Cheukting/mathqa huggingface dataset:
Question (physics): two trains of equal length , running with the speeds of 60 and 20 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 12.5 , b ) 8.01 , c ) 7.5 , d ) 26 , e ) 22
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 20 = 80 * 5 / 18 t = 2500 / 9 * 18 / 400 = 12.5 sec . answer : a"
Answer: a
Question (general): on the number line , the number p is twice as many units from - 2 as - 2 is from 7 . if p is less than – 2 , what is the value of p ?
Options: a ) – 20 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 7 = 9 since number p is twice as many units from - 2 as - 2 is from 7 , therefore p can be - 20 since , p is less than - 2 , the value of p = - 20 answer a"
Answer: a
Question (general): find value for x from below equation ? x + 1 = 4
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 4 - 1 2 . simplify both sides : x = 3 d"
Answer: d
Question (general): find large number from below question the difference of two numbers is 1325 . on dividing the larger number by the smaller , we get 5 as quotient and the 5 as remainder
Options: a ) 1650 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1325 ) . x + 1325 = 5 x + 5 4 x = 1320 x = 330 large number = 330 + 1320 = 1650 answer : a"
Answer: a
Question (other): jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 4 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 4 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 10 : 2 i . e . u : b = 20 : 2 answer : option d"
Answer: d
Question (general): if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a"
Answer: a
Question (general): 0.0005215 / 0.000305 x 6.2 = ?
Options: a ) 10.6 , b ) 11.3 , c ) 12.7 , d ) 13.4 , e ) 14.5
Rationale: "explanation : ? = 0.0005215 / 0.000305 x 6.2 = 10.6 answer : option a"
Answer: a
Question (general): the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 25 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 27 % , e ) 79 %
Rationale: "the original output increases by 10 % and then 25 % . total % change = a + b + ab / 100 total % change = 10 + 25 + 10 * 25 / 100 = 37.5 % now , you want to change it to 0 , so , 0 = 37.5 + x + 37.5 x / 100 x = - 37.5 ( 100 ) / 137.5 = 27 % approximately answer is d"
Answer: d
Question (gain): a and b started a business investing rs . 24,000 and rs 18,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 4 : 3 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 24000 : 18000 = 8 : 6 = 4 : 3 answer : a"
Answer: a
Question (general): find 283 / 1983 × 100
Options: a ) 14.29 , b ) 14.21 , c ) 14.22 , d ) 14.27 , e ) 14.23
Rationale: "never start finding common factors . adjust the denominator to 2000 . so we are introducing an error of 17 which is 171983 = 1117171983 = 1117 th of the denominator . 283002000 = 14.15283002000 = 14.15 but this answer is slightly less than actual answer . now 14 . 1511714.15117 = 0.12 approximately . adding 0.12 to 14.25 gives 14.27 . option b is correct ."
Answer: b
Question (probability): three unbiased coins are tossed . what is the probability of getting at least 2 tails ?
Options: a ) 0.75 , b ) 0.5 , c ) 0.25 , d ) 0.2 , e ) 0.3
Rationale: "explanation : s = { hhh , hht , hth , htt , thh , tht , tth , ttt } e = { htt , tht , tth , ttt } n ( s ) = 8 n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 0.5 answer is b"
Answer: b
Question (other): compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 342 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 280
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 342 gms of x have 342 * 10 / 12 = 280 gms of b and 342 - 280 = 62 gms of a . cross check : - a / b = 62 / 280 = 2 / 10 ( as given ) ans e"
Answer: e
Question (gain): a certain article of clothing was discounted during a special sale to 4 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 40 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 4 / 5 * $ 200 = $ 160 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 160 - 100 ) / 150 = 1 / 3 = 40 % . answer : c ."
Answer: c
Question (other): income and expenditure of a person are in the ratio 8 : 7 . if the income of the person is rs . 40000 , then find his savings ?
Options: a ) 5000 , b ) 6000 , c ) 7000 , d ) 8000 , e ) 9000
Rationale: "let the income and the expenditure of the person be rs . 8 x and rs . 7 x respectively . income , 8 x = 40000 = > x = 5000 savings = income - expenditure = 8 x - 7 x = x so , savings = rs . 5000 . answer : a"
Answer: a
Question (general): workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.50 lacs . how many workers were they ?
Options: a ) 220 , b ) 230 , c ) 500 , d ) 560 , e ) 1000
Rationale: "n * 50 = ( 350000 - 300000 ) = 50000 n = 50000 / 50 = 1000 e"
Answer: e
Question (general): how many positive integers less than 60 have a reminder 01 when divided by 4 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 4 . so , there are total of 15 numbers . answer : c ."
Answer: c
Question (physics): a boat goes 100 km downstream in 10 hours , and 200 km upstream in 25 hours . the speed of the stream is ?
Options: a ) 1 , b ) 22 1 / 7 , c ) 2 , d ) 22 1 / 2 , e ) 3
Rationale: "100 - - - 10 ds = 10 ? - - - - 1 200 - - - - 30 us = 8 ? - - - - - 1 s = ( 10 - 8 ) / 2 = 1 kmph . answer : a"
Answer: a
Question (general): if 25 % of x is 30 less than 20 % of 1000 , then x is ?
Options: a ) 188 , b ) 216 , c ) 156 , d ) 680 , e ) 121
Rationale: "25 % of x = x / 4 ; 20 % of 1000 = 20 / 100 * 1000 = 200 given that , x / 4 = 200 - 30 = > x / 4 = 170 = > x = 680 . answer : d"
Answer: d
Question (physics): mr . bhaskar is on tour and he has rs . 360 for his expenses . if he exceeds his tour by 4 days , he must cut down his daily expenses by rs . 3 . for how many days is mr . bhaskar on tour ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: if his tour is for x days and he is spending rs y per day , then xy = 360 x = 360 / y or y = 360 / x ( x + 4 ) * ( y - 3 ) = 360 or xy + 4 y - 3 x - 12 = 360 or 4 y - 3 x - 12 = 0 4 * 360 / x - 3 x - 12 = 0 solving it , we get x = 20 answer : b
Answer: b
Question (probability): a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability z that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability z = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Question (physics): a boat having a length 5 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 5 x 3 x 0.01 ) m 3 = 0.15 m 3 . mass of man = volume of water displaced × density of water = ( 0.15 × 1000 ) kg = 150 kg . answer e"
Answer: e
Question (general): a batsman in his 15 th inning makes a score of 75 and their by increasing his average by 3 . what is his average after the 15 th inning ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "14 x + 75 = 15 ( x + 3 ) x = 30 + 3 = 33 answer : c"
Answer: c
Question (general): a man purchased 3 blankets @ rs . 100 each , 1 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 1050 , b ) 2770 , c ) 1550 , d ) 5102 , e ) 5000
Rationale: "10 * 150 = 1500 3 * 100 + 1 * 150 = 450 1500 – 450 = 1050 answer : a"
Answer: a
Question (physics): five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8,10 seconds respectively . in 60 minutes , how many times do they toll together ?
Options: a ) 41 , b ) 10 , c ) 31 , d ) 16 , e ) 17
Rationale: l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 60 min they will toll 30 times . as they have initially tolled once , the answer will be 30 + 1 = 31 . answer : c
Answer: c
Question (physics): a cube of side 4 meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ?
Options: a ) 4069 , b ) 6048 , c ) 1000 , d ) 4096 , e ) 4060
Rationale: "along one edge , the number of small cubes that can be cut = 400 / 25 = 16 along each edge 16 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 16 * 16 * 16 = 4096 answer : d"
Answer: d
Question (general): on a certain date , pat invested $ 6,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24,000 , in how many years total will the total value of the investment plus interest increase to $ 48,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Question (general): if | y + 7 | = 12 , what is the sum of all the possible values of y ?
Options: a ) - 14 , b ) - 12 , c ) - 8 , d ) 8 , e ) 12
Rationale: there will be two cases y + 7 = 12 or y + 7 = - 12 = > y = 5 or y = - 19 sum of both the values will be - 19 + 5 = - 14 answer : a
Answer: a
Question (general): the tax on a commodity is diminished by 15 % and its consumption increased by 10 % . the effect on revenue is ?
Options: a ) 8.5 , b ) 6.5 , c ) 5.5 , d ) 5.6 , e ) 4.4
Rationale: "100 * 100 = 10000 85 * 110 = 9350 - - - - - - - - - - - 10000 - - - - - - - - - - - 650 100 - - - - - - - - - - - ? = > 6.5 % decrease answer : b"
Answer: b
Question (general): positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 25 . what is the value of x ?
Options: a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 25 ( y / 100 ) * x = 25 ( x / 400 ) * x = 25 x ^ 2 = 25 * 400 x = 100 the answer is d ."
Answer: d
Question (general): cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 78.2 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 5.75 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 78.2 - - > { original price } = $ 92 . { final price } = $ 78.2 * 1.25 = $ 97.75 . the difference = $ 97.75 - $ 92 = $ 5.75 answer : b ."
Answer: b
Question (gain): evaluate 20 % of 450 + 45 % of 200
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 180
Rationale: "explanation : = ( 20 / 100 ) * 450 + ( 45 / 100 ) * 200 = 180 option e"
Answer: e
Question (physics): which greatest possible length can be used to measure exactly 12 meter 34 cm , 8 meter 98 cm and 6 meter 65 cm
Options: a ) 1 cm , b ) 2 cm , c ) 24 cm , d ) 55 cm , e ) 50 cm
Rationale: explanation : convert first all terms into cm . i . e . 1234 cm , 898 cm , 665 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 1 . option a
Answer: a
Question (physics): working together , printer a and printer b would finish the task in 20 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 340
Rationale: "20 * a + 20 * b = x pages in 20 mins printer a will print = 20 / 60 * x pages = 1 / 3 * x pages thus in 20 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 20 mins printer b will print 80 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 80 = > x = 240 pages answer : c"
Answer: c
Question (geometry): a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 20,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is c ."
Answer: c
Question (general): if 20 liters of chemical x are added to 80 liters of a mixture that is 30 % chemical x and 70 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 32 % , b ) 35 % , c ) 38 % , d ) 41 % , e ) 44 %
Rationale: "the amount of chemical x in the solution is 20 + 0.3 ( 80 ) = 44 liters . 44 liters / 100 liters = 44 % the answer is e ."
Answer: e
Question (gain): the present population of a town is 60000 . the population increases annually at 10 % . find the population after 3 years .
Options: a ) 86000 , b ) 79860 , c ) 76300 , d ) 82900 , e ) none of these
Rationale: explanation : solution : the required population is 60000 ( 1 + 10 / 100 ) ^ 3 = 60000 * 110 / 100 * 110 / 100 * 110 / 100 = 79860 answer : b
Answer: b
Question (general): sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 4 more than 1 / 4 of the fine and peter paid $ 4 less than 1 / 3 of the fine , leaving pay $ 5 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 30 , b ) $ 25 , c ) $ 35 , d ) $ 40 , e ) $ 45
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 4 ] + [ ( 1 / 3 ) f – 4 ] + [ ( 1 / 2 ) f – 5 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 5 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 60 12 f = 13 f – 60 – f = – 60 f = 60 well , if the fine cost $ 60 , then sam paid the part not covered by joe or peter . half the fine is $ 30 , and sam paid $ 5 less than this : $ 25 . answer = b"
Answer: b
Question (general): the total car population in a chennai is 900 out of which 500 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red
Options: a ) 20.5 % , b ) 22.5 % , c ) 21.5 % , d ) 10.5 % , e ) 32.5 %
Rationale: "total honda brand red cars = 90 / 100 * 500 = 450 total red cars = 60 / 100 * 900 = 540 no . of non - honda cars = 900 - 500 = 400 no . of non - honda red cars = 540 - 450 = 90 % of non - honda red cars = 90 / 400 * 100 = 22.5 % answer : b"
Answer: b
Question (general): find the least number of 5 digits which is exactly divisible by 12 , 15 and 18 ?
Options: a ) 1080 , b ) 10080 , c ) 10025 , d ) 11080 , e ) 12080
Rationale: lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b
Answer: b
Question (geometry): the length of a rectangle is 3 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 92 square inches
Rationale: "if the width is 5 in and the length is 3 times the width , then the length is 3 * 5 = 15 in the area is given by 5 * 15 = 75 square inches correct answer b"
Answer: b
Question (gain): a certain sum amount to $ 1400 in 2 yrs and $ 2000 in 5 years on certain fixed simple interest . in how many yrs would the amount be $ 1640 had it been put at the rate of interest compounded annually ?
Options: a ) 4.5 , b ) 3.5 , c ) 3 , d ) 2 , e ) 1.5
Rationale: we can form equations as following : initial amount = p , total amount after interest = t , interest per year = i t = p + i given t 1 = p + 2 i = 1400 t 2 = p + 5 i = 2000 from this we get , p = 1000 i = 200 $ now we know that simple interest is < compound interest ( ci = si only after 1 st year if ci is compounded annually ) consider simple interest - after 1 st yer it is 200 $ , after 2 nd years it is 400 $ and after 3 rd year it is 600 $ . to get a 240 $ compound interest the duration have to be > 1 year and < 2 years . only option fitting : option e .
Answer: e
Question (physics): the h . c . f . of two numbers is 15 and their l . c . m . is 620 . if one of the numbers is 375 , then the other is :
Options: a ) 36.6 , b ) 42.8 , c ) 28.4 , d ) 11.6 , e ) 24.8
Rationale: "other number = ( 15 x 620 ) / 375 = 24.8 . answer : e"
Answer: e
Question (probability): from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn .
Options: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these
Rationale: "explanation : total number of cases = 52 total face cards = 16 [ favourable cases ] so probability = 16 / 52 = 4 / 13 option a"
Answer: a
Question (gain): what is 92 % of 3 / 5 ?
Options: a ) 0.552 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.69
Rationale: "92 % * ( 3 / 5 ) = 0.92 * 0.6 = 0.552 answer : a"
Answer: a
Question (general): if 9 a - b = 10 b + 80 = - 12 b - 2 a , what is the value of 2 a + 22 b ?
Options: a ) - 4 , b ) - 2 , c ) - 80 , d ) 2 , e ) 4
Rationale: "this implies 9 a - b = 10 b + 80 , 9 a - b = - 12 b - 2 a , 10 b + 80 = - 12 b - 2 a manipulating the second equation gives us 10 b + 80 = - 12 b - 2 a = = > 2 a + 22 b = - 80 answer is c"
Answer: c
Question (physics): a can do a work in 24 days and b can do it in 8 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 24 b ' s 1 day ' s work = 1 / 8 they work together = 1 / 24 + 1 / 8 = 6 days answer : option c"
Answer: c
Question (general): the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is :
Options: a ) 25 years , b ) 35 years , c ) 45 years , d ) 55 years , e ) 75 years
Rationale: "solution let their ages be x year and ( x + 10 ) years respectively . then , ( x + 10 ) - 15 = 2 ( x - 15 ) ⇔ x - 5 = 2 x - 30 ⇔ x = 25 . ∴ present age of the elder person = ( x + 10 ) = 35 years . answer b"
Answer: b
Question (general): sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 65 marks . how many sums did sandy get correct ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 65 5 x = 125 x = 25 the answer is d ."
Answer: d
Question (gain): a person distributed 20 % of his income to his 3 children each . he deposited 25 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 452000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 400000 , e ) e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 25 % orphan house = 5 % total = 60 + 25 + 5 = 90 % remaining = 100 - 90 = 10 % 10 % = 40000 100 % = 40000 * 100 / 10 = $ 400000 answer is d"
Answer: d
Question (general): the average weight of 4 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 71 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 4 × 1.5 = 6 kg so the weight of new person = 65 + 6 = 71 kg answer a"
Answer: a
Question (physics): convert 0.38 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none
Rationale: "answer 0.38 = 38 / 100 = 19 / 50 correct option : d"
Answer: d
Question (gain): on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) rs . 20 , b ) rs . 60 . , c ) rs . 40 , d ) rs . 30 , e ) rs . 90
Rationale: ( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : b
Answer: b
Question (probability): when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on either side all 5 times ?
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32
Rationale: "must be either 5 heads or 5 tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 32 + 1 / 32 = 1 / 16 answer : d"
Answer: d
Question (general): the average of 10 numbers is 210 . the average of first 5 numbers is 40 and the average of last 4 numbers is 200 . what is the middle number ?
Options: a ) a ) 200 , b ) b ) 2000 , c ) c ) 800 , d ) d ) 2100 , e ) e ) 1100
Rationale: the total of ten numbers = 10 x 210 = 2100 the total of first 5 and last 4 numbers is = 5 x 40 + 4 x 200 = 1000 so , the middle number is ( 2100 - 1000 ) = 1100 e
Answer: e
Question (gain): a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 10 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 36.55 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.9 = $ 14 - - > x = $ 15.55 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 15.55 + 21 = $ 36.55 . answer : a ."
Answer: a