Cheukting/mathqa huggingface dataset:
Question (gain): a certain company ’ s profit in 1996 was 15 percent greater than its profit in 1995 , and its profit in 1997 was 35 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 55.25 %
Rationale: "profit in 1995 - 100 profit in 1996 - 115 % increae profit in 1997 in comparison to 1995 = 15 + 115 * 35 % = 55.25 correct option : e"
Answer: e
Question (gain): a , b and c started a partnership business by investing rs . 12000 , rs . 16000 , rs . 20000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 86400 , d ) 90000 , e ) 50000
Rationale: "a : b : c = 12000 : 16000 : 20000 = 3 : 4 : 5 let total profit = p then p ã — 5 / 12 = 36000 p = ( 36000 ã — 12 ) / 5 = 86400 answer is c ."
Answer: c
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 24 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 3 : 1 , c ) 7 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 24 s = ( 27 x + 17 y ) / ( x + y ) = 24 = ( 27 x + 17 y ) / = 24 ( x + y ) = 3 x = 7 y = x / y = 7 / 3 answer : c"
Answer: c
Question (gain): sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 450 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25
Rationale: 7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 450 - - > x = 2 . 1.25 x = ~ 2.50 . answer : d .
Answer: d
Question (physics): at sandi ’ s pet shop , 25 cups of bird seed are used every 5 days to feed 15 parakeets . how many cups of bird seed would be required to feed 14 parakeets for 7 days ?
Options: a ) 40.5 , b ) 32.34 , c ) 6.23 , d ) 9 , e ) 15
Rationale: let ' s go step - by - step . 25 cups are used over a 5 day period , which means 5 cups a day . this feeds 15 parakeets , which means each parakeet needs 1 / 3 of a cup every day . for 14 parakeets , we need 14 * 1 / 3 cups = 4.62 cups a day . over 7 days , we need 32.34 cups . choice b .
Answer: b
Question (other): there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability e that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: e probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d
Answer: d
Question (general): a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 80 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 50
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 160 + ( d / 2 ) / v 8 d / 480 - 3 d / 480 = ( d / 2 ) / v d / 96 = d / 2 v and so v = 48 km / hr the answer is d ."
Answer: d
Question (gain): sonika deposited rs . 8000 which amounted to rs . 11200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 2277 , c ) 11680 , d ) 12068 , e ) 1212
Rationale: "( 8000 * 3 * 2 ) / 100 = 480 11200 - - - - - - - - 11680 answer : c"
Answer: c
Question (gain): a manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18 % . the wholesaler sells the same to retailer at a profit of 20 % . the retailer in turn sells them to a customer for rs . 30.09 , there by earning a profit of 25 % . the cost price for the manufacturer is :
Options: a ) rs . 15 , b ) rs . 16 , c ) rs . 17 , d ) rs . 18 , e ) rs . 19
Rationale: let the cost price for the manufacturer be rs . x . then , 125 % of 120 % of 118 % of x = 30.09 . 125 / 100 * 120 / 100 * 118 / 100 * x = 3009 / 100 177 / 100 x = 3009 / 100 = > x = 17 answer : c
Answer: c
Question (gain): how long will a boy take to run round a square field of side 40 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 48 sec , c ) 60 sec , d ) 25 sec , e ) 39 sec
Rationale: speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 40 * 4 = 160 m time taken = 160 * 3 / 10 = 48 sec answer is b
Answer: b
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 602 to 700 inclusive ?
Options: a ) 24,550 , b ) 28,550 , c ) 32,550 , d ) 36,550 , e ) 40,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 602 + 604 + . . . + 700 = 50 ( 600 ) + ( 2 + 4 + . . . + 100 ) = 30,000 + 2550 = 32,550 the answer is c ."
Answer: c
Question (general): the average runs scored by a batsman in 10 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 20 matches ?
Options: a ) 31 , b ) 35 , c ) 88 , d ) 13 , e ) 12
Rationale: "total score of the batsman in 10 matches = 400 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 20 matches = 700 . average score of the batsman = 700 / 20 = 35 . answer : b"
Answer: b
Question (general): there are 300 giraffes at a large zoo . the number of giraffes is 3 times the number of all the other animals combined . how many more giraffes are there than non giraffes animals at the zoo ?
Options: a ) 400 , b ) 360 , c ) 300 , d ) 290 , e ) 200
Rationale: answer is d . total giraffes = 300 = 3 * other animals ( x ) or x = 10 . so , difference in giraffes and x = 300 - 10 = 290 .
Answer: d
Question (general): bucket a is 1 / 4 full of sand , and bucket b , which has one - half the capacity of bucket a , is 3 / 8 full of sand . jana pours the contents of bucket b into bucket a . bucket a is now filled to what fraction of its capacity ?
Options: a ) 3 / 8 , b ) 7 / 16 , c ) 1 / 2 , d ) 5 / 8 , e ) 7 / 8
Rationale: let capapcity of a = x sand = x / 4 capacity of b = x / 2 sand = 3 x / 16 a total = x / 4 + 3 x / 16 = 7 x / 16 answer : b
Answer: b
Question (general): if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 15 . what is the value of f ( 6 ) ?
Options: a ) 4 , b ) 0 , c ) 1 , d ) 2 , e ) 24
Rationale: since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 15 then f ( 5 ) = 15 - 5 = 10 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 10 - 6 = 4 . answer : a . questions on funtions to practice :
Answer: a
Question (general): a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1100 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 14000 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 12012
Rationale: "[ 1100 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 14000 answer : a"
Answer: a
Question (general): andy solves problems 78 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 52 , c ) 51 , d ) 50 , e ) 48
Rationale: "125 - 78 + 1 = 48 ' e ' is the answer"
Answer: e
Question (general): a fair 2 sided coin is flipped 3 times . what is the probability that tails will be the result at least twice , but not more than 3 times ?
Options: a ) 5 / 8 , b ) 3 / 4 , c ) 3 / 8 , d ) 7 / 4 , e ) 5 / 6
Rationale: "at least twice , but not more than 3 timesmeans exactly 2 times , 3 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 3 c 2 / 2 ^ 3 = 3 / 8 option : c"
Answer: c
Question (general): a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the addition of the maximum and minimum possible values of ' a + b ' ?
Options: a ) 21 , b ) 34 , c ) 30 , d ) 25 , e ) 12
Rationale: "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 21 + 9 = 30 ans c"
Answer: c
Question (general): 3 / 5 of all married couples have more than one child . 2 / 5 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 2 / 5 of 100 couples have more than 3 kids = 40 couples . this implies that 40 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 20 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 40 = 20 . fraction will be 20 / 100 = 1 / 5 . option a
Answer: a
Question (physics): one pump drains one - half of a pond in 2 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1.3 hour , b ) 1.2 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 2 = 1 / 4 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 4 = 3 / 4 - - > time taken for the 2 nd pump to finish : 1 : 3 / 4 = 4 / 3 = 1.3 hours . a"
Answer: a
Question (general): if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18 , then n =
Options: a ) 3 , b ) 6 , c ) 17 , d ) 23 , e ) 24
Rationale: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18 = > 4 x 2 ^ 2 n = 4 ^ 24 = 2 ^ 36 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 36 = > 2 ^ ( 2 n + 2 ) = 2 ^ 36 = > 2 n + 2 = 36 = > n = 17 so . answer will be c ."
Answer: c
Question (gain): a fair price shopkeeper takes 10 % profit on his goods . he lost 40 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 42 % , c ) 34 % , d ) 12 % , e ) 22 %
Rationale: explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 60 . s . p . of each item = rs . 1.10 total sale = 1.10 * 60 = rs . 66 hence , loss % = 34 / 100 * 100 = 34 % answer : c
Answer: c
Question (physics): a and b go around a circular track of length 300 m on a cycle at speeds of 34 kmph and 50 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 60 sec , c ) 186 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 300 / ( 36 * 5 / 18 ) , 300 / ( 54 * 5 / 18 ) } = lcm ( 30 , 20 ) = 60 sec . answer : b"
Answer: b
Question (general): in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 3 / 4 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 120 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 3 / 4 ) of total igneous rocks . ( 2 / 3 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 4 / 3 ) = 40 total sedimentary rocks = 2 * total igneous rocks = 2 * 40 = 80 total number of rocks = 40 + 80 = 120 answer ( d )"
Answer: d
Question (other): two assembly line inspectors , smithy and glen , inspect widgets as they come off the assembly line . if smithy inspects every fifth widget , starting with the fifth , and glen inspects every third , starting with the third , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 50 , b ) 53 , c ) 55 , d ) 60 , e ) 65
Rationale: widgets inspected by smithy : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by glen : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 - 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 98 - 45 = 53 option b
Answer: b
Question (general): what is the sum of the numbers between 1 and 12 , inclusive ?
Options: a ) 99 , b ) 65 , c ) 79 , d ) 78 , e ) 80
Rationale: "sol . add the numbers between 1 and 12 . answer is d , 78 ."
Answer: d
Question (physics): the speed of a car is 120 km in the first hour and 70 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 75 kmph , c ) 95 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "s = ( 120 + 70 ) / 2 = 95 kmph answer : c"
Answer: c
Question (other): in a class of 60 children , 30 % children can speak only english , 20 % hindi and english both and the rest of the children can speak only hindi . how many children can speak hindi ?
Options: a ) 42 , b ) 36 , c ) 30 , d ) 48 , e ) none of these
Rationale: number of students who speak only english = 30 % of 60 = 18 ∵ number of students who speak hindi and english = 20 % of 60 = 12 ∵ number of students who speak only hindi = ( 60 – 30 = ) 30 ∵ no . of students who speak hindi = 30 + 12 = 42 answer a
Answer: a
Question (gain): 25 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 267 , e ) 1280
Rationale: "( 25 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 4 x = 320 x = 1280 answer : e"
Answer: e
Question (geometry): george ' s car calls for 8 ounces of oil for each cylinder used . his car ' s engine has 6 cylinders . if 16 ounces of oil has already been put into the engine used , then how many additional ounces of oil are needed ?
Options: a ) 16
b ) 48
c ) 64
d ) 32
e ) 8
Rationale: number of ounces per cylinder 8 number of cylinders 6 ounces needed 48 ounces used 16 answer d
Answer: d
Question (general): a car traveled 35 % of the way from town x to town y at an average speed of 35 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 45 , b ) 65 , c ) 55 , d ) 75 , e ) 85
Rationale: "assume total distance = 100 miles time taken for 35 miles = 35 / 35 = 1 hour time taken for the rest of the 65 miles = 65 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 65 / v hence v = 65 mph answer : b"
Answer: b
Question (gain): if the compound interest on a certain sum of money for 2 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 600 , b ) rs . 890 , c ) rs . 895 , d ) rs . 900 , 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 2 yrs = ( 3000 x 10 x 2 ) / 100 = 600 / - answer : a ."
Answer: a
Question (general): hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and two wrenches is one - third that of 8 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: x be the weight of a hammer and y be the weight of a wrench . ( 2 x + 2 y ) = 1 / 3 * ( 8 x + 5 y ) 3 ( 2 x + 2 y ) = ( 8 x + 5 y ) 6 x + 6 y = 8 x + 5 y y = 2 x ans - e
Answer: e
Question (other): tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 163 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 185.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 163 / 22.50 = 1 = â € º x - 163 = 22.50 = â € º x = 185.50 . hence , price of the third variety = rs . 175.50 per kg . answer c"
Answer: c
Question (general): in an examination , 25 % of total students failed in hindi , 40 % failed in english and 35 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 25 + 40 - 35 ) = 100 - 70 = 30 answer : c"
Answer: c
Question (general): the total circumference of two circles is 49 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 7.8 , b ) 6.0 , c ) 6.7 , d ) 9.7 , e ) 18.0
Rationale: "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 49 where 2 r = r thus : 2 π r + 4 π r = 49 6 π r = 49 r = approx 2.6 π r + 2 r π = 49 3 π r = 49 r = approx 5.2 r + r = approx 7.8 answer : a"
Answer: a
Question (general): a certain pair of used shoes can be repaired for $ 10.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 30.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 42.85 , b ) 44 , c ) 48 , d ) 38 , e ) 40
Rationale: "1 ) cost of repairing = 10.5 ( for one year ) , therefore for 2 years it would be $ 21 . 2 ) cost of new pair which will last for 2 years is $ 30.00 percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 30 - 21 ) / ( 21 ) * 100 = 42.85 % . ans is a"
Answer: a
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 17.5 , b ) 7.4 , c ) 7.9 , d ) 12.0 , e ) 7.1
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 6 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i . e . , 12 hrs . answer : d"
Answer: d
Question (gain): a and b invests rs . 8000 and rs . 9000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 45 , b ) 32 : 47 , c ) 32 : 45 , d ) 32 : 41 , e ) 32 : 42
Rationale: "a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 9000 * 6 ) + ( 6000 * 6 ) 64000 : 90000 32 : 45 . answer : a"
Answer: a
Question (physics): a runs twice as fast as b and gives b a start of 42 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 84 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 42 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 42 m is 42 / 1 = 42 m so the total time taken by a and b to reach = 2 * 42 = 84 m answer : c"
Answer: c
Question (other): in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135
Rationale: "the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b ."
Answer: b
Question (general): what is the 26 th digit to the right of the decimal point in the decimal form of 6 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "6 / 11 = 0.54545454 . . . the even numbered positions in the decimal expansion are all 4 . the answer is b ."
Answer: b
Question (geometry): what is the area of square field whose side of length 13 m ?
Options: a ) 169 , b ) 196 , c ) 266 , d ) 288 , e ) 261
Rationale: "13 * 13 = 169 sq m answer : a"
Answer: a
Question (gain): a can complete a certain job in 9 days . b is 80 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 5 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 4.8
Rationale: "let , total work unit = 90 units a can finish in 9 days = 90 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 80 / 100 ) * 10 = 18 unit work days in which b will complete the work alone = 90 / 18 = 5 days answer : option a"
Answer: a
Question (geometry): a metallic sheet is of rectangular shape with dimensions 50 m x 30 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 5 m , the volume of the box ( in m cube ) is :
Options: a ) 4120 m cube , b ) 4140 m cube , c ) 5140 m cube , d ) 5120 m cube , e ) none of these
Rationale: "explanation : l = ( 50 - 10 ) m = 40 m , [ because 5 + 5 = 10 ] b = ( 30 - 10 ) m = 20 m , h = 5 m . volume of the box = ( 40 x 20 x 5 ) m cube = 4000 m cube . option e"
Answer: e
Question (gain): in what time a sum of money double itself at 2 % per annum simple interest ?
Options: a ) 60 % , b ) 58 % , c ) 55 % , d ) 40 % , e ) 50 %
Rationale: p = ( p * 2 * r ) / 100 r = 50 % answer : e
Answer: e
Question (physics): a , b , c can complete a piece of work in 18 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 36 / 11 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 18 + 1 / 6 + 1 / 12 = 11 / 36 a , b , c together will complete the job in 36 / 11 days answer is d"
Answer: d
Question (physics): if the horse can run 10 miles / hour , how many days would it take for a horse to run from new york city to washington . d . c . ? ( 240 miles from nyc to d . c . )
Options: a ) 0.6 , b ) 0.8 , c ) 1 , d ) 1.2 , e ) 1.4
Rationale: the horse runs 10 miles / hour , thus it would take the horse 240 miles / 10 miles / hour to = 24 hours to run from nyc to d . c . there are 24 hours in a day , so days it take would be 24 hours / 24 hours / day = 1 day . correct option : 1
Answer: c
Question (general): solve below question 2 x + 1 = - 21
Options: a ) - 11 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 21 x = - 11 a"
Answer: a
Question (general): solution for 2.12 + . 004 + . 345
Options: a ) 2.91 , b ) 2.911 , c ) 2.469 , d ) 2.586 , e ) 2.499
Rationale: 2.12 + . 004 + . 345 0 = 0 - 2.12 - 0.004 - 0.345 0 = - 2.469 answer : c
Answer: c
Question (probability): in a throw of dice what is the probability of ge æ « ng number greater than 3
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Rationale: "explanation : number greater than 3 is 4 , 5 , 6 , so only 3 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 3 / 6 = 1 / 2 answer : a"
Answer: a