Cheukting/mathqa huggingface dataset:
Question (other): the ratio of two quantities is 7 to 12 . if each of the quantities is divided by 3 , what is the ratio of these 2 new quantities ?
Options: a ) 3.5 : 6 , b ) 14 : 24 , c ) 7 : 12 , d ) 2.3 : 4 , e ) it can not be determined from the information given
Rationale: "if both sides of a ratio are divided by the same number there is no change in the ratio . 5 : 6 means 7 x : 12 x . . . the ratio starts as 7 / ( 1 ) : 12 / ( 1 ) . so when you diveide by three it becomes 7 / ( 3 ) : 12 / ( 3 ) . . so if the xs are equal the ratio does not change . . answer : c"
Answer: c
Question (gain): if 45 % of z is 72 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 120 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 72 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 72 / 100 ) * ( 3 / 4 ) x i . e . z = ( 72 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.2 ) x = ( 120 / 100 ) x i . e . z is 120 % of x answer : option b"
Answer: b
Question (physics): a certain car can travel 40 minutes on a gallon of gasoline at 70 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 30 % , c ) 25 % , d ) 20 % , e ) 40 %
Rationale: let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 70 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 40 mins ( @ 60 miles / hr ) = ( 70 / 70 ) * 40 = 40 miles fuel used to travel 80 miles = ( 80 / 40 ) = 2 gallon i . e . used fuel = ( t - 8 ) = 2 gallon i . e . t = 10 gallons i . e . used fuel = ( 2 / 10 ) * 100 = 20 % d
Answer: d
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 420 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 620 , c ) 500 , d ) 520 , e ) 840
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 420 ) = 2 + 2 ( extra ) = > 2 x - 840 = x = > x = 840 . answer : e"
Answer: e
Question (gain): population of a city in 20004 was 1200000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 1300650
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1300650 e"
Answer: e
Question (physics): two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.15
Rationale: t = ( 111 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 6.85 answer : c
Answer: c
Question (gain): working alone , mary can pave a driveway in 5 hours and hillary can pave the same driveway in 2 hours . when they work together , mary thrives on teamwork so her rate increases by 33.33 % , but hillary becomes distracted and her rate decreases by 50 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 5 per hour hillary = 1 / 2 per hour rate when working together : mary = 1 / 5 + ( 1 / 3 * 1 / 5 ) = 1 / 4 per hour hillary = 1 / 2 - ( 1 / 2 * 1 / 2 ) = 1 / 4 per hour together they work 1 / 4 + 1 / 4 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Question (general): the two lines y = x and x = - 2 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 8 √ 2 , c ) 8 , d ) √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 2 , - 2 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 2 × 2 ) = 2 ; so z = 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 2 . clearly s = √ 2 , oranswer choice ( d ) ."
Answer: d
Question (general): sum of two numbers is 15 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) 5 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "explanation : x + y = 15 2 x – 3 y = 5 x = 10 y = 5 a )"
Answer: a
Question (gain): some of 50 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: 30 % is 10 % - points above 20 % and 20 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 2 : 1 . 2 / 3 of the original paint was replaced . the answer is c .
Answer: c
Question (physics): two women started running simultaneously around a circular track of length 1800 m from the same point at speeds of 10 km / hr and 20 km / hr . when will they meet for the first time any where on the track if they are moving in opposite directions ?
Options: a ) 72 , b ) 74 , c ) 76 , d ) 78 , e ) 80
Rationale: time taken to meet for the first time anywhere on the track = length of the track / relative speed = 1800 / ( 30 + 60 ) 5 / 18 = 1800 * 18 / 90 * 5 = 72 seconds . answer : a
Answer: a
Question (general): the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 20 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 46 , c ) 88 , d ) 33.33 , e ) 12
Rationale: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 200 . total score of the batsman in the 30 matches = 1000 . average score of the batsman = 1000 / 30 = 33.33 answer : d"
Answer: d
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 240 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 643 m , d ) 280 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 240 / 26 = 20 x + 240 = 520 x = 280 . answer : d"
Answer: d
Question (general): if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 2 a + 22 b ?
Options: a ) - 4 , b ) - 70 , c ) 0 , d ) 2 , e ) 4
Rationale: "this implies 9 a - b = 10 b + 70 , 9 a - b = - 12 b - 2 a , 10 b + 70 = - 12 b - 2 a manipulating the second equation gives us 10 b + 70 = - 12 b - 2 a = = > 2 a + 22 b = - 70 answer is b"
Answer: b
Question (physics): how much time will a train of length 300 m moving at a speed of 72 kmph take to cross another train of length 500 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 80 , c ) 88 , d ) 76 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 300 + 500 = 800 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 800 / 10 = 80 sec . answer : b"
Answer: b
Question (general): a certain number when divided by 39 leaves a remainder 17 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 4
Rationale: "explanation : 39 + 17 = 56 / 13 = 4 ( remainder ) answer : e"
Answer: e
Question (gain): a tank contains 8,000 gallons of a solution that is 4 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 3.40 % , b ) 4.40 % , c ) 5.40 % , d ) 6.40 % , e ) 7.40 %
Rationale: "we start with 8,000 gallons of a solution that is 4 % sodium chloride by volume . this means that there are 0.04 x 8,000 = 320 gallons of sodium chloride . when 3,000 gallons of water evaporate we are left with 5,000 gallons of solution . from here we can determine what percent of the 5,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 320 / 5,000 ) x 100 = ? 0.064 x 100 = ? = 6.4 % answer is d ."
Answer: d
Question (physics): x , y and z , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2000 , what will be z ' s share of the earnings ?
Options: a ) $ 1080.90 , b ) $ 1000.90 , c ) $ 1070.90 , d ) $ 1050.90 , e ) $ 1090.90
Rationale: the dollars earned will be in the same ratio as amount of work done 1 day work of z is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 z ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2000 = $ 1090.90 hence : e
Answer: e
Question (general): the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 is :
Options: a ) 504 , b ) 536 , c ) 544 , d ) 548 , e ) 568
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d"
Answer: d
Question (physics): nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 30 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 30 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 30 for cristina = c = 5 * t @ t = 15 , n = 75 c = 75 right answer ans : a"
Answer: a
Question (physics): how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6.6 m x 22.5 cm ?
Options: a ) 6400 , b ) 6410 , c ) 6440 , d ) 6500 , e ) 7040
Rationale: number of bricks = volume of wall / volume of bricks = 800 x 660 x 22.5 / 25 x 11.25 x 6 = = 7040 answer : e
Answer: e
Question (general): the total number of students in grades 1 and 2 is 30 more than the total number of students in grades 2 and 5 . how much lesser is the number of students in grade 5 as compared to grade 1 ?
Options: a ) 20 , b ) 30 , c ) 10 , d ) 40 , e ) 15
Rationale: ( grade 1 + grade 2 ) - ( grade 2 + grade 5 ) = 30 grade 1 - grade 5 = 30 answer : b
Answer: b
Question (general): a football player scores 5 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be
Options: a ) 14 , b ) 16 , c ) 18 , d ) 10 , e ) 21
Rationale: "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer e = 21 goals if . . . . total goals = 21 goals 5 th game = 5 goals 1 st 4 games = 16 goals avg . for 1 st 4 games = 16 / 4 = 4 goal / game avg . for all 5 games = 21 / 5 = 4.2 goals / game this is an exact match for what we ' re told in the prompt , so answer e must be the answer ."
Answer: e
Question (gain): a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 22 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 3 / 5 . hence , d is the correct answer ."
Answer: d
Question (physics): a jeep takes 4 hours to cover a distance of 620 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 148 kmph , b ) 152 kmph , c ) 106 kmph , d ) 103 kmph , e ) 165 kmph
Rationale: "time = 4 distance = 620 3 / 2 of 4 hours = 4 * 3 / 2 = 6 hours required speed = 620 / 6 = 103 kmph d )"
Answer: d
Question (general): the mean of 50 observations was 36 . it was found later that an observation 60 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 60 - 23 ) = 1837 . correct mean = 1837 / 50 = 36.7 answer : a"
Answer: a
Question (general): in a party every person shakes hands with every other person . if there were a total of 105 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 105 n ( n - 1 ) / 2 = 105 â ˆ ´ n = 15 answer : a"
Answer: a
Question (other): at a certain organisation , the number of male members went up by 12 % in the year 2001 from year 2000 , and the number of females members went down by 4 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 1
Rationale: "men increase by 12 % = = > 1.12 m = males in 2001 women decrease by 4 % = = > 0.96 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.12 m + 0.96 f = 1.012 * ( m + f ) 1.12 m + 0.96 f = 1.012 m + 1.012 f 1.12 m - 1.012 m = 1.012 f - 0.96 f 0.108 m = 0.052 f m / f = ( 0.052 ) / ( 0.108 ) = 52 / 108 = 1 / 2 answer = ( a )"
Answer: a
Question (general): what least value should be replaced by * in 842 * 124 so the number become divisible by 9
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : trick : number is divisible by 9 , if sum of all digits is divisible by 9 , so ( 8 + 4 + 2 + * + 1 + 2 + 4 ) = 21 + * should be divisible by 9 , 21 + 6 will be divisible by 9 , so that least number is 6 . answer : option d"
Answer: d
Question (general): there are 7 players in a bowling team with an average weight of 76 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 78 kg . , b ) 70 kg . , c ) 75 kg . , d ) 70 kg . , e ) 72 kg .
Rationale: "the new average will be = ( 76 * 7 + 110 + 60 ) / 9 = 78 kgs a is the answer"
Answer: a
Question (other): ratio between rahul and deepak is 4 : 3 , after 2 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 2 = 26 = > x = 6 so deepak age is = 3 ( 6 ) = 18 option b"
Answer: b
Question (physics): the sum of all consecutive odd integers from − 25 to 35 , inclusive , is
Options: a ) 130 , b ) 135 , c ) 155 , d ) 195 , e ) 235
Rationale: "the sum of the odd numbers from - 25 to + 25 is 0 . let ' s add the remaining numbers . 27 + 29 + 31 + 33 + 35 = 5 ( 31 ) = 155 the answer is c ."
Answer: c
Question (physics): a train crosses a platform of 130 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 887 , c ) 167 , d ) 197 , e ) 230
Rationale: "length of the train be ‘ x ’ x + 130 / 15 = x + 250 / 20 20 x + 2600 = 15 x + 3750 5 x = 1150 x = 230 m answer : e"
Answer: e
Question (physics): one computer can upload 100 megabytes worth of data in 4 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 20 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 2.5 , c ) 9 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4 * 5 = 20 seconds it can upload 5 * 100 = 500 megabytes worth of data , hence the second computer in 20 seconds uploads 1300 - 500 = 800 megabytes worth of data . the second computer can upload 100 megabytes of data in 2.5 seconds . answer : b ."
Answer: b
Question (general): the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 500 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 8 = 256 < 500 , then the greatest possible length of integer z is 8 . the answer is c ."
Answer: c
Question (gain): after decreasing 50 % in the price of an article costs rs . 620 . find the actual cost of an article ?
Options: a ) 1400 , b ) 1240 , c ) 1200 , d ) 1100 , e ) 1500
Rationale: "cp * ( 50 / 100 ) = 620 cp = 12.4 * 100 = > cp = 1240 answer : b"
Answer: b
Question (geometry): a cube has a volume of 27 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 216 , b ) 48 , c ) 64 , d ) 80 , e ) 100
Rationale: "volume = 27 = side ^ 3 i . e . side of cube = 3 new cube has dimensions 6 , 6 , and 6 as all sides are twice of teh side of first cube volume = 6 * 6 * 6 = 216 square feet answer : option a"
Answer: a
Question (gain): if the compound interest on a certain sum of money for 7 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 2100 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 7 yrs = ( 3000 x 10 x 7 ) / 100 = 2100 / - answer : d ."
Answer: d
Question (general): for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 4 + 3 and * 4 + 4 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 4 would be divisible by all numbers from 1 to 4 . = > * 4 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 4 is divisible by 3 ) in fact adding anyprimenumber between 1 to 4 to * 4 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 4 + 3 and * 4 + 11 then the answer would be 1 . for * 4 + 3 and * 4 + 13 , it is 2 and so on . . . a"
Answer: a
Question (general): in the hillside summer camp there are 50 children . 85 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 20 . , b ) 45 . , c ) 50 . , d ) 30 . , e ) 25 .
Rationale: given there are 50 students , 84 % of 50 = 42 boys and remaining 8 girls . now here 84 % are boys and 16 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 8 % . . if we add 50 to existing 45 then the count will be 92 and the girls number will be 8 as it . now boys are 92 % and girls are 8 % . ( out of 100 students = 92 boys + 8 girls ) . imo option c is correct .
Answer: c
Question (general): 4 , 5 , 7 , 11 , 19 , ( . . . )
Options: a ) 32 , b ) 22 , c ) 35 , d ) 27 , e ) 28
Rationale: "4 4 × 2 - 3 = 5 5 × 2 - 3 = 7 7 × 2 - 3 = 11 11 × 2 - 3 = 19 19 × 2 - 3 = 35 answer is c"
Answer: c
Question (general): a set s = { x , - 8 , - 5 , - 2 , 2 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) - 1 , e ) can not be determined
Rationale: "median of the set = ( - 2 + 2 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 17 - 15 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c"
Answer: c
Question (other): a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many acres q were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn q = 4 * 94 = 376 correct option - c
Answer: c
Question (gain): a sum fetched a total simple interest of $ 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8925
Rationale: "e 8925 principal = $ 100 x 4016.25 / 9 x 5 = $ 401625 / 45 = $ 8925 ."
Answer: e
Question (physics): a train running at 1 / 2 of its own speed reached a place in 8 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 4 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: time taken if run its own speed = 1 / 2 * 8 = 4 hrs time saved = 8 - 4 = 4 hrs answer : c
Answer: c
Question (general): the ratio 6 : 5 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 120 % , d ) 125 % , e ) none
Rationale: "solution 6 : 5 = 6 / 5 = ( 6 / 5 x 100 ) % . = 120 % . answer c"
Answer: c
Question (geometry): find the area of a parallelogram with base 20 cm and height 16 cm ?
Options: a ) 198 cm 2 , b ) 320 cm 2 , c ) 279 cm 2 , d ) 128 cm 2 , e ) 297 cm 2
Rationale: "area of a parallelogram = base * height = 20 * 16 = 320 cm 2 answer : b"
Answer: b
Question (gain): a part of certain sum of money is invested at 10 % per annum and the rest at 16 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 8 : 5 , b ) 4 : 9 , c ) 4 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: 16 : 10 = 8 : 5 answer : a
Answer: a
Question (physics): the h . c . f of two numbers is 12 and their l . c . m is 6600 . if one of the numbers is 288 , then the other is ?
Options: a ) 255 , b ) 260 , c ) 265 , d ) 270 , e ) 275
Rationale: "other number = ( 12 * 6600 ) / 288 = 275 . answer : e"
Answer: e
Question (general): the unit digit in the product ( 624 * 708 * 913 * 463 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 8 * 3 * 3 ) = 8 answer : d"
Answer: d