Cheukting/mathqa huggingface dataset:
Question (gain): the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 2090 . what was his original salary ?
Options: a ) 2277 , b ) 2999 , c ) 1000 , d ) 2651 , e ) 2000
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 2090 x * ( 11 / 10 ) * ( 1 / 100 ) = 22 x = 2000 answer : e"
Answer: e
Question (general): given f ( x ) = 2 x – 3 , for what value of x does 2 * [ f ( x ) ] – 21 = f ( x – 4 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "2 ( 2 x - 3 ) - 21 = 2 ( x - 4 ) - 3 2 x = 16 x = 8 the answer is e ."
Answer: e
Question (physics): a train passes a platform in 40 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 200 meter , d ) 300 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 40 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 40 = > 300 + l = 15 × 40 = 600 = > l = 600 - 300 = 300 meter answer : option d"
Answer: d
Question (geometry): a rectangular window is twice as long as it is wide . if its perimeter is 18 feet , then what are its dimensions in feet ?
Options: a ) 3 / 2 by 7 / 2
b ) 5 / 3 by 10 / 3
c ) 2 by 4
d ) 3 by 6
e ) 10 / 3 by 20 / 3
Rationale: let x be the width of the window . then the length is 2 x . x + 2 x + x + 2 x = 18 6 x = 18 x = 18 / 6 = 3 the width is 3 and the length is 6 . the answer is d .
Answer: d
Question (physics): a train running at the speed of 40 km / hr crosses a pole in 27 seconds . what is the length of the train ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
Rationale: "speed = ( 40 * 5 / 18 ) m / sec = ( 100 / 9 ) m / sec length of the train = ( speed x time ) = ( 100 / 9 * 29 ) m = 300 m . answer : b"
Answer: b
Question (general): find the least number of 5 digits , which is exactly divisible by 89 .
Options: a ) 27 , b ) 37 , c ) 932 , d ) 12 , e ) 91
Rationale: answer : a
Answer: a
Question (general): a rope of which a calf is tied is increased from 16 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 1217 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 858
Rationale: "π ( 232 – 162 ) = 858 answer : e"
Answer: e
Question (physics): the edges of a cuboid are 4 cm , 4 cm and 6 cm . find the volume of the cuboid ?
Options: a ) 90 , b ) 60 , c ) 96 , d ) 80 , e ) 72
Rationale: "4 * 4 * 6 = 96 answer : c"
Answer: c
Question (geometry): there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure m in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 m = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = 10 ans e ."
Answer: e
Question (physics): the sum of all consecutive odd integers from − 23 to 31 , inclusive , is
Options: a ) 96 , b ) 112 , c ) 158 , d ) 192 , e ) 235
Rationale: the sum of the odd numbers from - 23 to + 23 is 0 . let ' s add the remaining numbers . 25 + 27 + 29 + 31 = 112 the answer is b .
Answer: b
Question (general): david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 37 , c ) 26 , d ) 97 , e ) 27
Rationale: "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : a"
Answer: a
Question (physics): in a kilometer race , a beats b by 80 meters or 8 seconds . what time does a take to complete the race ?
Options: a ) 77 sec , b ) 92 sec , c ) 67 sec , d ) 16 sec , e ) 76 sec
Rationale: time taken by b run 1000 meters = ( 1000 * 8 ) / 80 = 100 sec . time taken by a = 100 - 8 = 92 sec . answer : b
Answer: b
Question (general): the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these
Rationale: explanation : l . c . m of 5 , 6 , 7 , 8 = 840 therefore required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 840 x 2 + 3 ) = 1683 . answer : b
Answer: b
Question (physics): a policeman noticed a criminal from a distance of 240 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 190 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 240 - 50 ) m = 190 m . answer : c"
Answer: c
Question (general): what least number must be added to 1120 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "49 * 23 = 1127 1127 - 1120 = 7 answer : e"
Answer: e
Question (physics): 24 men can complete a work in 16 days . 32 women can complete the same work in 24 days . 16 men and 16 women started working and worked for 12 days . how many more men are to be added to complete the remaining work in 2 days ?
Options: a ) 16 , b ) 24 , c ) 36 , d ) 48 , e ) 49
Rationale: explanation : 1 man ’ s 1 day work = 1 / 384 1 woman ’ s 1 day work = 1 / 768 work done in 12 days = 12 ( 16 / 384 + 16 / 768 ) = 12 * 3 / 48 = 3 / 4 remaining work = 1 / 4 ( 16 men + 16 women ) ’ s 2 day work = 2 ( 16 / 384 + 16 / 768 ) = 1 / 8 remaining work = 1 / 4 - 1 / 8 = 1 / 8 1 / 384 work is done in 1 day by 1 man 1 / 8 work will be done in 2 days by 384 x 1 / 8 x 1 / 2 = 24 men answer : option b
Answer: b
Question (gain): at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the women are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 6
Rationale: "2 x 2 table works perfect : - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married woman / total woman , so 50 / 60 = 5 / 6 e"
Answer: e
Question (gain): the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.08 * 80 90 x - 80 = 6.4 90 x = 86.64 x = 86.64 / 90 = 87 / 90 ( approx ) = 29 / 30 = 0.966 x is slightly under 0.9666 = 0.96 answer : b"
Answer: b
Question (physics): a group of men decided to do a work in 50 days , but 10 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 100 , e ) 25
Rationale: "original number of men = 10 * 60 / ( 60 - 50 ) = 60 answer is a"
Answer: a
Question (gain): 30 % of a number is more than 60 % of 50 by 30 . find the number ?
Options: a ) 120 , b ) 200 , c ) 180 , d ) 300 , e ) 140
Rationale: "( 30 / 100 ) * x – ( 60 / 100 ) * 50 = 30 2 / 7 x = 60 x = 200 answer : b"
Answer: b
Question (general): operation # is defined as adding a randomly selected two digit multiple of 8 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: any multiple of 8 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a .
Answer: a
Question (geometry): right triangle abc is the base of the prism in the figure above . if ab = ac = â ˆ š 10 and the height of the prism is 4 , what is the volume of the prism ?
Options: a ) 40 , b ) 85 , c ) 20 , d ) 60 , e ) 45
Rationale: "volume of prism = area of base * height = 1 / 2 * ( square root of 10 ) * ( square root of 10 ) * 4 = 20 answer : c"
Answer: c
Question (physics): a woman swims downstream 54 km and upstream 6 km taking 6 hours each time , what is the speed of the woman in still water ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "54 - - - 6 ds = 9 ? - - - - 1 6 - - - - 6 us = 1 ? - - - - 1 m = ? m = ( 9 + 1 ) / 2 = 5 answer : d"
Answer: d
Question (general): what is the least number which when divided by 7 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 230 , b ) 240 , c ) 236 , d ) 256 , e ) 266
Rationale: "explanation : lcm of 7 , 9 , 12 and 18 is 252 required number = 252 + 4 = 256 answer : option d"
Answer: d
Question (general): how many points ( x , y ) lie on the line segment between ( 15 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 15 ) = - 5 / 8 y = mx + b = > 12 2 / 3 = - 15 * 5 / 8 + b = > b = 1 y = - 75 x / 8 + 22 only integer values work , and the only multiples of 8 between 7 and 15 for x value is 8 , thus 1 point . a
Answer: a
Question (gain): a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 per cent is cut away . in the second week 20 per cent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 145 kg , c ) 165 kg , d ) 115 kg , e ) 100 kg
Rationale: "a 105 kg = 250 ã — 0.7 ã — 0.8 ã — 0.75 ."
Answer: a
Question (gain): a bowl was filled with 10 ounces of water , and 0.008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 008 * 100 / 2 = . 8 / 2 = . 4 percent of the original amount of water evaporated during this period = ( . 4 / 10 ) * 100 % = 4 % answer d"
Answer: d
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 260 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 278 , b ) 166 , c ) 151 , d ) 260 , e ) 109
Rationale: speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 260 ) / 26 = 20 x = 260 m . answer : d
Answer: d
Question (general): when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 150
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.08 = 12 / j 0.08 * j = 12 j = 12 / 0.08 = 1200 / 8 = 300 / 2 = 150 so j = 150 , answer = e ."
Answer: e
Question (general): q is a set of 8 distinct prime numbers . if the sum of the integers in q is even and the number x is a member of q , then what is the least value that x can be ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 ( discard as sum is odd ) 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 98 ( sum is even ) least number = 3 b
Answer: b
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 58 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.40 $ , b ) 383.40 $ , c ) 420.40 $ , d ) 450.40 $ , e ) 473.40 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 58 ) = 473.40 hence answer will be ( e )"
Answer: e
Question (geometry): in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,7 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 4 / 7 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 7 , e ) 1 / 2
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 7 = 14 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 14 = 4 / 7 the answer is a ."
Answer: a
Question (general): ( 565945 x 121 ) = ?
Options: a ) 68463812 , b ) 68463813 , c ) 68479345 , d ) 68463814 , e ) 68463814
Rationale: 565945 * 121 = 68479345 ans c
Answer: c
Question (gain): mixture a is 20 percent alcohol , and mixture b is 50 percent alcohol . if the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 3 gallons , b ) 4 gallons , c ) 5 gallons , d ) 10 gallons , e ) 12 gallons
Rationale: let a = number of gallons on mixture a in 15 gallon mixture b = number of gallons on mixture b in 15 gallon mixture ( 20 / 100 ) a + ( 50 / 100 ) b = ( 30 / 100 ) ( a + b ) - - 1 a + b = 15 - - 2 on solving equations 1 and 2 , we get a = 10 b = 5 answer d 10 gallons
Answer: d
Question (physics): sum of two numbers prime to each other is 14 and their l . c . m . is 45 . what are the numbers ?
Options: a ) 6 and 5 , b ) 8 and 5 , c ) 9 and 5 , d ) 8 and 5 , e ) 3 and 5
Rationale: "as two numbers are prime , satisfies all but option c will make the product of numbers i . e 45 answer : c"
Answer: c
Question (general): if 5 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 8 , b ) - 4 , c ) - 3 , d ) 1 , e ) 6
Rationale: "the phrase “ 5 is one solution of the equation ” means that one value of x is 5 . thus , we first must plug 5 for x into the given equation to determine the value of k . so we have 5 ^ 2 + ( 3 ) ( 5 ) + k = 10 25 + 15 + k = 10 40 + k = 10 k = - 30 next we plug - 30 into the given equation for k and then solve for x . x ^ 2 + 3 x – 30 = 10 x ^ 2 + 3 x – 40 = 0 ( x + 8 ) ( x - 5 ) = 0 x = - 8 or x = 5 thus , - 8 is the other solution . answer a ."
Answer: a
Question (general): if 350 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 88 , b ) 82 , c ) 86 , d ) 87 , e ) 80
Rationale: "the question actually asks the highest power of 10 which divides 350 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 350 factorial will have 86 as - 350 / 5 = 70 70 / 5 = 14 14 / 5 = 2 so answer will be ( c ) 86"
Answer: c
Question (general): a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 80 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50
Rationale: "200 men do the rest of the work in 100 - 80 = 20 days 100 men can do the rest of the work in 20 * 200 / 100 = 40 days required number of days = 40 - 80 = 40 days answer is a"
Answer: a
Question (gain): solve the quickfire maths brain teaser â ˆ š 4 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 20 %
Rationale: â ˆ š 4 % = > â ˆ š 4 / â ˆ š 100 = > 2 / 10 = > 20 / 100 = > 20 % e
Answer: e
Question (physics): the area of sector of a circle whose radius is 12 metre and whose angle at the center is 42 ° is ?
Options: a ) 52.7 m 2 , b ) 57.8 m 2 , c ) 52.8 metre sq , d ) 72.8 m 2 , e ) 52.8 m 2
Rationale: 42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c
Answer: c
Question (physics): in a race of 1000 meters , a can beat b by 100 meters , in a race of 800 meters , b can beat c by 100 meters . by how many meters will a beat c in a race of 600 meters ?
Options: a ) 125.5 meters , b ) 126.5 meters , c ) 127.5 meters , d ) 128.5 meters , e ) none of these
Rationale: explanation : when a runs 1000 meters , b runs 900 meters and when b runs 800 meters , c runs 700 meters . therefore , when b runs 900 meters , the distance that c runs = ( 900 x 700 ) / 800 = 6300 / 8 = 787.5 meters . so , in a race of 1000 meters , a beats c by ( 1000 - 787.5 ) = 212.5 meters to c . so , in a race of 600 meters , the number of meters by which a beats c = ( 600 x 212.5 ) / 1000 = 127.5 meters . answer : c
Answer: c
Question (gain): if a and b get profits of rs . 18,000 and rs . 15,000 respectively at the end of year then ratio of their investments are
Options: a ) 6 : 5 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: "ratio = 18000 / 15000 = 6 : 5 answer : a"
Answer: a
Question (other): he ratio between the sale price and the cost price of an article is 5 : 3 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 5 : 2 , e ) 2 : 5
Rationale: let c . p . = rs . 3 x and s . p . = rs . 5 x . then , gain = rs . 2 x required ratio = 5 x : 2 x = 5 : 2 answer : d
Answer: d
Question (general): the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 72 + x ) / 7 = 11 = > x = 5 . hence , the seventh observation is 5 . answer : c"
Answer: c
Question (other): a certain bag contains 100 balls â € ” 50 white , 20 green , 10 yellow , 17 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 20 + 10 ) / 100 = 80 / 100 = 0.8 . answer is d"
Answer: d
Question (general): simplify : 8888 + 888 + 88 + 8
Options: a ) 9872 , b ) 9782 , c ) 9827 , d ) 9287 , e ) none of them
Rationale: "8888 888 88 8 - - - - - - - 9872 answer is a ."
Answer: a
Question (general): for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 15 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 23 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 15 % of 300 seeds germinated , so 0.15 x 300 = 45 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 45 + 70 = 115 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 115 / 500 ) x 100 % , or 23 % . answer : c ."
Answer: c
Question (physics): a man sitting in a train which is travelling at 50 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed .
Options: a ) 62 kmph , b ) 58 kmph , c ) 52 kmph , d ) 50 kmph , e ) none of these
Rationale: "relative speed = ( 280 ⁄ 9 ) m / sec = ( 280 ⁄ 9 × 18 ⁄ 5 ) kmph = 112 kmph . ∴ speed of goods train = ( 112 – 50 ) kmph = 62 kmph . answer a"
Answer: a
Question (physics): a can do a work in 15 days and b in 20 days . if they work on it together then in how many days required to complete the work ?
Options: a ) 300 / 31 , b ) 300 / 35 , c ) 300 / 21 , d ) 300 / 15 , e ) 300 / 20
Rationale: person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( 300 / 35 ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work = 300 / 35 answer is b
Answer: b
Question (general): what is the average of 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 ?
Options: a ) 1345 , b ) 1334 , c ) 1313.33 , d ) 1350 , e ) 1325
Rationale: "add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 11820 11820 / 9 = 1313.33 c"
Answer: c
Question (physics): the speed of a car is 90 km in the first hour and 50 km in the second hour . what is the average speed of the car ?
Options: a ) 70 , b ) 75 , c ) 88 , d ) 54 , e ) 15
Rationale: "s = ( 90 + 50 ) / 2 = 70 kmph answer : a"
Answer: a
Question (gain): of the 200 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 45 percent of the employees prefer city y and 55 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 135
Rationale: "110 prefer x ( group 1 ) ; 90 prefer y ( group 2 ) . city y needs 150 people : letall 90 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 40 people : 110 - 60 = 40 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 90 + 40 = 130 . answer : d ."
Answer: d
Question (other): a starts business with rs . 3500 and after 9 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 21000 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 9 = 3 months . so there profit ratio = ( 3500 ã — 12 ) : ( 3 x ) = 2 : 3 â ‡ ’ x = 21000 answer : d"
Answer: d
Question (gain): a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 80 then it is marked down by 10 % = 80 - 8 = 72 . hence it is 72 % of the original price . hence answer is a"
Answer: a
Question (other): what is the sum of all the prime factors of 220 and 330 ?
Options: a ) 15 , b ) 21 , c ) 35 , d ) 41 , e ) 64
Rationale: "prime factorization of both the numbers is as follows 220 = 2 * 2 * 5 * 11 sum of the prime factors of 220 = 20 330 = 2 * 3 * 5 * 11 sum of prime factors of 330 = 21 addition of both = 20 + 21 = 41 answer d"
Answer: d
Question (general): mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 5 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "share of each child ( 5 no ) and ( total share of grand children together ) 1 no = 1 / ( 5 + 1 ) = 1 / 6 as the grand children again equally share the part given to them : share of each grand child = [ ( 1 / 6 ) / 6 ] = 1 / 36 = 2.8 % answer : e"
Answer: e