 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