Cheukting/mathqa huggingface dataset:
Question (geometry): what is the ratio e of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ?
Options: a ) 1 / 4
b ) 3 / 8
c ) 1 / 2
d ) 3 / 5
e ) 2
Rationale: one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area e = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )
Answer: d
Question (general): if the operation @ is defined for all a and b by the equation a @ b = ( a ^ b ) / 2 , then ( 3 @ 2 ) = ?
Options: a ) 4 , b ) 2 , c ) 9 / 2 , d ) - 9 / 2 , e ) - 8 / 2
Rationale: work within the parenthesis first so solve ( 3 @ 2 ) first ( 3 @ 2 ) = ( 3 ^ 2 ) / 2 = 9 / 2 so 9 / 2 is the answer . . . . this question is merely testing order of operations remember pemdas answer : c
Answer: c
Question (physics): a boat can travel with a speed of 10 km / hr in still water . if the speed of the stream is 8 km / hr , find the time taken by the boat to go 54 km downstream .
Options: a ) 4.25 hr , b ) 5.25 hr , c ) 3 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 10 km / hr speed of the stream = 8 km / hr speed downstream = ( 10 + 8 ) = 18 km / hr time taken to travel 68 km downstream = 54 â  „ 18 = 17 â  „ 4 = 3 hours answer is c"
Answer: c
Question (physics): there is enough provisions for 9600 women in an army camp for 400 days . if there were 4800 men less , how long will the provision last ?
Options: a ) 799 , b ) 800 , c ) 801 , d ) 802 , e ) 803
Rationale: we have , m 1 d 1 = m 2 d 2 9600 * 400 = 4800 * d 2 d 2 = 9600 * 400 / 4800 = 800 days . answer : b
Answer: b
Question (general): if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 3 .
Options: a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4
Rationale: "6 * 15 * 3 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 3 + 1 ) = ( √ 8 * 18 ) / 4 = ( √ 144 ) / 4 = 12 / 4 = 3 . answer is d ."
Answer: d
Question (physics): shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 60 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 48
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 48 hence answer is e"
Answer: e
Question (gain): a and b began business with rs . 6000 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 ) 240 , b ) 288 , c ) 277 , d ) 357 , e ) 361
Rationale: "( 6 * 8 + 5 * 4 ) : ( 4 * 8 + 5 * 4 ) 17 : 13 17 / 30 * 630 = 357 answer : d"
Answer: d
Question (general): a , b and c rents a pasture for rs . 950 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 295 , b ) 199 , c ) 676 , d ) 156 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 950 = 295 answer : a"
Answer: a
Question (general): in what ratio p : q should the mixture p of milk and water in the ratio of 2 : 1 be mixed with another mixture q of milk and water in the ratio 1 : 5 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 3 : 5 , e ) 3 : 1
Rationale: "( 2 / 3 ) * p + ( 1 / 6 ) * q = ( 1 / 3 ) * p + ( 5 / 6 ) * q 2 p = 4 q p / q = 2 / 1 the answer is b ."
Answer: b
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 350 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 2,900 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 350 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 350 x 8 = 2800 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 2900 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 2900 ( answer b )"
Answer: b
Question (general): ifaequals the sum of the even integers from 2 to 80 , inclusive , andbequals the sum of the odd integers from 1 to 79 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 40 , e ) 21
Rationale: "this is a solution from beatthegmat : even numbers : ( 80 - 2 ) / 2 + 1 = 40 even integers . ( 80 + 2 ) / 2 = 41 is the average of the even set . sum = avg * ( # of elements ) = 41 * 40 = 1640 = a odd numbers : ( 79 - 1 ) / 2 + 1 = 40 odd integers . ( 79 + 1 ) / 2 = 40 is the average of the odd set . sum = avg * ( # of elements ) = 40 * 40 = 1600 = b a - b = 1640 - 1600 = 40 . answer : d"
Answer: d
Question (gain): if 31 % of a number is 46.5 , the number is ?
Options: a ) 150 , b ) 155 , c ) 160 , d ) 165 , e ) none
Rationale: "answer let 31 % of a = 46.5 ⇒ ( 31 x a ) / 100 = 46.5 ∴ a = ( 46.5 x 100 ) / 31 = 150 correct option : a"
Answer: a
Question (general): if an average hard drive had a capacity of 0.6 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 768 , d ) 6144 , e ) 1536
Rationale: "0.6 * 2 ^ 10 = 0.6 * 1024 = 614.4 the answer is d ."
Answer: d
Question (general): two digits in father ' s age are the same as the digit in the son ' s age , but in reverse order . in 5 years father will be twice as old as son will be then . what is the difference in their current age ?
Options: a ) 18 , b ) 16 , c ) 34 , d ) 25 , e ) 12
Rationale: father ' s age = 10 x + y so son ' s age = 10 y + x . . after 5 years , 10 x + y + 5 = 2 * ( 10 y + x + 5 ) . . . . so 5 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 3 . . . so ages are 31 and 13 and ans as found correctly by u is a . . 18
Answer: a
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 278 m , c ) 300 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 18 ) m = 300 m . answer : c"
Answer: c
Question (general): the average monthly income of a and b is rs . 5050 . the average monthly income of b and c is rs . 6250 and the average monthly income of a and c is rs . 5200 . what is the monthly income of a ?
Options: a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6200
Rationale: "explanation : let monthly income of a = a monthly income of b = b monthly income of c = c a + b = 2 × 5050 . . . . ( equation 1 ) b + c = 2 × 6250 . . . . ( equation 2 ) a + c = 2 × 5200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > a + b + a + c - ( b + c ) = ( 2 × 5050 ) + ( 2 × 5200 ) - ( 2 × 6250 ) = > 2 a = 2 ( 5050 + 5200 - 6250 ) = > a = 4000 i . e . , monthly income of a = 4000 answer is c"
Answer: c
Question (general): x , y , and z are different prime numbers . the product x ^ 3 * y ^ 2 * z ^ 1 is divisible by how many different positive numbers ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "the exponents of x ^ 3 * y ^ 2 * z ^ 1 are 3 , 2 , and 1 . the number of factors is ( 3 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 24 the answer is a ."
Answer: a
Question (general): a man is 28 years older than his son . in four years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 25 years
Rationale: "explanation : let ' s son age is x , then father age is x + 28 . = > 2 ( x + 4 ) = ( x + 28 + 4 ) = > 2 x + 8 = x + 32 = > x = 24 years answer : option d"
Answer: d
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 529 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 23
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 529 / 3 = 176.33 sq m l b = 176.33 i . e . , l * l / 3 = 176.33 l ^ 2 = 529 = > l = 23 e"
Answer: e
Question (physics): walking at 5 / 6 th of its usual speed a cab is 8 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 40 m , d ) 50 m , e ) 62 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 8 m ut / 5 = 8 m ut = 40 m answer is c"
Answer: c
Question (physics): a and b can do a piece of work in 4 days . b and c can do it in 12 days and a and c in 16 days . working together they will complete the work in how many days ?
Options: a ) 4.05 days , b ) 5.05 days , c ) 14.76 days , d ) 8.05 days , e ) 15.05 days
Rationale: "a + b = 1 / 4 b + c = 1 / 12 c + a = 1 / 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ( a + b + c ) = 1 / 4 + 1 / 12 + 1 / 16 = 19 / 48 a + b + c = 19 / 96 96 / 19 = 5.05 days answer : b"
Answer: b
Question (physics): a certain machine produces 780 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 4 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 74,880 , d ) 100,000 , e ) 168,000
Rationale: "since 7 days consist of 24 * 4 hours the total is 96 hours . since every hour the machine produces 780 units of product p the total product during 96 hours is 96 * 780 = 74,880 . correct option : d"
Answer: d
Question (general): the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 39 ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "first , let ' s translate the expression 21 # 39 , using the definition given : 21 # 39 = 21 × 24 × 27 × 30 × 33 × 36 × 39 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 39 = 3 ^ 7 ( 7 × 8 × 9 × 10 × 11 × 12 × 13 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 39 = 3 ^ 7 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 × ( 2 ^ 2 × 3 ) × 13 ) let ' s group the prime bases : 21 # 39 = 2 ^ 6 × 3 ^ 10 × 5 × 7 × 11 × 13 the sum of the exponents is 6 + 10 + 1 + 1 + 1 + 1 = 20 the answer is d ."
Answer: d
Question (other): the cost of 3 pens and 5 pencils is rs . 200 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) rs . 600
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 200 15 x + 5 x = rs . 200 x = 200 / 20 = 10 : . cost of 1 pen = 5 x = 5 x 10 = 50 : . cost of 12 pens , i . e . ( one dozen ) = 50 x 12 = rs . 600 answer : option e"
Answer: e
Question (general): the captain of a cricket team of 11 members is 25 years old and the wicket keeper is 5 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: "let the average age of the whole team be x years . 11 x - ( 25 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is c ."
Answer: c
Question (gain): solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 72 % percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 48 % , b ) 54 % , c ) 60 % , d ) 64 % , e ) 68 %
Rationale: 72 % is 8 % - points below 80 % and 17 % - points above 55 % . so the ratio of solution p to solution q is 17 : 8 . mixture p is 17 / 25 = 68 % of the volume of mixture pq . the answer is e .
Answer: e
Question (general): there are 3 girls and 6 boys . how many kids are there ?
Options: a ) 10 , b ) 19 , c ) 20 , d ) 9 , e ) 12
Rationale: d
Answer: d
Question (physics): two numbers n and 16 have lcm = 48 and gcf = 8 . find n .
Options: a ) 11 , b ) 32 , c ) 24 , d ) 48 , e ) 50
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 48 * 8 n = 48 * 8 / 16 = 24 correct answer c"
Answer: c
Question (general): if y > 0 , ( 2 y ) / 5 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: can be reduced to 2 y / 5 + 3 y / 10 = 2 y / 5 = 70 % d
Answer: d
Question (physics): convert 200 inches into centimeter ?
Options: a ) 512 cm , b ) 520 cm , c ) 508 cm , d ) 510 cm , e ) 554 cm
Rationale: "1 inch = 2.54 cm 200 inches = 200 * 2.54 = 508 cm answer is c"
Answer: c
Question (physics): if an object travels at seven feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 25200 , e ) 18000
Rationale: "speed = 7 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 7 = 25200 answer d"
Answer: d
Question (general): evaluate : 2344 - 12 * 3 * 2 = ?
Options: a ) 2337 , b ) 1227 , c ) 3327 , d ) 5457 , e ) 7677
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 2344 - 12 * 3 * 2 = 2344 - 8 = 2337 correct answer a"
Answer: a
Question (gain): a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 27
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 20 % of the final price - - > ( final price ) * 0.8 = $ 18 - - > ( final price ) = $ 22.5 . answer : d ."
Answer: d
Question (general): the product of x and y is a constant . if the value of x is increased by 80 % , by what percentage must the value of y be decreased ?
Options: a ) 45 % , b ) 55 % , c ) 35 % , d ) 40 % , e ) 44.44 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.8 x ( 180 ) i . e . 180 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 180 = 55.55 i . e . y decreases from 100 to 55.55 i . e . decrease of 44.44 % answer : option e"
Answer: e
Question (physics): in what time will a train 100 meters long cross an electric pole , if its speed is 90 km / hr
Options: a ) 8.5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 4 seconds
Rationale: "first convert speed into m / sec speed = 90 * ( 5 / 18 ) = 25 m / sec time = distance / speed = 100 / 25 = 4 seconds answer : e"
Answer: e
Question (geometry): the roof of an apartment building is rectangular and its length is 7 times longer than its width . if the area of the roof is 847 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 66 . , d ) 44 . , e ) 46 .
Rationale: "answer is c : 66 let w be the width , so length is 7 w . therefore : w * 7 w = 847 , solving for , w = 11 , so 7 w - w = 6 w = 6 * 11 = 66"
Answer: c
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 . 3000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 600 , e ) 1200
Rationale: "explanation : 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 . 3000 = > 5 parts out of 15 parts is rs . 3000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 3000 ) = rs . 1200 answer : e"
Answer: e
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 9 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = 9 years . answer : c"
Answer: c
Question (geometry): the circumferences of two circles are 660 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2996 sq m , b ) 4774 sq m , c ) 4312 sq m , d ) 2768 sq m , e ) 2786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 660 and 2 ∏ l = 704 s = 660 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 330 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 330 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 330 - 352 ) ( 330 + 352 ) / ∏ = ( 22 ) ( 682 ) / ( 22 / 7 ) = 4774 sq m answer : b"
Answer: b
Question (physics): p is 30 % more efficient than q . p can complete a work in 23 days . if p and q work together , how much time will it take to complete the same work ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 13 , e ) 15
Rationale: "work done by p in 1 day = 1 / 23 let work done by q in 1 day = q q × ( 130 / 100 ) = 1 / 23 = > q = 100 / ( 23 × 130 ) = 10 / ( 23 × 13 ) work done by p and q in 1 day = 1 / 23 + 10 / ( 23 × 13 ) = 23 / ( 23 × 13 ) = 1 / 13 = > p and q together can do the work in 13 days option d"
Answer: d
Question (geometry): suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have
Options: a ) 4
b ) 6
c ) 9
d ) 10
e ) 5
Rationale: to arrange them as described i did as follows on my scratch paper ( see the file attached ) , where i counted 4 sides and bottom , hence 4 + 1 = 5 . e
Answer: e
Question (general): the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 48 , e ) 50
Rationale: "so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 difference = 50 - 25 = 25 answer : b ."
Answer: b
Question (general): how many positive integers less than 10,000 are such that the product of their digits is 30 ?
Options: a ) 12 , b ) 24 , c ) 36 , d ) 38 , e ) 50
Rationale: "30 = 1 * 30 , 2 * 15 , 3 * 10 , 5 * 6 we have the option of using single digits 1,2 , 3,5 and 6 no : of four digit numbers such that the product is 30 the possible combinations are using digits ( 1,2 , 3,5 ) & ( 1,1 , 5 , 6 ) such that the product 30 . no : of different combinations possible using ( 1,2 , 3,5 ) = 4 ! = 24 no : of different combinations possible using ( 5,6 , 1,1 ) = 4 ! / 2 ! = 12 ( ' 1 ' is repeated twice ) total 4 digit numbers so that the product is 30 is 24 + 12 = 36 no : of three digit numbers such that the product is 30 the possible combinations are using digits ( 2,3 , 5 ) & ( 1 , 5,6 ) no : of different combinations possible using ( 2 , 3,5 ) = 3 ! = 6 no : of different combinations possible using ( 1 , 5,6 ) = 3 ! = 6 total 3 digit numbers so that the product is 30 is 6 + 6 = 12 no : of 2 digit numbers such that the product is 30 is 2 ( 56 and 65 ) total numbers under 10000 such that the product is 30 is 36 + 12 + 2 = 50 e"
Answer: e
Question (physics): the speed at which a man can row a boat in still water is 16 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 100 metres ?
Options: a ) 23 , b ) 27 , c ) 28 , d ) 12 , e ) 18
Rationale: speed of the boat downstream = 16 + 4 = 20 kmph = 20 * 5 / 18 = 5.55 m / s hence time taken to cover 100 m = 100 / 5.55 = 18 seconds . answer : e
Answer: e
Question (gain): on the first of the year , james invested x dollars at proudstar bank in an account that yields 2 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 %
Rationale: "per quarter , interest = 2 % so for a year , interest = 8 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 8 % answer = 8.25 % = answer : d"
Answer: d
Question (gain): the sale price sarees listed for rs . 390 after successive discount is 14 % and 15 % is ?
Options: a ) 285 , b ) 277 , c ) 290 , d ) 662 , e ) 262
Rationale: "390 * ( 86 / 100 ) * ( 85 / 100 ) = 285 answer : a"
Answer: a
Question (physics): with both inlets open , a water tank will be filled with water in 42 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 7,000 , b ) 10,500 , c ) 11,750 , d ) 12,000 , e ) 13,000
Rationale: "the work done by inlet a and b together in 1 min = 1 / 42 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 42 ) - ( 1 / 120 ) = 1 / 65 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 65 ) - ( 1 / 120 ) = 50 cubic meter = 7000 cubic meter answer : option a"
Answer: a
Question (geometry): if a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 91 and a perimeter of 40 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 91 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . let ' s test answer b : 7 if . . . the shorter side = 7 . . . the area = 91 . . . . 91 / 7 = 13 = the longer side perimeter = 7 + 7 + 13 + 13 = 40 b"
Answer: b
Question (geometry): the ratio of the volumes of two cubes is 27 : 125 . what is the ratio of their total surface areas ?
Options: a ) 9 : 25 , b ) 9 : 35 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129
Rationale: "ratio of the sides = 3 √ 27 : 3 √ 125 = 3 : 5 ratio of surface areas = 3 ^ 2 : 5 ^ 2 = 9 : 25 answer : option a"
Answer: a