Cheukting/mathqa huggingface dataset:
Question (general): a student scored an average of 60 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 160 , c ) 76 , d ) 140 , e ) 26
Rationale: "given m + p + c = 60 * 3 = 180 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 180 = 140 answer : d"
Answer: d
Question (general): if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 21 - m ) then m = ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "2 m = 21 - m 3 m = 21 m = 7 the answer is c ."
Answer: c
Question (other): each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 29 have long fur , 17 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 9
Rationale: no of dogs = 45 long fur = 29 brown = 17 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 29 + 17 - both both = 9 answer e
Answer: e
Question (general): set a contains all the even numbers between 42 and 90 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "each term in set b is 20 more than the corresponding term in set a . the difference of the sums = 25 * 20 = 500 . the answer is e ."
Answer: e
Question (general): of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 6 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 29.4 % , e ) 11.1 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 6 is 1200 * 1 / 6 so it reduced 200 people , so there is 1000 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 1000 clerical left / 3400 people total you get ( a ) 29.4 % answer : d"
Answer: d
Question (geometry): an artist wishes to paint a circular region on a square poster that is 5 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) 2 / sqrt ( pi ) , d ) sqrt ( 12.5 / pi ) , e ) pi / 2
Rationale: "area of the poster is 5 x 5 = 25 1 / 2 the area = 12.5 pi * r ^ 2 = 12.5 r ^ 2 = 12.5 / pi r = sqrt ( 12.5 / pi ) answer ( d )"
Answer: d
Question (general): the tax on a commodity is diminished by 17 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8 % , c ) 4.5 % , d ) 6.5 % , e ) 1.5 %
Rationale: "100 * 100 = 10000 83 * 115 = 9545 - - - - - - - - - - - 10000 - - - - - - - - - - - 455 100 - - - - - - - - - - - ? = > 4.55 % decrease answer : c"
Answer: c
Question (general): if x is 20 percent greater than 80 , then x =
Options: a ) 68 , b ) 70.4 , c ) 96 , d ) 105.6 , e ) 108
Rationale: "x is 20 % greater than 80 means x is 1.2 times 80 ( in other words 80 + 20 / 100 * 80 = 1.2 * 80 ) therefore , x = 1.2 * 80 = 96.00 answer : c"
Answer: c
Question (physics): a pet groomer has 7 animals to groom for the day ( 2 cats and 5 dogs ) . if she randomly selects 4 animals to groom before lunch , what is the probability she will finish all the cats before lunch ?
Options: a ) 3 / 7 , b ) 2 / 7 , c ) 12 / 13 , d ) 5 / 11 , e ) 4 / 7
Rationale: combination probability formula : ncr = n ! / [ r ! ( n - r ) ! ] total possible , select 4 animals from 7 animals = 7 c 4 = 7 ! / [ 4 ! ( 7 - 4 ) ! ] = 35 . to finish all 2 cats there must be 2 dogs , select 2 dogs from 5 = 5 c 2 = 10 . and , select 2 cats from 2 = 2 c 2 = 1 . 2 cats and 2 dogs = ( 1 ) ( 10 ) = 10 probability = ( number outcomes favorable ) / ( total number outcomes ) = 10 / 735 = 2 / 7 answer : b
Answer: b
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.75 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,628 , e ) 2,256
Rationale: "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.75 = 0.45 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer d"
Answer: d
Question (general): a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 70 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 25 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 70 ⇒ 1.75 x = 70 ⇒ x = 40 coins answer c"
Answer: c
Question (general): how many positive integers less than 26 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 21 , c ) 24 , d ) 22 , e ) 20
Rationale: 9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 10 - 1 = 21 . answer : b .
Answer: b
Question (gain): how many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 5 percent sugar solution ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let x be the amount that needs to be evaporated . 0.04 ( 50 ) = 0.05 ( 50 - x ) 0.05 x = 2.5 - 2 x = 0.5 / 0.05 = 10 liters the answer is d ."
Answer: d
Question (gain): a person lent a certain sum of money at 6 % per annum at simple interest and in 8 years the interest amounted to $ 520 less than the sum lent . what was the sum lent ?
Options: a ) 800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "p - 520 = ( p * 6 * 8 ) / 100 p = 1000 the answer is b ."
Answer: b
Question (general): there are 30 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 435 , d ) 60 , e ) 90
Rationale: "30 players are there . two players play one game with one another . so 30 c 2 = 30 * 29 / 2 = 435 so option c is correct"
Answer: c
Question (general): a wholesaler wishes to sell 100 pounds of mixed nuts at $ 1.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 1.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is a ."
Answer: a
Question (general): a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 90 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 18 * 4 = 72 now half on their horses so remaining on the walk so 9 men 9 men has 18 legs so , 18 + 72 = 90 legs walking answer : e"
Answer: e
Question (gain): 240 is increased by 20 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 180 , d ) 288 , e ) 220
Rationale: explanation final number = initial number + 20 % ( original number ) = 240 + 20 % ( 240 ) = 240 + 48 = 288 . answer d
Answer: d
Question (physics): convert 20 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 20 miles = 20 * 1760 = 35200 yards answer is b"
Answer: b
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 25 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 25 % , d ) 23 % , e ) can not be determined
Rationale: answer : c .
Answer: c
Question (general): the average of 10 consecutive integers is 11 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 5 , b ) 5.5 , c ) 6 , d ) 6.5 , e ) 7
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d ."
Answer: d
Question (general): let the number which when multiplied by 15 is increased by 196 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 15 x - x = 196 ‹ = › 14 x = 196 x ‹ = › 14 . answer a"
Answer: a
Question (general): running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets ?
Options: a ) 36 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 6 * 6 = 36 days to produce 2 w widgets . answer : a"
Answer: a
Question (geometry): a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , then what is the area of the parking space in square feet ?
Options: a ) 46
b ) 81
c ) 126
d ) 252
e ) none of these
Rationale: solution clearly , we have : l = 9 and l + 2 b = 37 or b = 14 . ∴ area = ( l × b ) = ( 9 × 14 ) sq . ft . = 126 sq . ft . answer c
Answer: c
Question (general): lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 64,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.14544 , c ) 0.21978 , d ) 0.35466 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 364000 x \ therefore required percentage = \ inline \ frac { 800 x } { 364000 } \ times 100 = 0.21978 c"
Answer: c
Question (general): if p / q = 4 / 5 , then the value of 6 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 10 / 7 , d ) 2 , e ) 3
Rationale: "answer given exp . = 6 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 6 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 6 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 6 / 7 + 6 / 14 = 6 / 7 + 3 / 7 = 10 / 7 correct option : c"
Answer: c
Question (gain): two persons start at the same point , walk in opposite directions with 6 km / hr and 7 km / hr respectively . what is the distance separated after 3 and half hrs ?
Options: a ) 45.5 km , b ) 27.250 km , c ) 28.250 km , d ) 29.250 km , e ) 25.250 km
Rationale: as the two persons are moving in the opposite direction , so they will be separateed in 1 hour = 6 + 7 = 13 km . they will be separated in 2.5 hours = 13 * 3.5 = 45.5 km answer : a
Answer: a
Question (general): on day one , a store sold 86 cups . on each of the next d days , the company sold 50 cups . if the average daily sales of cups over this time period ( including day one ) is 53 cups , what is the value of d ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: 86 + 50 d = 53 ( d + 1 ) . 3 d = 33 . d = 11 . the answer is c .
Answer: c
Question (gain): what is the value of â ˆ š 36 % ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 60 % , e ) 40 %
Rationale: "explanation : br > â ˆ š 16 % = â ˆ š 36 / â ˆ š 100 = 6 / 10 = 60 / 100 = 60 % correct answer is d ) 60 %"
Answer: d
Question (gain): there are two concentric circles with radii 8 and 4 . if the radius of the outer circle is increased by 25 % and the radius of the inner circle decreased by 25 % , by what percent does the area between the circles increase ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 64 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 48 pi . when the big circle ' s radius increases , the new area is 100 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 91 pi . the ratio of a 2 / a 1 is 91 / 48 = 1.9 which is an increase of 90 % . the answer is d ."
Answer: d
Question (physics): alice can bake a pie in 5 minutes . bob can bake a pie in 6 minutes . compute how many more pies alice can bake than bob in 60 minutes .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: alice can bake 60 / 5 = 12 pies in 60 minutes . bob can bake 60 / 6 = 10 pies in 60 minutes . alice can therefore bake 12 - 10 = 2 more pies than bob . correct answer b
Answer: b
Question (general): a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6100 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6470 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6100 * 6 ) – 30,130 ] = rs . ( 36600 – 30,130 ) = rs . 6470 answer c"
Answer: c
Question (general): when a random experiment is conducted , the probability that event a occurs is 1 / 6 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 17 / 216 , b ) 19 / 216 , c ) 23 / 216 , d ) 25 / 216 , e ) 35 / 216
Rationale: "one case is : 1 / 6 * 1 / 6 * 5 / 6 * 5 / 6 = 25 / 1296 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 25 / 1296 ) = 25 / 216 the answer is d ."
Answer: d
Question (general): a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , c receives :
Options: a ) s . 14,000 , b ) s . 14,200 , c ) s . 4,400 , d ) s . 8,400 , e ) s . 4,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 x 12 / 50 ) = rs . 8,400 . d"
Answer: d
Question (physics): a building contractor employs 20 male , 15 female and 5 child workers . to a male worker he pays rs . 35 per day , to a female worker rs . 20 per day and a child worker rs . 8 per day . the average wage per day paid by the contractor is ?
Options: a ) 22 , b ) 23 , c ) 28 , d ) 29 , e ) 26
Rationale: "20 15 5 35 20 8 500 + 300 + 40 = 1040 / 40 = 26 answer : e"
Answer: e
Question (general): ( ( 1 ^ 5 m ) / ( 5 ^ 5 m ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ?
Options: a ) 7 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: ( ( 1 ^ 5 m ) / ( 5 ^ 5 m ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ 5 m ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ 5 m = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ 5 m ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 7 answer a
Answer: a
Question (general): eggs are sold in packages of 6 or 11 only . if doris bought 79 eggs exactly , what could be the number of large packs doris bought ?
Options: a ) 6 . , b ) 2 . , c ) 3 . , d ) 5 . , e ) 4 .
Rationale: no strategy involved . simple question demanding fast calculation . 11 x 5 = 55 = > 79 - 55 = 24 = > 24 / 6 is an integer ans d . 5 . good luck
Answer: d
Question (physics): how long does a train 200 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 82.1 sec , b ) 12.1 sec , c ) 16.1 sec , d ) 13.1 sec , e ) 16.6 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 200 + 132 = 332 m . required time = 332 / 20 = 16.6 sec . answer : e"
Answer: e
Question (physics): two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 125 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 6 , b ) 14 , c ) 16 , d ) 20 , e ) 18
Rationale: "sol . speed of the first train = [ 150 / 10 ] m / sec = 15 m / sec . speed of the second train = [ 150 / 15 ] m / sec = 10 m / sec . relative speed = ( 15 + 10 ) = m / sec = 25 m / sec . ∴ required time = ( 125 + 125 ) / 25 secc = 6 sec . answer a"
Answer: a
Question (geometry): in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 6 , 0 ) , ( 0 , - 3.5 ) , ( - 6 , 0 ) ?
Options: a ) 42 , b ) 56 , c ) 88 , d ) 112 , e ) 116
Rationale: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 6 + 6 = 12 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 12 * 7 = 42 a is the answer"
Answer: a
Question (geometry): the perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 30
b ) 31
c ) 32
d ) 34
e ) 35
Rationale: area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 28 / 2 = 35 cm 2 answer : option e
Answer: e
Question (general): find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 year ?
Options: a ) 306.06 , b ) 306.02 , c ) 306.04 , d ) 306.09 , e ) 306.12
Rationale: "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"
Answer: c
Question (physics): micheal and adam can do together a piece of work in 20 days . after they have worked together for 14 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 50 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 14 = 7 / 10 left work = 1 - 7 / 10 = 3 / 10 adam completes 3 / 10 work in 10 day so he took 10 * 10 / 3 = 100 / 3 days to complete the left work alone . thus the rate of adam is 3 / 100 rate of micheal = 1 / 20 - 3 / 100 = 1 / 50 thus micheal takes 50 days to complete the whole work . ans . a"
Answer: a
Question (probability): a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 3 or 17 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
Rationale: "number of multiples of 3 from 1 through 30 = 30 / 3 = 10 number of multiples of 17 from 1 through 30 = 30 / 17 = 1 number of multiples of 3 and 17 both from 1 through 30 = number of multiples of 17 * 3 ( = 51 ) = 0 total favourable cases = 10 + 1 - 0 = 11 probability = 11 / 30 answer : option e"
Answer: e
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 35 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 416 , b ) s . 480 , c ) s . 429 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 35 % = 35 % of 640 = rs . 224 sp = cp - loss = 640 - 224 = rs . 416 answer : a"
Answer: a
Question (gain): a present value of a machine is $ 900 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 729
Rationale: "p = $ 900 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 900 * 9 / 10 * 9 / 10 = $ 729 answer is e"
Answer: e
Question (general): a motorist knows 6 different routes from bristol to birmingham . from birmingham to sheffield he knows 3 different routes and from sheffield to carlisle he knows two different routes . how many routes does he know from bristol to carlisle ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 24 , e ) 36
Rationale: explanation : total number of routes from bristol to carlisle = ( 6 x 3 x 2 ) = 36 . answer : e
Answer: e
Question (general): the grade point average of one third of the classroom is 54 ; the grade point average of the rest is 45 . what is the grade point average of the whole class ?
Options: a ) 52 , b ) 54 , c ) 48 , d ) 58 , e ) 60
Rationale: "let n = total students in class total points for 1 / 3 class = 54 n / 3 = 18 n total points for 2 / 3 class = 45 * 2 n / 3 = 30 n total points for whole class = 18 n + 30 n = 48 n 48 n total class points / n total students = 48 grade point average for total class answer : c"
Answer: c
Question (physics): in what time will a train 100 m long cross an electric pole , it its speed be 72 km / hr ?
Options: a ) 2.5 , b ) 5 , c ) 2.4 , d ) 2.8 , e ) 2.1
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 100 / 20 = 5 sec . answer : b"
Answer: b
Question (general): if x is an integer that has exactly 3 positive divisors ( these include 1 and x ) , how many positive divisors does x ^ 3 have ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: since factors of ' 4 ' are { 1 , 2,4 } 4 ^ 3 = 64 number of factors / divisors of 64 = 2 ^ 6 we know that when a number is expressed as a product of the prime factors as below : n = a ^ x * b ^ y * c ^ z then no . of divisors = ( x + 1 ) * ( y + 1 ) * ( z + 1 ) then here ( 6 + 1 ) = 7 answer : d
Answer: d