Cheukting/mathqa huggingface dataset:
Question (general): the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 44 , what is the value of x ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the areas are ( x + 4 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 4 and 2 x - 5 . if we add the two perimeters : 4 ( x + 4 ) + 4 ( 2 x - 5 ) = 44 12 x = 48 x = 4 the answer is b ."
Answer: b
Question (probability): what is the probability of getting exactly three heads on five flips of a fair coin ?
Options: a ) 1 / 32 , b ) 3 / 32 , c ) 1 / 4 , d ) 5 / 16 , e ) 1 / 2
Rationale: "5 flips of a fair coin to get = hhhtt = no . of ways this can be achieved = 5 ! / 3 ! x 2 ! = 10 probability to get any of the above 10 arrangements ( hhhtt ) = ( 1 / 2 ) ^ 5 = 1 / 32 total probability = 1 / 32 x 10 = 5 / 16 answer : d"
Answer: d
Question (gain): simple interest on a certain sum of money for 4 years at 10 % per annum is half the compound interest on rs . 3000 for 3 years at 12 % per annum . the sum placed on simple interest is
Options: a ) rs . 3000 , b ) rs . 607.39 , c ) rs . 1214.78 , d ) rs . 1518.48 , e ) none
Rationale: "solution c . i . = rs [ 3000 x ( 1 + 12 / 100 ) 3 - 3000 ] rs . ( 3000 x 112 / 100 x 112 / 100 x 112 / 100 - 3000 ) = rs . 1214.78 . sum = rs . [ 607.39 x 100 / 4 x 10 ] = rs . 1518.48 . answer d"
Answer: d
Question (general): in a certain lottery , the probability that a number between 14 and 20 , inclusive , is drawn is 1 / 6 . if the probability that a number 14 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 3 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 14 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 14 or moreor 20 or lessor both ) 2 / 3 + p ( set 2 ) - 1 / 6 = 1 p ( set 2 ) = 1 / 2 answer ( c )"
Answer: c
Question (general): x is the product of each integer from 1 to 50 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 0 , b ) 5 , c ) 6 , d ) 10 , e ) 12
Rationale: x = 1 * 2 * 3 * 4 * 5 * . . . . . . * 49 * 50 = 50 ! y = 100 ^ k 100 = 10 ^ 2 = 2 ^ 2 * 5 ^ 2 on prime factorization of x , power of 5 will always be greater than power of 2 concept : in every factorial value ( x ! ) , on prime factorization , the power of bigger prime number > the power of smaller prime number also , power of any prime number in any factorial can be calculated by following understanding power of prime x in n ! = [ n / x ] + [ n / x ^ 2 ] + [ n / x ^ 3 ] + [ n / x ^ 4 ] + . . . and so on where , [ x ] = greatest integer less than or equal to x and the explanation of terms is as follows [ n / x ] = no . of integers that are multiple of x from 1 to n [ n / x ^ 2 ] = no . of integers that are multiple of x ^ 2 from 1 to n whose first power has been counted in previous step and second is being counted at this step [ n / x ^ 3 ] = no . of integers that are multiple of x ^ 3 from 1 to n whose first two powers have been counted in previous two step and third power is counted at this step and so on . . . . . where [ n / x ] is greatest integer value of ( n / x ) less than or equal to ( n / x ) i . e . [ 100 / 3 ] = [ 33.33 ] = 33 i . e . [ 100 / 9 ] = [ 11.11 ] = 11 etc . power of 5 in x = [ 50 / 5 ] + [ 50 / 5 ^ 2 ] + [ 50 / 5 ^ 3 ] . . . = 10 + 2 + 0 = 12 power of 2 in x = [ 50 / 2 ] + [ 50 / 2 ^ 2 ] + [ 50 / 2 ^ 3 ] . . . = 25 + 12 + 6 + 3 + 1 = 47 i . e . x = 50 ! = 2 ^ 47 * 5 ^ 12 * . . . = 10 ^ 12 * . . . = 100 ^ 6 * . . . i . e . x is divisible by a 6 th power of 100 at the most i . e . y = 100 ^ k = 100 ^ 6 i . e . k = 6 answer : option c
Answer: c
Question (general): in a can , there is a mixture of milk and water in the ratio 3 : 7 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 7 . find the capacity of the can ?
Options: a ) 16.6 , b ) 44 , c ) 27 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 3 / 10 ( t - 8 ) after adding milk , quantity of milk in the mixture = 4 / 11 t . 4 t / 11 - 8 = 3 / 10 ( t - 8 ) 37 t = 880 - 264 = > t = 16.6 . answer : a"
Answer: a
Question (general): dawson and henry are in a relay race . dawson runs the first leg of the course in 38 seconds . henry runs the second leg of the course in 7 seconds . what was the average time they took to run a leg of the course ?
Options: a ) 20.5 , b ) 21.5 , c ) 22.5 , d ) 23.5 , e ) 24.5
Rationale: ( 38 seconds + 7 seconds ) / 2 = 22.5 seconds correct option is : c
Answer: c
Question (gain): if 1500 is increased by 20 % , and then reduced by y % , yielding 1080 , what is y ?
Options: a ) 20 % , b ) 40 % , c ) 60 % , d ) 80 % , e ) 100 %
Rationale: soln : - 1,500 * 1.2 = 1,800 . 1,800 ( 1 - y / 100 ) = 1,080 - - > ( 1 - y / 100 ) = 0.6 - - > y = 40 % . answer : b
Answer: b
Question (physics): if a is thrice as fast as b and together can do a work in 24 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 32 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 24 = 3 + 1 / 3 x = 4 / 3 x = 1 / 24 x = 24 * 4 / 3 = 32 answer : d"
Answer: d
Question (physics): the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit u on the height of vehicles that are allowed to use the tunnel ?
Options: a ) 5 ½ ft , b ) 7 ½ ft , c ) 8 ½ ft , d ) 9 ½ ft , e ) 10 ft
Rationale: "let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer u is 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b"
Answer: b
Question (general): find the product of the local value and absolute value of 4 in 20468 ?
Options: a ) 1000 , b ) 1200 , c ) 1340 , d ) 1450 , e ) 1600
Rationale: "local value of 4 = 4 x 100 = 400 place value of 4 = 4 there fore = 4 x 400 = 1600 e"
Answer: e
Question (physics): a train 500 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 28 , c ) 49 , d ) 64 , e ) 21
Rationale: "s = ( 500 + 300 ) / 45 = 800 / 45 * 18 / 5 = 64 answer : d"
Answer: d
Question (gain): a and b invests rs . 3000 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 0 , d ) 9 : 2 , e ) 9 : 1
Rationale: "( 3 * 6 + 6 * 6 ) : ( 4 * 12 ) 54 : 48 = > 9 : 8 answer : b"
Answer: b
Question (general): we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 30 , and the difference between the total number of strawberries and the total number of blueberries would increase by 100 . each blue box contains how many blueberries ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "let x be the number of blueberries in each blue box . then there are x + 30 strawberries in each red box . x + ( x + 30 ) = 100 x = 35 the answer is a ."
Answer: a
Question (general): there are an average of 117 jellybeans in each of 34 bags of various sizes . after adding another bag , the average number of jellybeans per bag increases by 7 . how many jellybeans are in the new bag ?
Options: a ) 124 , b ) 97 , c ) 117 , d ) 229 , e ) 362
Rationale: total jellybeans in 34 bags = 34 * 117 = 3978 total jellybeans in 35 bags = 35 * 124 = 4340 number of jellybeans in new bag = 3978 - 4340 = 362 jellybeans answer is e
Answer: e
Question (general): a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 89 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 800 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 175 + 89 33 x / 100 = 264 x = 800 answer is c"
Answer: c
Question (general): a solution of 90 litres contains milk and water in the ratio 7 : x . if 10 litres of water is added to the solution , the ratio becomes 3 : 2 , find the value of x ?
Options: a ) 2 , b ) 1.5 , c ) 3.5 , d ) 2.5 , e ) 3
Rationale: exp . total new quantity = original sol + water = 90 + 10 = 100 new ratio = 3 : 2 , new quantity of milk = 3 / 5 * 100 = 60 lit , new quantity of water = 2 / 5 * 100 = 40 lit water present initially = ( 40 - 10 ) = 30 lit ratio = 60 / 30 = 7 / x there for x = 3.5 answer : c
Answer: c
Question (geometry): a rectangle has a perimeter of 176 inches . the length of the rectangle is 8 inches more than its width . what is the area of the rectangle ?
Options: a ) 1,408 square inches
b ) 1,920 square inches
c ) 1,936 square inches
d ) 2,304 square inches
e ) none of these
Rationale: explanation : we have : ( l - b ) = 8 and 2 ( l + b ) = 176 or ( l + b ) = 88 . solving the two equations , we get : l = 48 and b = 40 . area = ( l x b ) = ( 48 x 40 ) in 2 = 1920 in 2 . correct answer : b
Answer: b
Question (gain): in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 240 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 280 ( 40 * 6 = 240 ) 100 % - - - - - > 600 ( 100 * 6 = 600 ) answer : option a"
Answer: a
Question (physics): in covering a distance of 42 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7 kmph , e ) 7.8 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 42 / x - 42 / 2 x = 3 6 x = 42 x = 7 km / hr . answer : option d"
Answer: d
Question (gain): a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 96 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 81 , b ) 84 , c ) 85 , d ) 88 , e ) 90
Rationale: let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 96 or 1 / 7 t + 1 t = 96 therefore t = 96 * 7 / 8 = 84 b
Answer: b
Question (physics): the length of the bridge , which a train 140 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 328 , b ) 279 , c ) 235 , d ) 288 , e ) 211
Rationale: speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 140 + x ) / 30 = 25 / 2 = = > 2 ( 140 + x ) = 750 = = > x = 235 m . answer : c
Answer: c
Question (general): maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability t , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , t = 9 provide the desired outcome , making the answer e ."
Answer: e
Question (general): evaluate : 86 x 863 - 86 x 237
Options: a ) 45823 , b ) 53836 , c ) 44824 , d ) 66524 , e ) none of them
Rationale: "86 x 863 + 986 x 237 = 986 x ( 863 - 237 ) = 86 x 626 = 53836 . answer is b"
Answer: b
Question (physics): a man complete a journey in 40 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 30 km / hr . find the total journey in km .
Options: a ) 960 km , b ) 224 km , c ) 230 km , d ) 232 km , e ) 234 km
Rationale: "0.5 x / 20 + 0.5 x / 30 = 40 - - > x / 20 + x / 30 = 80 - - > 5 x = 60 x 80 - - > x = ( 60 x 80 ) / 5 = 960 km . answer : a"
Answer: a
Question (general): a large box contains 19 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 475 , b ) 350 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 19 * 25 = 475 correct answer a"
Answer: a
Question (probability): a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 7
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 4 bottles of apple juice is 6 c 4 * 4 c 2 = 15 * 6 = 90 p ( selling 4 bottles of apple juice ) = 90 / 210 = 9 / 21 = 3 / 7 the answer is e ."
Answer: e
Question (other): in a class of 50 students , 18 take chorus , 26 take band , and 2 take both chorus and band . how many students in the class are not enrolled in either chorus or band ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: 16 + 2 + 24 + x = 50 42 + x = 50 x = 8 students a )
Answer: a
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 34.9 % . 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 ) data inadequate , e ) 42
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 + 34.9 ) / ( 100 â ˆ ’ 5 ) = 142 hence , required % profit = 142 â € “ 100 = 42 % answer e"
Answer: e
Question (gain): how long will a boy take to run round a square field of side 30 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 25 sec , e ) 36 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 30 * 4 = 120 m time taken = 120 * 3 / 10 = 36 sec answer is e"
Answer: e
Question (general): the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 280 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 280 hence , x = 200 . so , number of timeshare condos available at playa del mar = 200 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 2 / 5 x = 3 / 5 ( 200 ) = 120 the correct answer is c"
Answer: c
Question (gain): the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 350 , by what percent is the price to be reduced ?
Options: a ) 70 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 350 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 350 ) * 100 / 500 = 70 % answer : option a"
Answer: a
Question (general): ratio of two numbers x and y is 7 : 9 . if x is increased by 20 % and y is increased by 33 then the new ratio becomes 1 : 5 . what is the ratio 2 y : ( x + 4 )
Options: a ) 18 : 11 , b ) 8 : 1 , c ) 11 : 18 , d ) 1 : 8 , e ) 1 : 1
Rationale: let : x = 7 n y = 9 n 8.4 n / ( 9 n + 33 ) = 1 / 5 42 n = 9 n + 33 n = 1 so , x = 7 ; y = 9 2 y / ( x + 4 ) = 18 / 11 answer = a
Answer: a
Question (general): of 70 players on a football team , 52 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 64 , e ) 92
Rationale: "total = 70 thrower = 52 rest = 70 - 52 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 52 + 12 = 64 so d . 64 is the right answer"
Answer: d
Question (physics): a man can row upstream at 15 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 65 , b ) 86 , c ) 30 , d ) 78 , e ) 25
Rationale: "us = 15 ds = 35 m = ( 35 + 15 ) / 2 = 25 answer : e"
Answer: e
Question (other): 39 ! is divided by 41 . then what is the remainder ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a"
Answer: a
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 ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 40000 / y = 2 / 3 ‹ = › y = ( 40000 × 3 / 2 ) . ‹ = › y = 60000 . answer c"
Answer: c
Question (physics): if the product of two numbers is 82500 and their h . c . f . is 55 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 1500 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 82500 , because we know product of two numbers = product of hcf and lcm lcm = 82500 / 55 = 1500 option c"
Answer: c
Question (geometry): what is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150 o ?
Options: a ) 24 sq units
b ) 48 sq units
c ) 24 under root 3
d ) 48 under root 3
e ) such a triangle does not exist
Rationale: explanatory answer if two sides of a triangle and the included angle ' y ' is known , then the area of the triangle = 1 / 2 * ( product of sides ) * sin y substituting the values in the formula , we get 1 / 2 * 8 * 12 * sin 150 o = 1 / 2 * 8 * 12 * 1 / 2 . note : sin 150 o = 1 / 2 area = 24 sq units . choice a
Answer: a
Question (physics): tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 8 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4.5 mph , e ) 0.5 mph
Rationale: "( 1 mph + 8 mph ) / 2 = 4.5 mph correct option is : d"
Answer: d
Question (general): the average age of boys in a class is 16 years and that of the girls is 15 years . what is the average age for the whole class ?
Options: a ) 15 , b ) 16 , c ) 15.5 , d ) insufficient data , e ) 17
Rationale: explanation : we do not have the number of boys and girls . hence we can not find out the answer . answer : option d
Answer: d
Question (general): there were totally 100 men . 84 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 84 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 16 - 25 - 15 - 30 = 100 - 86 = 14 answer : d"
Answer: d
Question (general): excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 35 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 24 , d ) 20 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 35 km with stoppages . stoppage time = time take to travel ( 60 - 35 ) km i . e 25 km at 60 km / hr . stoppage time = 25 / 60 hrs = 24 min . answer : c"
Answer: c
Question (general): one paper sheet can be used to create 8 paper boats or 6 paper planes . if total exact 80 paper toys are to be made , minimum how many sheets need to be used to make paper boats ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: let us say x sheets are used to create paper boats and y sheets are used to create paper planes . since total 80 paper toys are to be created , 8 x + 6 y = 80 . = > 8 x = 80 - 6 y = > x = 10 - ( 6 / 8 ) y = > x = 10 - ( 3 / 4 ) y to minimize x , we need to maximize y . and y needs to be multiple of 4 . y = 4 , x = 10 - ( 3 / 4 ) 4 = 7 y = 8 , x = 10 - ( 3 / 4 ) 8 = 4 y = 12 , x = 10 - ( 3 / 4 ) 12 = 1 beyond this , x will become negative for greater values of y . so , minimum 1 sheet is required to be used for creating paper boats . answer : e
Answer: e
Question (physics): the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 60 , find the other ?
Options: a ) 100 , b ) 240 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 60 = 120 answer is c"
Answer: c
Question (general): 1604 x 1604 = ?
Options: a ) a ) 2572816 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1604 x 1604 = ( 1604 ) 2 = ( 1600 + 4 ) 2 = ( 1600 ) 2 + ( 4 ) 2 + ( 2 x 1600 x 4 ) = 2560000 + 16 + 12800 . = 2572816 . a )"
Answer: a