Cheukting/mathqa huggingface dataset:
Question (other): a bag contains 5 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 19 / 39
Rationale: "drawing two balls of same color from five green balls can be done in 5 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 5 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 19 / 39 answer : e"
Answer: e
Question (general): find the 10 th term of an arithmetic progression whose first term is 8 and the common difference is 2 .
Options: a ) 45 , b ) 26 , c ) 44 , d ) 40 , e ) 46
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 8 + ( 10 - 1 ) * 2 , = 8 + 18 = 26 . answer : b"
Answer: b
Question (general): if ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 , then what is the value of x ?
Options: a ) 3 , b ) - 3 , c ) 10 / 3 , d ) 3 / 10 , e ) - 10 / 3
Rationale: ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 = > 18 ( 10 x + 2 ) / 4 - ( 3 x - 6 ) = 18 ( 2 x + 4 ) / 3 = > 4.5 ( 10 x + 2 ) - 3 x + 6 = 6 ( 2 x + 4 ) = > 45 x + 9 - 3 x + 6 = 12 x + 24 = > 45 x - 3 x - 12 x = 24 - 9 - 6 = > 30 x = 9 = > x = 9 / 30 = > x = 3 / 10 answer : d
Answer: d
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 8 m wide at the top and 6 m wide at the bottom and the area of cross - section is 700 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 100 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 8 + 6 ) = 700 d = 100 answer : b"
Answer: b
Question (geometry): the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.80 per metre .
Options: a ) 2399 , b ) 6336 , c ) 2999 , d ) 5808 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.80 ) = rs . 6336 . answer : b ) 6336"
Answer: b
Question (gain): a man bought 20 shares of rs . 50 at 5 discount , the rate of dividend being 4 % . the rate of interest obtained is
Options: a ) 5 % , b ) 5.28 % , c ) 5.30 % , d ) 5.50 % , e ) 6 %
Rationale: "shares = 20 shares 50 at 5 discount rate divident 4 % req = = = > 5.28 % answer b"
Answer: b
Question (physics): a train 150 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 2 sec , b ) 6 sec , c ) 8 sec , d ) 9 sec , e ) 5 sec
Rationale: "d 9 sec speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 150 m at 50 / 3 m / sec = 150 * 3 / 50 sec = 9 sec"
Answer: d
Question (physics): convert the 13 / 54 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 0.86 , d ) 1.1 , e ) 1.2
Rationale: "13 / 54 m / s = 13 / 54 * 18 / 5 = 13 / 15 = 0.86 kmph . answer : c"
Answer: c
Question (physics): in a 300 m race a beats b by 22.5 m or 6 seconds . b ' s time over the course is :
Options: a ) 86 sec , b ) 80 sec , c ) 76 sec , d ) 96 sec , e ) none of these
Rationale: "runs 45 / 2 m in 6 sec . b covers 300 m in 6 x 2 / 45 x 300 sec = 80 sec . answer : b"
Answer: b
Question (physics): annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 30 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 30 minutes , sam rides 6 km so sam will be 4 km ahead . it will take annie 80 minutes to catch sam . the answer is d .
Answer: d
Question (gain): john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.60 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 40 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.60 - - > 15 p - 13.5 p = 60 - - > p = 40 . answer : d ."
Answer: d
Question (physics): a certain industrial loom weaves 0.126 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 119
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.126 : 15 : : 1 : x = > 0.126 * x = 15 = > x = 15 / 0.126 = > x = 119 answer : e"
Answer: e
Question (physics): a cistern is normally filled in 8 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: if leakage / hour = 1 / x , then 1 / 8 - 1 / x = 1 / 10 , solving 1 / x = 1 / 40 so in 40 hours full cistern will be empty . answer : d
Answer: d
Question (general): oil cans x and y are right circular cylinders and the height and radius of y are each 4 times those of x . if the oil in can x filled to capacity sells for $ 2 , how much does the oil in y sell for if y is only half filled ?
Options: a ) $ 60 , b ) $ 52 , c ) $ 63 , d ) $ 64 , e ) $ 68
Rationale: formula for vol of a cyl is pi * r ^ 2 * h so vy = 64 * vy y when half filled will cost 32 times x so ans is d
Answer: d
Question (physics): a searchlight on top of the watch - tower makes 6 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "6 revolutions per minute = 1 revolution every 10 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 10 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 10 seconds ) = 1 - p ( man in dark for max of 10 seconds ) = 1 - 10 / 10 = 1 - 1 = 0 or the other way would be : p ( man in dark for at least 10 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 10 seconds because that is the max . in this approach it would be 10 / 10 seconds = 1 . answer is e"
Answer: e
Question (gain): jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 4000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 4000 ) solving for x , we get the shares as 14000 . ans : ( option d )"
Answer: d
Question (general): how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 15 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 13
Rationale: so i can write this as in - 3 i + 4 < = 15 or in - 3 i < = 11 so n can have - 8 to 14 = 13 true values . . . . e
Answer: e
Question (physics): a man rows his boat 75 km downstream and 45 km upstream , taking 5 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 5 kmph , c ) 2 kmph , d ) 3 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 75 / ( 5 ) = 15 kmph speed upstream = d / t = 45 / ( 5 ) = 9 kmph the speed of the stream = ( 15 - 9 ) / 2 = 3 kmph answer : d"
Answer: d
Question (physics): an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 25 metre of cloth ?
Options: a ) 194 seconds , b ) 195 seconds , c ) 196 seconds , d ) 197 seconds , e ) none of these
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 25 : x = > x = 25 ∗ 1 / 0.128 = > x = 195.31 so time will be approx 195 seconds option b"
Answer: b
Question (physics): at what time between 5 and 6 o ' clock are the hands of a 3 minutes apart ?
Options: a ) 24 , b ) 55 , c ) 66 , d ) 88 , e ) 21
Rationale: in this type of problems the formuae is ( 5 * x + or - t ) * 12 / 11 here x is replaced by the first interval of given time . here x is 5 . t is spaces apart case 1 : ( 5 * x + t ) * 12 / 11 ( 5 * 5 + 3 ) * 12 / 11 28 * 12 / 11 = 336 / 11 = min therefore the hands will be 3 min apart at 31 5 / 11 min past 5 . case 2 : ( 5 * x - t ) * 12 / 11 ( 5 * 5 - 3 ) * 12 / 11 22 * 12 / 11 = 24 min therefore the hands will be 3 min apart at 24 min past 5 answer : a ) 24 min
Answer: a
Question (probability): the probability is 1 / 2 that a certain coin turns up heads on any given toss . if the coin is tossed 6 times , what is the probability that the coin turns up tails on at least one of the tosses ?
Options: a ) 15 / 16 , b ) 21 / 32 , c ) 31 / 32 , d ) 63 / 64 , e ) 51 / 64
Rationale: p ( 6 heads ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 . p ( at least one tail ) = 1 - 1 / 64 = 63 / 64 . the answer is d .
Answer: d
Question (geometry): a football field is 8400 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3500 square yards ?
Options: a ) 450 , b ) 600 , c ) 500 , d ) 2400 , e ) 3200
Rationale: "answer a ) 4800 yards need 1200 lbs 1 yard will need 1200 / 8400 = 1 / 7 lbs 3600 yards will need 1 / 7 * 3500 yards = 500 lbs c"
Answer: c
Question (general): the lowest number which should be added to 11390 so that the sum is exactly divisible by 7 , 9 , 10 and 12 is :
Options: a ) 1010 , b ) 2210 , c ) 1250 , d ) 1210 , e ) 1110
Rationale: l . c . m . of 7 , 9 , 10 and 12 = 1260 . on dividing 11390 by 1260 , the remainder is 50 . number to be added = ( 1260 - 50 ) = 1210 . answer : option ' d '
Answer: d
Question (general): a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 26 , c ) 24 , d ) 22 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : b"
Answer: b
Question (gain): 120 students represent x percent of the boys at a school . if the boys at the school make up 30 % of the total school population of x students , what is x ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 200 , e ) 250
Rationale: "let b be the number of boys in the school . 120 = xb / 100 b = 0.3 x 12000 = 0.3 x ^ 2 x ^ 2 = 40000 x = 200 the answer is d ."
Answer: d
Question (general): a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has rs . 1400 left with him , find his expenditure on food and conveyance .
Options: a ) 1000 , b ) 2000 , c ) 3000 , d ) 4000 , e ) 5000
Rationale: "part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) let the monthly salary be rs . x then , 7 / 40 of x = 1400 x = ( 1400 * 40 / 7 ) = 8600 expenditure on food = rs . ( 3 / 10 * 800 ) = rs . 2400 expenditure on conveyence = rs . ( 1 / 8 * 8000 ) = rs . 1000 answer is a ."
Answer: a
Question (general): find the average of all prime numbers between 10 and 30 .
Options: a ) 30 , b ) 33.6 , c ) 39.8 , d ) 18.6 , e ) none
Rationale: "sol . there are six prime numbers between 10 and 30 . they are 11 , 13 , 17 , 19 , 23 , 29 â ˆ ´ required average = [ 11 + 13 + 17 + 19 + 23 + 29 / 6 ] = 112 / 6 = 18.6 answer d"
Answer: d
Question (other): of the diplomats attending a summit conference , 17 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 17 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 150 . answer : e ."
Answer: e
Question (gain): in a recent election , geoff received 15 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,571 more votes to win the election , what is the value of x ?
Options: a ) 74.5 , b ) 54 , c ) 56 , d ) 60 , e ) 63
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 900 votes he needs 3571 more votes so : 900 + 3571 = 4471 now what ' s the problem wants ? ? a x % . . . . . . . . 4471 is what % of total votes 6000 . . . . . . . . translating : 4471 = x / 100 * 6000 - - - x = 74.5 % . . . . . . . . . . a"
Answer: a
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 6 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 33 , b ) 44 , c ) 48 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 6 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 6 = 4 / 9 ( t - 6 ) 10 t = 594 - 264 = > t = 33 . answer : a"
Answer: a
Question (geometry): a lady grows broccoli in her garden that is in the shape of a square . each broccoli takes 1 square foot of area in her garden . this year , she has increased her output by 79 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did she produce this year ?
Options: a ) 1600
b ) 1500
c ) 1650
d ) 1700
e ) can not be determined
Rationale: explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 79 , the area would have increased by 79 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 79 ( x + y ) ( x - y ) = 79 . 79 is a prime number and hence it will have only two factors . i . e . , 79 and 1 . therefore , 79 can be expressed as product of 2 numbers in only way = 79 * 1 i . e . , ( x + y ) ( x - y ) = 79 * 1 so , ( x + y ) should be 79 and ( x - y ) should be 1 . solving the two equations we get x = 40 and y = 39 . therefore , number of broccoli produced this year = x 2 = 402 = 1600 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 1500,1650 and 1700 are not the square of any number . check choice a : if this year ' s produce is 1600 , last year ' s produce would have been 1600 - 79 = 1521 1521 is the square of 39 . so , 1600 is the answer . choice a
Answer: a
Question (physics): a train 120 m long is running at 60 kmph . in how much time will it pass a platform 240 m long ?
Options: a ) 15.6 seconds , b ) 24.6 seconds , c ) 21.6 seconds , d ) 30.6 seconds , e ) 35.6 seconds
Rationale: distance travelled = 120 + 240 m = 360 m speed = 60 * 5 / 8 = 50 / 3 m time = 360 * 3 / 50 = 21.6 seconds answer : c .
Answer: c
Question (physics): a is twice as good a workman as b and together they complete a work in 12 days . in how many days a alone can do the work ?
Options: a ) 32 , b ) 33 , c ) 34 , d ) 35 , e ) 36
Rationale: a ’ s one day ’ s work : b ’ s one day ’ s work = 2 : 1 ( a + b ) ’ s one day ’ s work = 1 / 12 b ’ s one day ’ s work = 1 / 12 * 1 / 3 = 1 / 36 b alone can do the work in 36 days answer : e
Answer: e
Question (physics): 10 women can complete a work in 5 days and 10 children take 10 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 2
Rationale: "1 women ' s 1 day work = 1 / 50 1 child ' s 1 day work = 1 / 100 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 50 + 10 / 100 ) = 1 / 5 5 women and 10 children will complete the work in 5 days . b"
Answer: b
Question (general): if p # q denotes the least common multiple of p and q , then e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c .
Answer: c
Question (general): if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 6 - m ) then m = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: ( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 6 - m ) = 4 ^ ( ( 6 - m ) / 2 ) therefore , m = ( 6 - m ) / 2 2 m = 6 - m m = 2 answer b
Answer: b
Question (physics): a train passes a platform in 44 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 240 , b ) 250 , c ) 360 , d ) 230 , e ) 220
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 36 = > 300 + l = 15 × 44 = 660 = > l = 660 - 300 = 360 meter answer is c ."
Answer: c
Question (gain): exactly 35 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 50 % , e ) 84 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 35 % ofall reporters reporters covering politics / all reporters = 35 / 70 = 1 / 2 reporters not covering politics / all reporters = 1 / 2 = 50 % = d"
Answer: d
Question (general): if rs . 10 be allowed as true discount on a bill of rs . 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :
Options: a ) rs . 20 , b ) rs . 21.81 , c ) rs . 22 , d ) rs . 18.33 , e ) none
Rationale: "solution s . i . on rs . ( 110 - 10 ) for a certain time = rs . 10 . s . i . on rs . 100 for double the time = rs . 20 . t . d . on rs . 120 = rs . ( 120 - 100 ) = rs . 20 . t . d . on rs . 110 = rs . ( 20 / 120 x 120 ) = rs . 18.33 . answer d"
Answer: d
Question (physics): the speed at which a man can row a boat in still water is 150 kmph . if he rows downstream , where the speed of current is 48 kmph , what time will he take to cover 390 metres ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "speed of the boat downstream = 150 + 48 = 198 kmph = 198 * 5 / 18 = 30 m / s hence time taken to cover 390 m = 390 / 30 = 13 seconds . answer : d"
Answer: d
Question (general): a shopkeeper gave an additional 20 per cent concession on the reduced price after giving 30 per cent standard concession on an article . if arun bought that article for 1120 , what was the original price ?
Options: a ) 3000 , b ) 4000 , c ) 2400 , d ) 2000 , e ) none of these
Rationale: original price = 1120 × 100 ⁄ 70 × 100 ⁄ 80 = 2000 answer d
Answer: d
Question (general): if x , y , and z are positive integers and 3 x = 4 y = 7 z , then the least possible value of x - y + z is
Options: a ) 33 , b ) 40 , c ) 49 , d ) 19 , e ) 61
Rationale: x - y + z = - 3 x / 4 + x + 3 x / 7 = ( - 21 + 28 + 12 ) x / 28 = 19 x / 28 19 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - d
Answer: d
Question (general): a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of cows will be :
Options: a ) 30 , b ) 23 , c ) 24 , d ) 26 , e ) 22
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 48 . . . . ( i ) and 2 x + 4 y = 140 x + 2 y = 70 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 22 . the required answer = 22 . answer : e"
Answer: e
Question (gain): a man buys an article for $ 100 . and sells it for $ 130 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 130 gain = $ 30 gain % = 30 / 100 * 100 = 30 % answer is e"
Answer: e
Question (physics): how many cubes of 20 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 177 cm , b ) 125 cm , c ) 786 cm , d ) 617 cm , e ) 187 cm
Rationale: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 20 â ˆ — 20 â ˆ — 20 = 125 note : 1 m = 100 cm answer : b"
Answer: b
Question (probability): 3 houses are available in a new flat . 3 persons apply for the houses . each applies for 1 house without consulting others . the probability that all the 3 apply for the same house is ?
Options: a ) 1 / 7 , b ) 1 / 9 , c ) 2 / 7 , d ) 3 / 7 , e ) 2 / 9
Rationale: one person can select one house out of 3 = \ inline { \ color { black } 3 c _ { 1 } } ways = 3 . hence , three persons can select one house out of 3 in 3 x 3 x 3 = 9 . therefore , probability that all thre apply for the same house is 1 / 9 b
Answer: b
Question (general): if log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 , then x is equal to :
Options: a ) 1 , b ) 5 , c ) 3 , d ) 2 , e ) 6
Rationale: log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + log 10 10 log 10 [ 5 ( 5 x + 1 ) ] = log 10 [ 10 ( x + 5 ) ] 5 ( 5 x + 1 ) = 10 ( x + 5 ) 5 x + 1 = 2 x + 10 3 x = 9 = > x = 3 answer c
Answer: c
Question (physics): the sum of 4 consecutive even numbers is 140 . what would be the smallest number ?
Options: a ) 32 , b ) 88 , c ) 70 , d ) 123 , e ) 12
Rationale: let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x - 2 ) = 32 answer : a
Answer: a
Question (physics): a train speeds past a pole in 15 seconds and a platform 100 m long in 30 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 200 m , e ) 145 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 30 = x / 15 x = 200 m . answer : d"
Answer: d