Cheukting/mathqa huggingface dataset:
Question (other): 24 oz of juice p and 25 oz of juice q are mixed to make smothies x and y . the ratio of p to q in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to q ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice v will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice v = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice q = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d
Answer: d
Question (gain): a shirt goes on sale for 90 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 81 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 90 then it is marked down by 10 % = 90 - 9 = 81 . hence it is 81 % od the original price . hence answer is b ."
Answer: b
Question (gain): in a certain parking lot , 2 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 4 % , b ) 6 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 20 % * y y / x = 1 / 10 = 10 % the answer is d .
Answer: d
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 : 5 . if the sum of their ages is 145 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , 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 : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 145 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"
Answer: b
Question (general): a is an integer greater than 29 but less than 41 , b is an integer greater than 39 but less than 51 , what is the range of a / b ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 5 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 30 and b = 50 so , a / b = 3 / 5 max value of a / b will be when b is lowest and a is highest - - - > a = 40 and b = 40 so , a / b = 1 range is 1 - ( 3 / 5 ) = 2 / 5 answer should be c ."
Answer: c
Question (general): in one year , the population , of a village increased by 5 % and in the next year , it decreased by 5 % . if at the end of 2 nd year , the population was 9975 , what was it in the beginning ?
Options: a ) 7787 , b ) 10000 , c ) 1988 , d ) 1277 , e ) 2081
Rationale: "x * 105 / 100 * 95 / 100 = 9975 x * 0.9975 = 9975 x = 9975 / 0.9975 = > 10000 answer : b"
Answer: b
Question (general): if 2 ^ ( 2 w ) = 8 ^ ( w − 1 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 1 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 1 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 3 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 3 w = 3 the answer is a ."
Answer: a
Question (physics): a person travels equal distances with speeds of 7 km / hr , 8 km / hr and 9 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 7 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 7 + x / 8 + x / 9 = 47 / 60 36 x / 95 = 47 / 60 = > x = 2.07 . total distance = 3 * 2.07 = 6.2 km . answer : a"
Answer: a
Question (physics): a leak in the bottom of a tank can empty the full tank in 9 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 12960 , c ) 8290 , d ) 8640 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 9 - 1 / 12 ) = 1 / 36 work done by the inlet in 1 min . = ( 1 / 36 × 1 / 60 ) = 0.000463 volume of 0.000463 part = 6 litres . therefore , volume of whole = 1 / 0.000463 x 6 ‹ = › 12960 litres . answer b"
Answer: b
Question (general): if k ^ 2 is divisible by 240 what is the least possible value of integer k ?
Options: a ) 60 , b ) 30 , c ) 12 , d ) 90 , e ) 120
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for k ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option c because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : a"
Answer: a
Question (gain): you enter a weight loss challenge game and manage to lose 11 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 11 % ) * ( 100 % + 2 % ) = 0.89 * 1.02 = 9.22 % the weigh in records your weight loss at 9.22 % ! the answer is b"
Answer: b
Question (general): in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 2200 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2200 = 1 * 5 ^ 2 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Question (other): solution a is 40 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 1
Rationale: forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 40 ) = 3 / 1 so the volume of the two solutions will be equal . answer has to be 3 : 1 . e
Answer: e
Question (general): a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 40 as remainder . find the no . is ?
Options: a ) 220044 , b ) 145778 , c ) 220400 , d ) 220014 , e ) 220040
Rationale: "( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220040 e"
Answer: e
Question (gain): a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1500 . the difference between the profit shares of a and c is ?
Options: a ) 8867 , b ) 299 , c ) 279 , d ) 600 , e ) 2612
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1500 = > 5 parts out of 15 parts is rs . 1500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1500 ) = rs . 600 . answer : d"
Answer: d
Question (general): a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 2 of the mixture is water , and the remaining 8 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 46 , e ) 48
Rationale: "let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 2 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 2 ) x = ( 1 / 6 ) x = 8 x = 48 then answer will be e = 48"
Answer: e
Question (gain): machine a and machine b are each used to manufacture 330 sprockets . it takes machine a 10 hours longer to produce 330 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 3.3 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 330 qt = 300 for a : ( t + 10 ) ( q ) = 330 qt + 10 q = 330 300 + 10 q = 330 q = 3 so a can produce 3 / hour . then b can produce = 3 ( 1.1 ) = 3.3 / hour . a"
Answer: a
Question (general): albert is 2 times mary ’ s age and 4 times as old as betty . mary is 14 years younger than albert . how old is betty ?
Options: a ) 5 , b ) 7 , c ) 10 , d ) 15 , e ) 18
Rationale: "a = 2 m = m + 14 m = 14 a = 28 a = 4 b , and so b = 7 the answer is b ."
Answer: b
Question (general): how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 35 % solution ?
Options: a ) a ) 6.7 , b ) b ) 38.5 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 35 / 100 200 + 20 x = 700 + 7 x 13 x = 500 x = 28.5 answer is b"
Answer: b
Question (general): when y is divided by 276 , the remainder is 42 . what is the remainder when the same y is divided by 23 ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "y = 276 * a + 42 = ( 23 * 12 ) * a + 23 + 19 the answer is d ."
Answer: d
Question (general): when 200 is divided by positive integer x , the remainder is 2 . what is the remainder when 398 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "f 200 / x leaves a reminder 2 then ( 200 - 2 ) i . e . 198 is divisible by x so ( 200 + 198 ) / x leaves a reminder rem ( 200 / x ) + rem ( 198 / x ) = > 2 + 0 = 2 answer : a"
Answer: a
Question (gain): what quantity of water should taken out to concentrate 12 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 4 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 12 ( 60 - 40 ) / 60 = 4 liters answer is a"
Answer: a
Question (gain): john had a stock of 700 books in his bookshop . he sold 50 on monday , 82 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 26.5 % , b ) 50 % , c ) 46.5 % , d ) 56.5 % , e ) 60 %
Rationale: "let n be the total number of books sold . hence n = 50 + 82 + 64 + 78 + 135 = 280 let m be the books not sold m = 700 - n = 700 - 280 = 420 percentage books not sold / total number of books = 420 / 700 = 0.60 = 60 % correct answer e"
Answer: e
Question (general): if it takes a tub 4 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 36 seconds , d ) 2 minutes , 14 seconds , e ) 4 minutes , 12 seconds
Rationale: "if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 4 minutes to drain 5 / 7 th of tub it takes 4 * ( 7 / 5 ) minutes to drain the entire tub and 4 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 8 / 5 minutes or 1 3 / 5 minutes or 1 minute 36 seconds so answer is c"
Answer: c
Question (general): a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this ordert ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75
Rationale: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . t = 12.5 * 6 = 75 . e
Answer: e
Question (general): when a merchant imported a certain item , he paid a 9 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 85.50 , what was the total value of the item ?
Options: a ) $ 1,150 , b ) $ 1,350 , c ) $ 1,550 , d ) $ 1,750 , e ) $ 1,950
Rationale: "let x be the value in excess of $ 1,000 . 0.09 x = 85.5 x = $ 950 the total value was $ 950 + $ 1,000 = $ 1,950 . the answer is e ."
Answer: e
Question (general): how many different 3 - digit multiples of 5 can be composed of digits 2 , 7 , 4 , and 5 if none of the digits is repeated ?
Options: a ) 3 , b ) 6 , c ) 10 , d ) 12 , e ) 18
Rationale: = 3 c 2 x 2 = 6 can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 3 possible choices . x can be any of the 2 possible choices . 2 + 3 + 1 = 6 b
Answer: b
Question (other): in a class of 38 children , 19 play tennis , 21 play squash and 10 play neither sport . ( 1 ) how many children play both sports ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 19
Rationale: 28 play some sport 19 + 21 - both = 28 both = 12 answer is b
Answer: b
Question (physics): a train 440 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 72 sec , b ) 24 sec , c ) 44 sec , d ) 62 sec , e ) 21 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 440 * 3 / 55 ] sec = 8 sec answer : b"
Answer: b
Question (general): firm a ' s revenues are described by the equation ra = 17.12 x and its costs by ca = 12.87 x + 2400 . firm b ' s revenues are described by the equation rb = 13.27 x and its costs by cb = 8.77 x + 1500 . ( x denotes the quantity of sales ) . if a ' s volume of sales increases from 1000 to 3000 over the same period that b ' s volume increases from 2000 to 3000 , the percent increase in profits for the firm with the biggest dollar increase in profits is
Options: a ) 20 % , b ) 30 % , c ) 60 % , d ) 50 % , e ) 33 %
Rationale: ok , i do not know whether it is exactly what you want to hear but i did it that way : first look at difference between revenue and variable cost = > take the bigger one ( b ) which gives you : 4.5 x - 1500 just plug in 2000 and 3000 . you get 7500 and 12000 ( difference 4500 ) . 4500 > 0.5 * 7500 so 30 % b
Answer: b
Question (physics): how many seconds will a 500 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 33 , b ) 87 , c ) 30 , d ) 88 , e ) 77
Rationale: "explanation : distance = 500 m speed of the train relative to man = ( 63 - 3 ) km / hr = 60 km / hr = m / s = m / s time taken to pass the man = distance / speed = sec = 30 sec answer : c ) 30"
Answer: c
Question (physics): a and b together can do a piece of work in 6 days and a alone can do it in 9 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 18 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 9 work in 1 day b alone can do ( 1 / 6 - 1 / 9 ) = 1 / 18 work in 1 day = > complete work can be done in 18 days by b answer : option c"
Answer: c
Question (gain): √ 6 percent of 6 √ 6 =
Options: a ) 0.3 , b ) 0.25 , c ) 0.1 , d ) 0.95 , e ) 0.35
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 √ 3 ≈ 1.7 √ 5 ≈ 2.2 √ 6 ≈ 2.4 so , √ 6 percent of 6 √ 6 ≈ 2.4 percent of ( 6 ) ( 2.4 ) ≈ ( 2.4 / 100 ) ( 14.4 ) ≈ 34.56 / 100 ≈ 0.34 check the answer choices to see that e is the only answer that ' s close . answer : e"
Answer: e
Question (physics): 20 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 24 , b ) 18 , c ) 17 , d ) 16 , e ) 10
Rationale: "binders books days 20 1400 21 x 1600 20 x / 20 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 24 answer : a"
Answer: a
Question (physics): a man can do a job in 20 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 20 + 1 / 20 + 1 / 25 ) = 7 / 50 so , all three together will complete the work in 300 / 47 = 7.1 days . answer : c"
Answer: c
Question (general): what will be the vulgar fraction of 0.4
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.4 = 40 / 100 = 2 / 5 option b"
Answer: b
Question (other): in a school 10 % of the boys are same in number as 1 / 4 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 4 g 10 b / 100 = g / 4 b = 5 g / 2 b / g = 5 / 2 b : g = 5 : 2 answer is a"
Answer: a
Question (physics): the volume of a cistern is 840 cubic meters and water is flowing into the cistern . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate , in cubic meters per minutes , at which the water is flowing into the cistern ?
Options: a ) 0.125
b ) 0.25
c ) 0.5
d ) 0.75
e ) not enough information to determine the rate
Rationale: there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate . the correct answer is e .
Answer: e
Question (other): two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 6 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 31 : 1 , b ) 31 : 4 , c ) 31 : 8 , d ) 31 : 9 , e ) 31 : 2
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 6 = 21 / 4 litres quantity of alcohol in the mixture formed = 5 / 2 + 21 / 4 = 31 / 4 = 7.75 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 7.75 : 2.25 = 31 : 9 . answer : d"
Answer: d
Question (general): a number whose fifth part increased by 2 is equal to its fourth part diminished by 2 is ?
Options: a ) 160 , b ) 80 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 2 = ( n / 4 ) - 2 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 4 â ‡ ’ ( 5 n - 4 n ) / 20 = 4 â ˆ ´ n = 80 option : b"
Answer: b
Question (physics): if an object travels at four feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 14400 , e ) 18000
Rationale: "speed = 4 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 4 = 1800 x 10 = 14400 answer d"
Answer: d
Question (physics): a 230 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 250 m , d ) 260 m , e ) 270 m
Rationale: "speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 230 + x therefore , d = speed * time thus 230 + x = 500 / 9 * 9 x = 500 - 230 = 270 m answer : e"
Answer: e
Question (general): if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 90 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 90 , c ) 100 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 180 - - 2 subtracting 1 from 2 we have c - a = 90 ; answer : b"
Answer: b
Question (geometry): the diagonals of a rhombus are 17 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 186 , c ) 150 , d ) 170 , e ) 172
Rationale: "1 / 2 * 17 * 20 = 170 answer : d"
Answer: d
Question (general): ? x 240 = 173 x 240
Options: a ) 173 , b ) 685 , c ) 865 , d ) 495 , e ) 534
Rationale: "let y x 240 = 173 x 240 then y = ( 173 x 240 ) / 240 = 173 answer : a"
Answer: a
Question (general): at a summer camp with 900 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 900 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 64 % , b ) 66 2 / 3 % , c ) 62 % , d ) 60 % , e ) 56 %
Rationale: "total - 900 participants campers are aged 8 to 12 = ( 1 / 2 ) * 900 = 450 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 450 = 600 percentage = ( 600 / 900 ) * 100 = 66 2 / 3 % answer : option b"
Answer: b
Question (geometry): a rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles , all of the same size . the minimum number of such tiles is :
Options: a ) 425
b ) 430
c ) 440
d ) 450
e ) 460
Rationale: l = 378 cm and b = 525 cm maximum length of a square tile = hcf of ( 378,525 ) = 21 cm number of tiles = ( 378 × 525 ) / ( 21 × 21 ) = ( 18 × 25 ) = 450 answer is d .
Answer: d
Question (general): 12 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Options: a ) a ) 35 , b ) b ) 34 , c ) c ) 42 , d ) d ) 25 , e ) e ) 26
Rationale: explanation : let the present age of p and q be 3 x and 4 x respectively . twelve years ago , p was half of q in age = > 2 ( 3 x – 12 ) = ( 4 x – 12 ) = > 6 x – 24 = 4 x – 12 = > 2 x = 12 = > x = 6 7 x = 7 * 6 = 42 answer : option c
Answer: c
Question (physics): a can do a piece of work in 6 days and b can do it in 6 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 1 / 2 , c ) 3 / 4 , d ) 9 / 11 , e ) 10 / 11
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 6 ( a + b ) ’ s one day work = 1 / 6 + 1 / 6 = 2 / 3 = = > time = 3 / 2 = 1 1 / 2 days answer : option b"
Answer: b
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 20 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 20 = 6 k + 4 k k = 2 total red ' s in bag a will be 2 k = 4 c"
Answer: c
Question (general): a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number n is
Options: a ) 74 , b ) n = 75 , c ) n = 175 , d ) n = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b