Cheukting/mathqa huggingface dataset:
Question (general): if x is an integer and 2.134 × 10 ^ x is less than 21000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "if x = 4 2.134 × 10 ^ 4 = 21340 > 21000 so , x = 3 answer : e"
Answer: e
Question (physics): the sum of two consecutive number is 97 . which is the larger number ?
Options: a ) 42 , b ) 49 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 97 2 x + 1 = 97 2 x = 96 x = 48 therefore larger number is x + 1 = 49 answer : b"
Answer: b
Question (general): 3,10 , 29,66 , __
Options: a ) 125 , b ) 165 , c ) 145 , d ) 127 , e ) 112
Rationale: "3 = 1 * 1 * 1 + 2 10 = 2 * 2 * 2 + 2 29 = 3 * 3 * 3 + 2 66 = 4 * 4 * 4 + 2 similarly 5 * 5 * 5 + 2 = 127 answer : d"
Answer: d
Question (gain): the sale price sarees listed for rs . 450 after successive discount is 20 % and 15 % is ?
Options: a ) 321 , b ) 276 , c ) 306 , d ) 265 , e ) 162
Rationale: "explanation : 450 * ( 80 / 100 ) * ( 85 / 100 ) = 306 answer : c"
Answer: c
Question (general): if there are 200 questions in a 3 hr examination . among these questions are 15 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 72 min , b ) 25.11628 min , c ) 70 min , d ) 74.11682 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 185 x + 15 * 2 x = 180 x = 180 / 215 x = 0.837209 time taken for type a problem = 15 * 2 * 0.837209 = 25.11628 min answer : b"
Answer: b
Question (physics): express 45 mps in kmph ?
Options: a ) 170 , b ) 160 , c ) 162 , d ) 130 , e ) 122
Rationale: "45 * 18 / 5 = 162 kmph answer : c"
Answer: c
Question (gain): a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a
Options: a ) rs . 300 , b ) rs . 56 , c ) rs . 100 , d ) rs . 240 , e ) rs . 90
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = rs . 240 answer : d"
Answer: d
Question (physics): express a speed of 126 kmph in meters per second ?
Options: a ) 10 mps , b ) 35 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "126 * 5 / 18 = 35 mps answer : b"
Answer: b
Question (general): the product of two numbers is 2028 and their h . c . f is 13 . the number of such pairs is ?
Options: a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 9
Rationale: "let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer : b"
Answer: b
Question (gain): a cricket bat is sold for $ 850 , making a profit of $ 245 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "245 / ( 850 - 245 ) = 245 / 605 = 49 / 121 = 40 % . answer : e ."
Answer: e
Question (physics): the speed of a car is 90 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 54 , e ) 15
Rationale: "s = ( 90 + 60 ) / 2 = 75 kmph answer : b"
Answer: b
Question (other): if shares of two persons in profits are rs . 300 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "total profit = 1000 ratio = 300 / 600 = 1 : 2 answer : e"
Answer: e
Question (probability): a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 8 managers , if 2 managers will not attend the meeting together ?
Options: a ) 40 , b ) 36 , c ) 42 , d ) 45 , e ) 47
Rationale: "we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together so 6 c 5 + ( 6 c 4 * 2 c 1 ) this is 6 + 30 = 36 answer : b"
Answer: b
Question (gain): a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % sunflower , and brand b , which is 65 % millet and 35 % sunflower . if a customer purchases a mix of the two types of birdseed that is 50 % sunflower , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "yes there is a simple method : consider the following method brand a : 40 % millet and 60 % sunflower brand b : 65 % millet and 35 % sunflower mix : 50 % sunflower here the weighted average is 50 % , now brand a has 60 % sunflower , which is 10 % more than the weighted average of mix = + 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 35 % sunflower , which is 15 % less than the weighted average of mix = - 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 3 : 5 = ( 3 / 5 ) * 100 = 60 % here is a pictorial representation : brand a = 60 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 above average , a times - - - - - - - - - - - - - - - - - total below = + 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 35 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 below average , b times - - - - - - - - - - - - - - - - - total above = - 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore a / total = 3 : 5 = 60 % answer : e"
Answer: e
Question (physics): sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is :
Options: a ) 15 , b ) 16 , c ) 22 , d ) 18 , e ) 25
Rationale: "work done by sakshi in 1 day = 1 / 20 since tanya is 25 % efficient than sakshi , she completes 25 % more work in a day than sakshi . = > tanya ' s 1 day work = 1 / 20 + 1 / 20 * 25 / 100 = 1 / 16 so time taken by tanya to finish the work = 16 days answer : b"
Answer: b
Question (gain): in an election a candidate who gets 60 % of the votes is elected by a majority of 1504 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1504 20 x / 100 = 1504 x = 1504 * 100 / 20 = 7520 answer is d
Answer: d
Question (physics): two boats are heading towards each other at constant speeds of 5 miles / hr and 21 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 13 / 30 , e ) 1 / 5
Rationale: the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 21 = 26 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 26 * 1 / 60 = 13 / 30 miles apart . answer : d .
Answer: d
Question (physics): 36 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 12 , b ) 18 , c ) 22 , d ) 24 , e ) 26
Rationale: "solution let the required number of days be x . then , less men , more days ∴ 27 : 36 : : 18 : x ⇔ 27 × x = 36 × 18 ⇔ x = 36 x 18 / 27 x = 24 . answer d"
Answer: d
Question (general): of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 2 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 2 is 1200 * 1 / 2 so it reduced 600 people , so there is 600 clerical people left but since 600 people left , it also reduced from the total of 3600 so there are 3000 people total since 600 clerical left / 3000 people total you get ( c ) 20 %"
Answer: c
Question (general): toby is 4 years younger than debby . thrice the sum of the ages of toby and debby equals their mother ’ s age . if the age of the mother is 60 , find the ages of toby and debby ?
Options: a ) 8 and 12 , b ) 5 and 9 , c ) 6 and 10 , d ) 5 and 10 , e ) 12 and 16
Rationale: let the age of debby be x and toby be x - 4 3 ( x + x - 4 ) = 60 x = 12 the ages of toby and debby are 8 and 12 . answer : a
Answer: a
Question (gain): if a lends rs . 2800 to b at 15 % per annum and b lends the same sum to c at 18.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 294 , b ) 289 , c ) 240 , d ) 233 , e ) 200
Rationale: "( 2800 * 3.5 * 3 ) / 100 = > 294 answer : a"
Answer: a
Question (general): find the average of all prime numbers between 20 and 30
Options: a ) 15 , b ) 20 , c ) 18 , d ) 32 , e ) 26
Rationale: "prime numbers between 20 and 30 are 23,29 required average = ( 23 + 29 ) / 2 = 52 / 2 = 26 answer is e"
Answer: e
Question (physics): a and b together can complete work in 4 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 4 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 4 - 1 / 6 = 1 / 12 b alone can complete the work in 12 days so half of the work in 6 days answer : option d"
Answer: d
Question (gain): sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1 % more . she would get how much ?
Options: a ) 9440 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 1 ) / 100 = 240 9200 - - - - - - - - 9440 answer : a"
Answer: a
Question (general): john is 3 times as old as sam . if john will be twice as old as sam in 9 years , how old was sam two years ago ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7
Rationale: j = 3 s after 9 years j + 9 = 2 ( s + 9 ) j = 2 s + 9 2 s + 9 = 3 s s = 9 two years ago s = 9 - 2 = 7 e is the answer
Answer: e
Question (gain): a bowl of fruit contains 14 apples and 23 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 23 - x ) = 37 - x 14 / ( 37 - x ) = 7 / 10 = > 20 = 37 - x = > x = 17 answer d
Answer: d
Question (general): √ ( 49 ) 2
Options: a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 49 ) 2 = ? or , ? = 49 answer c"
Answer: c
Question (physics): one woman and one man can build a wall together in three hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them five hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 2 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 22 / 7
Rationale: "solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 3 - - > ( 1 ) , w + 2 g = 1 / 3 - - > ( 2 ) and m + g = 1 / 5 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 15 , m = 2 / 15 and w = 1 / 5 . so , n = 1 / ( 2 / 5 ) = 5 / 2 option , a"
Answer: a
Question (physics): two trains each 170 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 55 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely .
Options: a ) 15 sec , b ) 11.6 sec , c ) 31.6 sec , d ) 12.6 sec , e ) 23 sec
Rationale: explanation : d = 170 m + 170 m = 340 m rs = 55 + 50 = 105 * 5 / 18 = 146 / 5 t = 340 * 5 / 146 = 11.6 sec answer : option b
Answer: b
Question (general): 8 cups of water are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of water should be poured into the 8 - cup bottle ?
Options: a ) 2 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 8 / 3 , e ) 16 / 3
Rationale: let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : e
Answer: e
Question (gain): a candidate got 30 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 2028 , c ) 2775 , d ) 10000 , e ) 6851
Rationale: "30 % - - - - - - - - - - - l 70 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 40 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 10000 answer : d"
Answer: d
Question (general): the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 15 years old . what is the value of n ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "14 n + 32 = 15 ( n + 1 ) n = 17 the answer is e ."
Answer: e
Question (general): the average of 7 numbers is 26 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 130
Rationale: "explanation : average of new numbers = 26 * 5 = 130 answer : option e"
Answer: e
Question (gain): if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 345 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 100 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 345 = 5 x / 20 = 5 = > x = 100 answer : c"
Answer: c
Question (general): the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 88 , what is the difference between the ages of patrick and monica ?
Options: a ) 22 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 88 x = 2 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 2 = 22 answer a"
Answer: a
Question (geometry): 14 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 189 , e ) 45
Rationale: "there are 14 business exec and in each handshake 2 business execs are involved . hence 14 c 2 = 91 also , each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake . total = 91 + 98 = 189 ans : d"
Answer: d
Question (general): 5 n - 3 > 12 and 7 n - 5 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9
Rationale: 5 n - 3 > 12 5 n > 15 n > 3 7 n - 5 < 44 7 n < 49 n < 7 so n must be between 3 and 7 3 < n < 7 correct answer d
Answer: d
Question (general): if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 12 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 12 . then 4 n < 12 and n < 3 . the largest possible integer is n = 2 . the answer is b ."
Answer: b
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 11 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 6.24 , b ) 7.4 , c ) 7.92 , d ) 6.28 , e ) 7.24
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 11 ) = 7 / 44 the cistern will be filled in 44 / 7 hrs i . e . , 6.28 hrs . answer : d"
Answer: d
Question (general): what is 3 / 7 of 7 / 8 of 1 / 3 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 9 / 16 , d ) 1 / 8 , e ) 16 / 9
Rationale: 3 / 7 * 7 / 8 * 1 / 3 = 1 / 8 answer : d
Answer: d
Question (general): the least number which should be added to 2400 so that the sum is exactly divisible by 5 , 6,4 and 3 is :
Options: a ) 3 , b ) 13 , c ) 20 , d ) 33 , e ) 43
Rationale: solution l . c . m . of 5 , 6,4 and 3 = 60 . on dividing 2400 by 60 , the remainder is 40 . ∴ number to be added = ( 60 - 40 ) = 20 . answer c
Answer: c
Question (general): in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 82 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 8400 , b ) 8200 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 82 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 82 = > total appeared candidates in state b = 82 x 100 = 8200 = > total appeared candidates in state a = total appeared candidates in state b = 8200"
Answer: b
Question (general): a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 100 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 34 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 100 = 340 m . time taken = 340 / 10 = 34 sec . answer : c"
Answer: c
Question (general): in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 8720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 8720 32.5 k = 32.5 k / 100 k * 8720 = 2834 the number of valid votes polled in favour of b is 2834 . answer : c"
Answer: c
Question (physics): a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ?
Options: a ) $ 1200 , b ) $ 1005.8 , c ) $ 555.6 , d ) $ 1009.2 , e ) $ 1490.7
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2500 = $ 555.6"
Answer: c
Question (general): 23 , 29 , 31 , 37 , 41 , 43 , ( . . . )
Options: a ) 53 , b ) 48 , c ) 59 , d ) 47 , e ) 50
Rationale: "all are prime numbers in their order , starting from 23 hence , next number is 47 answer is d"
Answer: d
Question (gain): rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 81 . how much was lent at 5 % ?
Options: a ) 299 , b ) 666 , c ) 778 , d ) 900 , e ) 977
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 81 5 x / 100 + 90 – 6 x / 100 = 81 x / 100 = 9 = > x = 900 answer : d"
Answer: d
Question (gain): what will be the difference between simple and compound interest at 16 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 164.19 , b ) 164.12 , c ) 170.6 , d ) 167.1 , e ) 165.11
Rationale: "s . i . = ( 1000 * 16 * 4 ) / 100 = rs . 640 c . i . = [ 1000 * ( 1 + 16 / 100 ) 4 - 1000 ] = rs . 810.6 difference = ( 810.6 - 640 ) = rs . 170.6 answer : c"
Answer: c
Question (physics): in what time will a train 350 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.95 sec , c ) 1.3 sec , d ) 8.75 sec , e ) 1.85 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 100 / 40 = 8.75 sec . answer : d"
Answer: d
Question (physics): an aeroplane covers a certain distance of 530 kmph in 5 hours . to cover the same distance in 3 2 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 540 , c ) 640 , d ) 722 , e ) 250
Rationale: "speed of aeroplane = 530 kmph distance travelled in 5 hours = 530 * 5 = 2650 km speed of aeroplane to acver 2650 km in 11 / 3 = 2650 * 3 / 11 = 722 km answer d"
Answer: d
Question (other): there are 4 red books and 4 blue books on a shelf . if 2 books are selected at random from the shelf , what is the probability that both books selected are red books ?
Options: a ) 2 / 7 , b ) 3 / 7 , c ) 3 / 14 , d ) 5 / 28 , e ) 9 / 28
Rationale: the number of ways of choosing 2 books from the shelf is 8 c 2 = 28 . the number of ways of choosing 2 red books is 4 c 2 = 6 . p ( 2 red books ) = 6 / 28 = 3 / 14 . the answer is c .
Answer: c
Question (probability): on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 4 attempts ?
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 11 / 16 , e ) 15 / 16
Rationale: p ( missing all 4 ) = ( 1 / 2 ) ^ 4 = 1 / 16 p ( success on at least one attempt ) = 1 - 1 / 16 = 15 / 16 the answer is e .
Answer: e
Question (general): a no . when divided by 222 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 10 , e ) 15
Rationale: "222 + 43 = 265 / 17 = 10 ( remainder ) d"
Answer: d
Question (other): the ratio of the arithmetic mean of two numbers to one of the numbers is 4 : 7 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 8 , b ) 1 : 7 , c ) 1 : 6 , d ) 1 : 5 , e ) 1 : 4
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 4 : 7 , thus the smaller number must have a ratio of 1 . the ratio of the smaller number to the larger number is 1 : 7 . the answer is b ."
Answer: b
Question (geometry): when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 5 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 5 then x = 5 / 1000 = 0.005 . the answer is a"
Answer: a