Cheukting/mathqa huggingface dataset:
Question (general): after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 80 % full . if the original contents of the reservoir totaled 200 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 50 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 200 + 120 = 320 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 320 / 0.8 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 200 / 400 ) * 100 = 50 % option c"
Answer: c
Question (general): find the ones digit of 73 ^ 356
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 356 will be the same as the units digit of 3 ^ 356 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 356 = 356 + 0 = ( multiple of 4 ) + 0 , then the units digit of 3 ^ 356 will be thus 1 . answer : a ."
Answer: a
Question (probability): a classroom has 3 electric lamps . from a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps . find the probability that the room is lighted .
Options: a ) 1 / 6 , b ) 4 / 120 , c ) 29 / 30 , d ) 1 / 9 , e ) none of these
Rationale: explanation : out of 10 electric bulbs , 3 are selected in 10 c 3 ways . so , number of possible outcomes = t = 10 c 3 = 120 . the room is lighted i . e at least one fo the 3 bulbs chosen at random is a good bulb . wherever ' at least one ' is present , it is easier to do the problem using complement of the event ( i . e room is dark and all 3 bulbs are bad ) . p ( room is dark ) = f / t = p ( none of the bulbs is good ) = > 4 c 3 / 120 . [ since 4 bulbs are bad ] . p ( room is lighted ) = 1 - ( 4 c 3 / 120 ) . [ room is lighted if at least one bulb is good ] . or p ( at least one ) = 1 - ( 4 / 120 ) . = 29 / 30 . answer : c
Answer: c
Question (gain): if a population of women in a town is 90 % of men . what is the population of men as a % of population of women ?
Options: a ) 108 % , b ) 105 % , c ) 111 % , d ) 112 % , e ) 114 %
Rationale: we ' re told that the number of women in a town is equal to 90 % of the number of men in that town . if . . . . men = 10 women = 9 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 9 = 1 1 / 9 = 1.111111 = 111 % answer : c
Answer: c
Question (physics): two trains 135 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.18 , b ) 7.12 , c ) 7.3 , d ) 7.45 , e ) 7.51
Rationale: "t = ( 135 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.45 answer : d"
Answer: d
Question (general): 4 numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number .
Options: a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112
Rationale: answer : a
Answer: a
Question (general): rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is :
Options: a ) rs 200 , b ) rs 300 , c ) rs 400 , d ) rs 500 , e ) rs 600
Rationale: let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) x 700 ) = 400 answer : c
Answer: c
Question (physics): a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 24 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : e"
Answer: e
Question (general): find the greatest number that will divide 150 , 230 and 175 leaving 50 , 5 and 25 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 32 , d ) 9 , e ) 8
Rationale: explanation : answer will be hcf of ( 150 - 50 , 230 - 5 , 175 - 25 ) hcf of ( 100 , 225 , 150 ) = 32 option c
Answer: c
Question (physics): how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 16.8 , b ) 17.8 , c ) 15.9 , d ) 13.2 , e ) 12.4
Rationale: "d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec answer a"
Answer: a
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum x of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum x = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Question (general): in track last week , the boys ran 27 laps . the girls ran 9 more laps . each lap is a 3 - fourth of a mile . how many miles did the girls run ?
Options: a ) 24 miles , b ) 25 miles , c ) 26 miles , d ) 27 miles , e ) 28 miles
Rationale: the girls ran 27 + 9 = 36 laps . 36 x 3 / 4 = 108 / 4 , which reduces to 27 . the girls ran 27 miles correct answer d
Answer: d
Question (gain): if tim had lunch at $ 50.20 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 60.24
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.20 = ( 20 / 100 ) * 50.20 = $ 10.04 total spent 50.20 + 10.04 = $ 60.24 correct answer e"
Answer: e
Question (general): if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 8 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 640 , e ) 760
Rationale: "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 8 € 40 = 2 * 8 * 40 = 640 hence , answer is d"
Answer: d
Question (gain): a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 24,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,500 , e ) s . 7,200
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 24000 x 3 / 10 = rs . 7,200 . e"
Answer: e
Question (general): every year an amount increases by 1 / 6 th of itself . how much will it be after two years if its present value is rs . 64000 ?
Options: a ) 87111 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 81022
Rationale: "64000 * 7 / 6 * 7 / 6 = 87111 answer : a"
Answer: a
Question (physics): a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 305 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 440 , c ) 550 , d ) 625 , e ) 700
Rationale: let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 305 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 605 a + b + c = 55 per hour so for eight hrs = 55 * 8 = 440 = answer = b
Answer: b
Question (geometry): how many odd numbers between 10 and 1200 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 33 which includes 15 numbers . the answer is d ."
Answer: d
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 5 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 961 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 30 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 961 96 + 225 + 490 + 5 x = 961 5 x = 150 = > x = 30 . answer : b"
Answer: b
Question (other): 300 liters of a mixture contains milk and water in the ratio 3 : 2 if 15 liters of this mixture be replaced by 15 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 12 : 8 , b ) 12 : 4 , c ) 13 : 8 , d ) 14 : 5 , e ) 13 : 5
Rationale: "quantity of milk in 300 liters if mix = 300 * 3 / 5 = 180 liters quantity of milk in 315 liters of new mix = 180 + 15 = 195 liters quantity of water in it = 315 - 195 = 120 liters ratio of milk and water in new mix = 90 : 20 = 13 : 8 answer isc"
Answer: c
Question (physics): a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 12 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 492 km
Rationale: "the total distance covered by the car in the first 12 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 = sum of 12 terms in ap whose first term is 30 and last term is 52 = 12 / 2 [ 30 + 52 ] = 492 km . answer : e"
Answer: e
Question (gain): a chemical supply company has 60 liters of a 25 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 25 % hno 3 solution means hno 3 = 15 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 15 + x = 50 % of ( 60 + x ) or x = 30 . hence , e"
Answer: e
Question (physics): in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 140 m . then , a wins by
Options: a ) 60 m , b ) 40 m , c ) 20 m , d ) 10 m , e ) 50 m
Rationale: "solution to reach the winning post a will have to cover a distance of ( 500 - 140 ) m , i . e , 360 m . while a covers 3 m , b covers 4 m . while a covers 360 m , b covers ( 4 / 3 x 360 ) m = 480 m thus , when a reaches the winning post , b covers 480 m and therefore remains 20 m behind . ∴ a wins by 20 m . answer c"
Answer: c
Question (physics): pipe a can fill a tank in 2 hours . due to a leak at the bottom , it takes 3 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 10 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 3 = > 1 / x = 1 / 2 - 1 / 3 = ( 3 - 2 ) / 6 = 1 / 6 = > x = 6 . answer : d"
Answer: d
Question (general): a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 752 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 752 - 640 = 112 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 112 / 28 = 28 / 7 = 4 total hrs = 40 + 4 = 44 answer c 44"
Answer: c
Question (physics): if the weight of 12 meters long rod is 12.2 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 6.1 kg , e ) none
Rationale: "answer ∵ weight of 12 m long rod = 12.2 kg ∴ weight of 1 m long rod = 12.2 / 12 kg ∴ weight of 6 m long rod = 12.2 x 6 / 12 = 6.1 kg option : d"
Answer: d
Question (other): x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 45000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 4 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 45000 × 9 = 45 × 12 : 45 × 9 = 3 × 12 : 2 × 9 = 4 : 3 answer is e ."
Answer: e
Question (other): find the fraction which has the same ratio to 2 / 5 that 3 / 7 has to 6 / 5
Options: a ) 2 / 4 , b ) 6 / 78 , c ) 4 / 7 , d ) 3 / 5 , e ) 1 / 7
Rationale: "p : 2 / 5 = 3 / 7 : 6 / 5 as the product of the means is equal to the product of the extremes . p * 6 / 5 = 2 / 5 * 3 / 7 p * 6 / 5 = 6 / 35 p = 1 / 7 = > p = 1 / 7 answer : e"
Answer: e
Question (physics): a student traveled 25 percent of the distance of the trip alone , continued another 20 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 150
Rationale: "let x be the total length of the trip . 0.25 x + 20 miles + 0.5 x = x 20 miles = 0.25 x x = 80 miles the answer is b ."
Answer: b
Question (general): david obtained 72 , 60 , 35 , 62 and 84 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 62.6 , c ) 87 , d ) 165 , e ) 11
Rationale: explanation : average = ( 72 + 60 + 35 + 62 + 84 ) / 5 = 313 / 5 = 62.6 . answer : b
Answer: b
Question (gain): mohit sold an article for $ 12000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 25000 , c ) 10000 , d ) 18000 , e ) 17000
Rationale: "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 12000 - 10 / 100 ( 12000 ) = 12000 - 1200 = $ 10800 = > 1.08 x = 10800 = > x = 10000 c"
Answer: c
Question (other): a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 1.80 , what total number of pens and pencils did the customer purchase ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y there are three possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 and 3 pencils for $ 0.25 each . that ' s 3 pens and 3 pencils for a total of 6 pens and pencils . choice ( a ) is correct ."
Answer: a
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 1 / 2 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 29 % , c ) 60 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 1 / 2 sp 1 cp = 100 sp 2 = 80 1 / 2 sp 1 = 80 sp 1 = 160 100 - - - 160 = > 60 % answer : c"
Answer: c
Question (general): williams works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 10 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 5 / 8 , b ) 7 / 8 , c ) 6 / 8 , d ) 2 / 9 , e ) 1 / 7
Rationale: "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 10 x total tips for all months = 6 * x + 10 x = 16 x tips for august / total tips for all months = 10 x / 16 x = 5 / 8 answer : a"
Answer: a
Question (physics): how many seconds will it take for a car that is traveling at a constant rate of 77 miles per hour to travel a distance of 21 yards ? ( 1 mile = 1,160 yards )
Options: a ) . 1 , b ) 0.3 , c ) 0.6 , d ) 2 , e ) 1.6
Rationale: "speed = 77 miles / hr = 37.64 yard / s distance = 21 yards time = distance / speed = 21 / 37.64 = 0.6 sec ans - c"
Answer: c
Question (gain): by selling an article at rs . 400 , a profit of 25 % is made . find its cost price ?
Options: a ) 228 , b ) 320 , c ) 287 , d ) 480 , e ) 811
Rationale: "sp = 400 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 400 * [ 100 / ( 100 + 25 ) ] = 400 * [ 100 / 125 ] = rs . 320 answer : b"
Answer: b
Question (general): a certain galaxy is known to comprise approximately 4 x 10 ^ 12 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 80,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 4 * 10 ^ 12 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 4 * 10 ^ 12 / 50 * 10 ^ 6 = 40 * 10 ^ 4 / 5 = 80000 therefore answer is c"
Answer: c
Question (gain): 12.5 % of 192 = 50 % of ?
Options: a ) 48 , b ) 96 , c ) 24 , d ) none of these , e ) can not be determined
Rationale: "answer let 12.5 % of 192 = 50 % of a , ⇒ ( 12.5 x 192 ) / 100 = ( 50 x a ) / 100 ∴ a = ( 12.5 x 192 ) / 50 = 48 correct option : a"
Answer: a
Question (gain): a 9 % stock yields 25 % . the market value of the stock is :
Options: a ) rs 45 , b ) rs 25 , c ) rs 40 , d ) rs 39 , e ) rs 36
Rationale: "explanation : for an income of rs . 25 , investment = rs . 100 . for an income of rs 9 , investment = rs . 100 / 25 x 9 = rs 36 market value of rs . 100 stock = rs 36 answer is e"
Answer: e
Question (general): find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 asquotient and the 15 as remainder ?
Options: a ) 1245 , b ) 1567 , c ) 1678 , d ) 1335 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Question (physics): ‘ a ’ completes a work in 12 days . ‘ b ’ completes the same work in 15 days . ‘ a ’ started working alone and after 3 days b joined him . how many days will they now take together to complete the remaining work ?
Options: a ) 5 , b ) 8 , c ) 6 , d ) 4 , e ) none of these
Rationale: work done by ‘ a ’ in 3 days = 1 ⁄ 12 × 3 = 1 ⁄ 4 ∴ remaining work = 1 - 1 ⁄ 4 = 3 ⁄ 4 work done by a and b together = 12 × 15 / 27 = 20 / 3 ∴ remaining work done by a and b together in = 3 ⁄ 4 × 20 ⁄ 3 = 5 days answer a
Answer: a
Question (general): the sum of ages of 5 children born 3 years different each is 50 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . x + 12 = 4 + 12 = 16 d"
Answer: d
Question (general): in a coconut grove , ( x + 2 ) trees yield 40 nuts per year , x trees yield 120 nuts per year and ( x – 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "( x + 2 ) × 40 + x × 120 + ( x − 2 ) × 180 / ( x + 2 ) + x + ( x − 2 ) = 100 ⇒ 340 x − 280 / 3 x = 100 ⇒ 40 x = 280 ⇒ x = 7 answer e"
Answer: e
Question (general): find value for x from given equation ? x + 1 = - 3
Options: a ) 1 , b ) x = - 4 , c ) - 3 , d ) - 5 , e ) 5
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = - 3 - 1 2 . simplify both sides : x = - 4 b"
Answer: b
Question (geometry): rectangular tile each of size 25 cm by 65 cm must be laid horizontally on a rectangular floor of size 150 cm by 390 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 40 , c ) 25 , d ) 36 , e ) 45
Rationale: "area of tile = 25 * 65 = 1625 area of floor = 150 * 390 = 58500 no of tiles = 58500 / 1625 = 36 so , the no of tile = 36 answer : d"
Answer: d
Question (general): of the 3,600 employees of company x , 1 / 6 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 13 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 4 is 1200 * 1 / 4 so it reduced 150 people , so there is 450 clerical people left but since 150 people left , it also reduced from the total of 3600 so there are 3450 people total since 450 clerical left / 3450 people total you get ( a ) 13 % answer : a"
Answer: a
Question (geometry): the area of a triangle is with base 3 m and height 6 m ?
Options: a ) 88 m 2 , b ) 9 m 2 , c ) 66 m 2 , d ) 77 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 3 * 6 = 9 m 2 answer : b"
Answer: b
Question (general): 9886 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9886 = 3314 option : e"
Answer: e
Question (general): if x is a sum of all even integers on the interval 13 . . . 45 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 16 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 44 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 44 ) / 2 * 16 = 29 * 16 . gcd of 16 and 29 * 16 is 16 . answer : b ."
Answer: b
Question (physics): in a stream running at 2 kmph , a motor boat goes 6 km upstream and back again to the starting point in 33 minutes . find the speed of the motorboat in still water .
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) none of them
Rationale: let the speed of the motarboat in still water be x kmph . then , 6 / x + 2 + 6 / x - 2 = 33 / 60 11 x 2 - 240 x - 44 = 0 11 x 2 - 242 x + 2 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 . answer is a
Answer: a
Question (physics): a cistern is filled by a tap in 5 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 66 , e ) 68
Rationale: "filling rate - leak rate = net rate 1 / 5.5 - leak rate = 1 / 6 leak rate = 2 / 11 - 1 / 6 = 1 / 66 the answer is d ."
Answer: d
Question (gain): ajay bought 15 kg of dal at the rate of rs 14.50 per kg and 10 kg at the rate of rs 13 per kg . he mixed the two and sold the mixture at the rate of rs 15 per kg . what was his total gain in this transaction ?
Options: a ) rs 1.10 , b ) rs 11 , c ) rs 16.50 , d ) rs 27.50 , e ) none of these
Rationale: explanation : cost price of 25 kg = rs . ( 15 x 14.50 + 10 x 13 ) = rs . 347.50 . sell price of 25 kg = rs . ( 25 x 15 ) = rs . 375 . profit = rs . ( 375 — 347.50 ) = rs . 27.50 . answer : d
Answer: d
Question (physics): speed of a boat in standing water is 10 kmph and speed of the stream is 2 kmph . a man can rows to a place at a distance of 100 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 24 hours , b ) 21 hr 30 min , c ) 20 hr 50 min , d ) 18 hr 15 min , e ) 22 hrs
Rationale: speed upstream = 8 kmph speed downstream = 12 kmph total time taken = 100 / 8 + 100 / 12 = 20 hours 50 min answer is c
Answer: c
Question (general): shekar scored 76 , 65 , 82 , 67 and 95 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 77 , c ) 75 , d ) 85 , e ) 90
Rationale: explanation : average = ( 76 + 65 + 82 + 67 + 95 ) / 5 = 385 / 5 = 77 hence average = 77 answer : b
Answer: b