Cheukting/mathqa huggingface dataset:
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 27.3 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) 34 % , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 27.3 ) / ( 100 â ˆ ’ 5 ) = 100 ã — 127.3 / 95 = 134 hence , required % profit = 134 â € “ 100 = 34 % answer d"
Answer: d
Question (gain): in town x , 64 percent of the population are employed , and 45 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 45 % , c ) 32 % , d ) 40 % , e ) 28 %
Rationale: "answer b male - employed - 64 % female - employed - 19 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 19 / 64 = 28 e"
Answer: e
Question (gain): x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40,000 , the amount invested by y is
Options: a ) 33488 , b ) 63809 , c ) 60000 , d ) 37887 , e ) 77824
Rationale: "explanation : suppose y invested rs . y . then 40000 / y = 2 / 3 or y = 60000 . answer : c ) 60000"
Answer: c
Question (other): 135 kg of an alloy a is mixed with 145 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 5 and alloy b has tin and copper in the ratio 2 : 3 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 142 kg , c ) 135 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 135 kg of a = 135 * 5 / 8 = 84 kg quantity of tin in 145 kg of b = 145 * 2 / 5 = 58 kg quantity of tin in the new alloy = 84 + 58 = 142 kg answer is b"
Answer: b
Question (general): a sum of money lent out at s . i . amounts to a total of $ 520 after 2 years and to $ 820 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 340 , b ) $ 360 , c ) $ 380 , d ) $ 400 , e ) $ 420
Rationale: "s . i for 5 years = $ 820 - $ 520 = $ 300 the s . i . is $ 60 / year s . i . for 2 years = $ 120 principal = $ 520 - $ 120 = $ 400 the answer is d ."
Answer: d
Question (gain): a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 61 ⁄ 4 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 6 1 ⁄ 4 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 254 × 21 / 00 = 625 his overall gain in 2 years = rs . 625 - rs . 400 = rs . 225 his overall gain in 1 year = 2252 = rs . 112.5 answer : option d"
Answer: d
Question (physics): a small water pump would take 4 hours to fill an empty tank . a larger pump would take 1 / 2 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 1 / 6 , b ) 4 / 9 , c ) 1 / 4 , d ) 5 / 9 , e ) 1 / 3
Rationale: "rate of the small pump is 1 / 4 tank / hour rate of the larger pump is 1 / ( 1 / 2 ) or 2 tank / hour ; combined rate of the two pumps is 1 / 4 + 2 = 9 / 4 tank / hour , together they will fill the empty tank in 1 / ( 9 / 4 ) ) = 4 / 9 hours ( time = job / rate ) . answer : b"
Answer: b
Question (physics): a man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 / 2 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 9 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 9 , d = 9 b - 9 c ; every 3 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 3 , d = 3 b + 3 c ; d = 9 b - 9 c = 3 b + 3 c , - - > b = 2 c , - - > d = 9 b - 9 b / 2 = 9 b / 2 . interval = \ frac { d } { b } = \ frac { 9 / 2 b } { b } = 9 / 2 answer : d ( 9 / 2 minutes ) ."
Answer: d
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took 2 2 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 6 hours , b ) 8 hours , c ) 9 hours , d ) 10 hours , e ) 12 hours
Rationale: "explanation : solution 1 the pump can fill the tank in 2 hour . but , because of the leak , it took 2 2 / 3 hours to fill the tank . i . e . , the additional water filled by the pump in 2 / 3 hour is emptied by the leak in 2 2 / 3 = 8 / 3 hours . therefore , the water filled by pump in 2 bour can be emptied by the leak in 8 / 3 x 3 = 8 hours . i . e . , the leak can drain all the water of the tank in 8 hours . answer is b"
Answer: b
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of the above
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 + 250 ) / 26 ) = 20 x + 250 = 520 x = 270 . d"
Answer: d
Question (physics): if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 22.5 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 120
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 22.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 22.5 miles in 90 mins so answer 30 + 90 = 120 mins . ( answer e )"
Answer: e
Question (general): what is the average of first 21 multiples of 5 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 55 , d ) d ) 81 , e ) e ) 82
Rationale: required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 5 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 55 c
Answer: c
Question (gain): the sale price sarees listed for rs . 560 after successive discount is 20 % and 30 % is ?
Options: a ) 321 , b ) 314 , c ) 316 , d ) 265 , e ) 162
Rationale: "explanation : 560 * ( 80 / 100 ) * ( 70 / 100 ) = 314 answer : b"
Answer: b
Question (probability): 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be a couple ?
Options: a ) 1 / 200 , b ) 1 / 100 , c ) 90 / 2900 , d ) 17 / 2700 , e ) 1 / 20
Rationale: "in how many ways we can select a girl and a boy from 45 lady and 60 gentlemen ? in 45 * 60 = 2,700 ways . we have a total of 17 couples so , the probability of selecting a couple is 17 / 2,700 = 17 / 2700 . ans - d"
Answer: d
Question (physics): a can complete a work in 12 days and b can do the same work in 8 days . if a after doing 2 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 4 1 / 2 days , c ) 6 1 / 2 days , d ) 7 3 / 4 days , e ) 10 days
Rationale: the required answer = ( 12 - 2 ) * 8 / 12 = 80 / 12 = 6 1 / 2 days answer is c
Answer: c
Question (physics): a train 800 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 2 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 1800 , c ) 500 , d ) 297 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 2 min = 120 sec . let the length of the train be x meters . then , ( 800 + x ) / 120 = 65 / 3 x = 1800 m . answer : b"
Answer: b
Question (general): given that e and f are events such that p ( e ) = 25 , p ( f ) = 75 and p ( e n f ) = 75 , find p ( e | f ) and p ( f | e )
Options: a ) 5 , b ) 46 , c ) 52 , d ) 12 , e ) 3
Rationale: here , e and f are events p ( e | f ) = p ( enf ) / p ( f ) = 75 / 25 = 3 p ( f | e ) = p ( enf ) / p ( e ) = 75 / 75 = 1 . e )
Answer: e
Question (physics): a train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train ?
Options: a ) 90 , b ) 60 , c ) 120 , d ) 180 , e ) 360
Rationale: "length = speed * time speed = l / t s = 2500 / 100 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : a"
Answer: a
Question (general): if integer k is equal to the sum of all even multiples of 35 between 280 and 630 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 11 * 455
Rationale: "if we break down what the stem is asking what is the sum of all mult of 30 between 300 and 600 . using arithmetic progression to find n : 630 = 280 + ( n - 1 ) 35 350 + 35 = 35 n 385 = 35 n = > n = 11 the sum would be : 11 * mean mean = [ 630 + 280 ] / 2 = 455 11 * 455 = e"
Answer: e
Question (general): if 360 is divided into 4 parts proportional to 5 , 7 , 4 , 8 then the smallest part is :
Options: a ) 50 , b ) 60 , c ) 40 , d ) 18 , e ) 22
Rationale: given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24 : . the smallest part = ( 360 * 4 / 24 ) = 60 answer : b
Answer: b
Question (general): 1370 , 1320 , 1070 , - 180 , - 6430 , x
Options: a ) - 37680 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 - 6430 - 50 * ( 5 ^ 4 ) = - 37680 answer : a ."
Answer: a
Question (general): a scale 10 ft . 5 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 25 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 10 * 12 ) + 5 = 125 inches length of each of the 5 parts = 125 / 5 = 25 inches answer : a"
Answer: a
Question (physics): a train 150 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 84 kmph
Rationale: "speed of train relative to man : 150 / 6 * 18 / 5 km / hr = 90 km / hr let speed of train = x therefore x + 6 = 90 x = 90 - 6 x = 84 km / hr answer : e"
Answer: e
Question (physics): a thief runs away from a with a speed of 20 km / hr . a police from a station 60 km away started chasing him after 1 hr . with a speed of 40 km / hr . time taken by the police to catch the thief is :
Options: a ) 4 hrs , b ) 4.5 hrs , c ) 5.4 hrs , d ) 6 hrs . , e ) none of these
Rationale: explanation : solution : distance traveled by the thief in 1 hr . = 20 km . total distance of them after 1 hr = ( 60 + 20 ) km = 80 km . their relative speed = ( 40 - 20 ) = 20 km / hr . time taken to catch the thief = 80 / 20 = 4 hrs . answer : a
Answer: a
Question (other): what is the square root of 16 , divided by 2 ?
Options: a ) 9 , b ) 2 , c ) 122 , d ) 6 , e ) 1
Rationale: "square root is a number times itself square root of 16 = 4 , 4 / 2 = 2 ( b ) 2"
Answer: b
Question (general): the value of ( 4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31 ) is :
Options: a ) 0.47 , b ) 47 , c ) 470 , d ) 4700 , e ) none of these
Rationale: solution given expression = 4.7 × ( 13.26 + 9.43 + 77.31 ) = 4.7 × 100 = 470 . answer c
Answer: c
Question (general): an ant walks an average of 500 meters in 60 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 1.0 , b ) 0.5 , c ) 0.75 , d ) 0.425 , e ) 0.3
Rationale: "the ant walks an average of 500 meters in 60 minutes 500 meters in 1 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 60 minutes 0.425 km in 1 hours speed = 0.425 * 1 = 0.425 km / h i guess option d should be 0.425"
Answer: d
Question (general): a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 10 gallons of water and 20 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 20 gallons salt is added and 10 gallons of water is added . so salt now becomes - > ( 0.2 x + 20 ) and water - - > ( 0.6 x + 10 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 20 ) = ( 0.6 x + 10 ) / 2 , solving , x = 150 . answer : d"
Answer: d
Question (general): roses can be purchased individually for $ 2.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 325 , d ) 324 , e ) 326
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 2.3 = ~ 13 roses for that amount . total = 312 + 13 = 325 . answer : c ."
Answer: c
Question (general): in the land of oz only one or two - letter words are used . the local language has 65 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 130
Rationale: the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 65 letters is 65 ; the number of 2 letter words ( xx ) that can be made from 65 letters is 65 * 65 , since each x can take 65 values . total : 65 + 65 * 65 . similarly : the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . the difference is ( 65 + 65 * 65 ) - ( 64 + 64 * 64 ) = 130 . answer : e .
Answer: e
Question (general): baker ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each cake box is 8 inches by 7 inches by 5 inches , then what is the maximum number of cake boxes that can be placed in each carton ?
Options: a ) 330 , b ) 300 , c ) 252 , d ) 225 , e ) 210
Rationale: baker ram is storing cake boxes in cartons the dimensions of the carton are 25 x 42 x 60 and those of each cake box are 8 x 7 x 5 . to maximize number of boxes try and fit maximum into the base of the box . if you take the base as 25 x 42 and fit 5 x 6 boxes of 5 x 7 , then the total number of boxes is 5 x 6 x integer ( 60 / 8 ) = 5 x 6 x 7 = 210 . alternatively you could try taking the base as 60 x 42 and fit 12 x 6 boxes of 5 x 7 , then the total number of boxes is 12 x 6 x integer ( 25 / 8 ) = 12 x 6 x 3 = 216 . but since that is not an answer option , i go with ( e ) 210 .
Answer: e
Question (general): a 40 - liter solution of alcohol and water is 5 percent alcohol . if 4.5 liters of alcohol and 5.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 7 % , b ) 10 % , c ) 13 % , d ) 16 % , e ) 19 %
Rationale: the percent of alcohol in the solution is ( 0.05 ( 40 ) + 4.5 ) / 50 = 6.5 / 50 = 13 % the answer is c .
Answer: c
Question (physics): a snail , climbing a 20 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 12 , b ) 16 , c ) 17 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 16 days it will climb 16 feet on the 17 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 17 answer : c"
Answer: c
Question (geometry): if n is the smallest integer such that 432 times n is the square of an integer , what is the value of n ?
Options: a ) 2
b ) 3
c ) 6
d ) 12
e ) 24
Rationale: the prime factorization of a square has to have even powers of all its prime factors . if the original number has a factor , say of 7 , then when it ’ s squared , the square will have a factor of 7 ^ 2 . another way to say that is : any positive integer all of whose prime factors have even powers must be a perfect square of some other integer . look at the prime factorization of 432 432 = ( 2 ^ 4 ) * ( 3 ^ 3 ) the factor of 2 already has an even power — - that ’ s all set . the factor of 3 currently has an odd power . if n = 3 , then 432 * n would have an even power of 2 and an even power of 3 ; therefore , it would be a perfect square . thus , n = 3 is a choice that makes 432 * n a perfect square . answer : b .
Answer: b
Question (general): the average of the marks of 12 students in a class is 36 . if the marks of each student are doubled , find the new average ?
Options: a ) 72 , b ) 23 , c ) 29 , d ) 26 , e ) 13
Rationale: "sum of the marks for the 12 students = 12 * 36 = 432 . the marks of each student are doubled , the sum also will be doubled . the new sum = 432 * 2 = 864 . so , the new average = 864 / 12 = 72 . answer : a"
Answer: a
Question (physics): a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 20 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 21 , b ) 28 , c ) 90 , d ) 85 , e ) 11
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 20 = rs . 85 . answer : d"
Answer: d
Question (gain): if the simple interest on $ 1500 increase by $ 20 , when the time increase by 2 years . find the rate percent per annum .
Options: a ) 0.6 % , b ) 0.5 % , c ) 0.1 % , d ) 0.2 % , e ) 0.7 %
Rationale: applying the above formula , we have 20 = 1500 * r * 2 / 100 r = 20 * 100 / 1500 * 2 = 0.7 % . answer is e
Answer: e
Question (gain): a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 8.40 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 8.40 when c . p = ( 100 * 8.40 ) / 21 = 40 answer : b"
Answer: b
Question (general): the sum of two numbers is 29 and the difference of their squares is 145 . the difference between the number is
Options: a ) 13 , b ) 5 , c ) 8 , d ) 11 , e ) 12
Rationale: "explanation : let the numbers be x and y . we know that , ( x − y ) = x 2 − y 2 / ( x + y ) = 145 / 29 = 5 correct option : b"
Answer: b
Question (geometry): the cube root of what integer power of 2 is closest to 50 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: integer powers of 2 = 2 , 2 ^ 2 , 2 ^ 3 , 2 ^ 4 , 2 ^ 5 , 2 ^ 6 , 2 ^ 7 etc . let , cube root of x is closest to 50 i . e . x is closest to cube of 50 = 50 * 50 * 50 = 125000 but x must be equivalent to an integer power of 2 2 ^ 10 = 1024 2 ^ 7 = 128 i . e . 2 ^ 17 = 128 * 1024 = 128000 ( approx . ) i . e . 2 ^ 18 = 256 * 1024 = 256000 ( approx . ) i . e . 2 ^ 16 = 64 * 1024 = 64000 ( approx . ) i . e . 2 ^ 17 which is closest to 125000 i . e . integer power of 2 must be 7 answer : option b
Answer: b
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 190 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 1009 , c ) s . 1007 , d ) s . 1357.1 , e ) s . 1002
Rationale: "explanation : 90 % 104 % - - - - - - - - 14 % - - - - 190 100 % - - - - ? = > rs . 1357.1 answer : d"
Answer: d
Question (general): if 3 ^ x * 4 ^ y = 19683 and x – y = 9 , then x = ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b .
Answer: b
Question (geometry): in triangle pqr , the angle q = 90 degree , pq = 2 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 1.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
Rationale: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 2 = 8 : 10 - - > qy = 1.6 . answer : a ."
Answer: a
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 210 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 14 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 210 rs . 5 m + 5 m + 5 m - - - - - 210 rs . 15 m - - - - - - 210 rs . = > 1 m = 14 rs . answer : e"
Answer: e
Question (general): in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 62 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 110 / 100 = 66 in june total income = 66 + 40 = 106 % of mrs lee ' s income = 66 / 106 = 62.26 ( a )"
Answer: a
Question (physics): express a speed of 60 kmph in meters per second ?
Options: a ) 10 mps , b ) 16.67 mps , c ) 97.67 mps , d ) 17.67 mps , e ) 18 mps
Rationale: "60 * 5 / 18 = 16.67 mps answer : b"
Answer: b
Question (general): a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 50 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 50 , d ) 60 , e ) 50
Rationale: 200 men do the rest of the work in 100 - 50 = 50 days 100 men can do the rest of the work in 50 * 200 / 100 = 100 days required number of days = 100 - 50 = 50 days answer is c
Answer: c
Question (general): how many multiples of 6 are there between 30 and 140 , 30 and 140 inclusive ?
Options: a ) 18 , b ) 16 , c ) 17 , d ) 19 , e ) 15
Rationale: "6 multiples are . . . 30 , 36,42 , 48,54 , 60,66 , 72,78 , 84,90 , 96,102 , 108,114 , 120,126 , 132,138 , . . . , . . . , the answer is = 19 answer is d"
Answer: d
Question (physics): how many seconds will a 400 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 46 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 36
Rationale: "explanation : speed of train relatively to man = ( 46 - 6 ) km / hr = 40 km / hr = ( 40 x 5 / 18 ) m / sec = 11.11 m / sec time taken to pass the man = ( 400 / 11.11 ) sec = 36 sec . answer : e"
Answer: e
Question (general): if x + y = 24 , x - y = 40 , for integers of x and y , x = ?
Options: a ) 20 , b ) 23 , c ) 25 , d ) 32 , e ) 42
Rationale: "x + y = 24 x - y = 40 2 x = 64 x = 32 answer is d"
Answer: d