Cheukting/mathqa huggingface dataset:
Question (general): how many positive integers less than 5,000 are evenly divisible by neither 14 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 14 5000 / 14 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 14 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 14 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4349 answer e ."
Answer: e
Question (general): a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 110 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 277 , d ) 124 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 110 x = 124 answer : d"
Answer: d
Question (physics): a solid yellow stripe is to be painted in the middle of a certain highway . if 1 gallon of paint covers an area of q square feet of highway , how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long ? ( 1 mile = 5,280 feet and 1 foot = 12 inches )
Options: a ) ( 5,280 mt ) / 12 q
b ) ( 5,280 pt ) / 12 m
c ) ( 5,280 pmt ) / 12
d ) ( 5,280 ) ( 12 m ) / pt
e ) ( 5,280 ) ( 12 p ) / mt
Rationale: given that : 1 gallon of paint covers an area ofqsquare feet . question : how many gallonsof paint will be needed . . . in any case you will have : ( total area in square feet ) / ( gallons per feet ) = ( total area in square feet ) / q , so q must be in the denominator : eliminate all but a and d . now , lets see where should be t : ( area in square feet ) = ( width in feet ) * ( length in feet ) - - > width = tinchesas 1 feet = 12 inchesthent inches = t / 12 feet , so ( area in square feet ) = ( t / 12 ) * ( length in feet ) , so t must be in the nominator : only a is left . answer : a .
Answer: a
Question (gain): a man buys 20 lts of liquid which contains 30 % of the liquid and the rest is water . he then mixes it with 20 lts of another mixture with 20 % of liquid . what is the % of water in the new mixture ?
Options: a ) 59 , b ) 95 , c ) 80 , d ) 75 , e ) 65
Rationale: "30 % in 20 lts is 6 . so water = 20 - 6 = 14 lts . 20 % of 20 lts = 4 . so water in 2 nd mixture = 20 - 4 = 16 lts . now total quantity = 20 + 20 = 40 lts . total water in it will be 14 + 16 = 30 lts . % of water = ( 100 * 30 ) / 40 = 75 . answer : d"
Answer: d
Question (geometry): the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 7 cm , e ) none
Rationale: "solution 4 î r 2 = 2 î 7 x 14 â ‡ ’ r 2 = ( 7 x 14 / 2 ) â ‡ ’ 49 â ‡ ’ r = 7 cm . answer d"
Answer: d
Question (physics): if 8 men or 12 women can do a piece of work in 30 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 18 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 30 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 30 = 1 / 360 so , 20 women work = 20 / 360 = 1 / 18 ans : 18 days answer : e"
Answer: e
Question (general): how many positive integer solutions does the equation 8 x + 2 y = 100 have ?
Options: a ) 50 , b ) 84 , c ) 16 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 8 * 2 ) = 84 answer : b"
Answer: b
Question (general): set s consists of integers { 8 , 11 , 12 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 25 % . what is the value of integer n ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: the average of the numbers in set s is 12 . if we increase the mean by 25 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d .
Answer: d
Question (general): the average marks obtained by 50 candidates in a certain examination is 40 . find the total marks .
Options: a ) 1800 , b ) 2000 , c ) 1640 , d ) 2200 , e ) 2400
Rationale: following the above formula , we have the total marks = 50 * 40 = 2000 answer is b
Answer: b
Question (physics): a man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction , takes 18 seconds to pass him . if the goods train is 420 m long , find its speed .
Options: a ) 32 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "relative speed = ( 420 / 18 ) m / s = ( 420 / 18 ) * ( 18 / 5 ) = 84 kmph speed of goods train = 84 - 64 = 20 kmph answer is d"
Answer: d
Question (physics): the speed of a car is 95 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 77.5 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 95 + 60 ) / 2 = 77.5 kmph answer : c"
Answer: c
Question (gain): an article is bought for rs . 675 and sold for rs . 800 , find the gain percent ?
Options: a ) 38 % , b ) 28 % , c ) 18 % , d ) 22 % , e ) 13 %
Rationale: "675 - - - - 125 100 - - - - ? = > = 18 % answer : c"
Answer: c
Question (gain): a company recently conducted a survey and found that 40,000 of its customers live in rural areas . if the number of customers who live in urban areas is 137 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 90,000 , b ) 91,200 , c ) 92,400 , d ) 93,600 , e ) 94,800
Rationale: the number of customers in urban areas is 40,000 + 1.37 * 40,000 = 94,800 . the answer is e .
Answer: e
Question (physics): a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 30 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 7.5 , b ) 15 , c ) 17.5 , d ) 25 , e ) 32.5
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 30 = 2.5 km . the time it takes the hiker to complete this distance is 2.5 / 4 hours = 37.5 minutes the cyclist needs to wait 37.5 - 5 = 32.5 minutes the answer is e ."
Answer: e
Question (general): 3 ltr of water is added with 9 ltr of a solution containing 57 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 41.5 % , b ) 42.75 % , c ) 43 % , d ) 45 % , e ) 45.75 %
Rationale: "we have a 9 litre solution containing 57 % of alcohol in the water . = > quantity of alcohol in the solution = 9 ã — 57 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 9 + 3 = 12 percentage of alcohol in the new solution = 9 ã — 57 / 100 12 ã — 100 = 9 ã — 5710012 ã — 100 = 9 ã — 4.75 / 100 = 42.75 % b"
Answer: b
Question (general): if x = 3 ^ 9 and x ^ x = 3 ^ k , what is k ?
Options: a ) 3 ^ 11 , b ) 3 ^ 13 , c ) 3 ^ 25 , d ) 3 ^ 27 , e ) 3 ^ 81
Rationale: solution : we know that x = 3 ^ 9 which implies x ^ x = ( 3 ^ 9 ) ^ ( 3 ^ 9 ) = 3 ^ ( 9 * 3 ^ 9 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 3 ^ ( 3 ^ 2 * 3 ^ 9 ) = 3 ^ ( 3 ^ ( 2 + 9 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 3 ^ ( 3 ^ 11 ) given that x ^ x = 3 ^ k so 3 ^ ( 3 ^ 11 ) = 3 ^ k since the base is same the exponent will also be same therefore k = 3 ^ 11 answer : a
Answer: a
Question (general): carol spends 1 / 4 of her savings on a stereo and 1 / 2 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 3 / 8 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 2 ) ( 1 / 4 ) s = ( 1 / 2 ) * ( 1 / 4 ) * s = ( 1 / 8 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 8 ) / s = 3 / 8 answer : d"
Answer: d
Question (gain): a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 11.00 ?
Options: a ) 40 , b ) 60 , c ) 90 , d ) 132 , e ) 240
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 11 ( 1 / 12 ) * x = 11 x = 132 answer : d"
Answer: d
Question (general): for all numbers a and b , the operation is defined by ab = ( a + 2 ) ( b – 3 ) . if 3 x = – 20 , then x =
Options: a ) – 15 , b ) – 6 , c ) 3 , d ) 6 , e ) - 1
Rationale: ( 3 + 2 ) ( x - 3 ) = - 20 . . x - 3 = - 4 . . x = - 1 e
Answer: e
Question (geometry): the length and breadth of a rectangle is increased by 5 % and 15 % respectively . what is the increase in the area ?
Options: a ) 21.25 , b ) 22.75 , c ) 19.25 , d ) 20.75 , e ) 22.25
Rationale: "100 * 100 = 10000 105 * 115 = 12075 - - - - - - - - - - - 2075 10000 - - - - - - 2075 100 - - - - - ? = > 20.75 answer d"
Answer: d
Question (physics): a train running at the speed of 40 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 150 metres , e ) 100 meters
Rationale: "speed = 40 x 5 / 18 m / sec = 100 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 100 / 9 x 9 m = 100 m . answer : e"
Answer: e
Question (gain): a chemical supply company has 60 liters of a 35 % 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 ) 18 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 35 % hno 3 solution means hno 3 = 21 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 21 + x = 50 % of ( 60 + x ) or x = 18 hence , a"
Answer: a
Question (general): in how many no . between 10 and 30 exactly two of the digits is 2 ?
Options: a ) 25 , b ) 1 , c ) 35 , d ) 45 , e ) 50
Rationale: "it ' s simple can be solved by elimination of answer choices . option a and c are too large , not possible . even de are large to have correct choice . ans : b"
Answer: b
Question (general): the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 140 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 367 , c ) 269 , d ) 177 , e ) 174
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 140 x + ( x - 140 ) = 208 2 x = 348 x = 174 runs answer : e"
Answer: e
Question (general): if m ^ 2 - 8 m + 1 = 0 , then m ^ 3 + m ^ ( - 3 ) = ?
Options: a ) 487 , b ) 488 , c ) 489 , d ) 457 , e ) 495
Rationale: here from equation 1 we will get m ^ 2 - 8 m + 1 = 0 m ^ 2 = 8 m - 1 m = ( 8 m - 1 ) / m . . . . . . . . . ( 1 ) m = 8 - 1 / m so m + 1 / m = 8 now in equation 2 m ^ 3 + 1 / m ^ 3 ( m + 1 / m ) ( m ^ 2 - m * 1 / m + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 - 1 + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 + 1 / m ^ 2 - 1 ) ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 m * 1 / m - 1 } { since a ^ 2 + b ^ 2 = ( a + b ) ^ 2 - 2 ab } ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 - 1 } now putting the value of m from equation 1 8 ( 8 ^ 2 - 2 - 1 ) 8 ( 64 - 3 ) = 488 answer : b
Answer: b
Question (general): if 3 a – 3 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c
Answer: c
Question (other): a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 3 : 4 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 75 , b ) 150 , c ) 300 , d ) 450 , e ) 600
Rationale: "originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 4 / 9 ) * 1350 = 600 acres were planted with tobacco . thus 600 - 300 = 300 more acres were planted with tobacco . the answer is c ."
Answer: c
Question (other): in a group of 100 cars , 47 cars do not have air conditioning . if at least 55 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 45 , b ) 47 , c ) 49 , d ) 51 , e ) 53
Rationale: "lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 55 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 55 . . we have to assign atleast 8 tocars with ac and racing stripes . hence ac = 53 - 8 = 45 . the answer is a"
Answer: a
Question (gain): at a certain conference , 78 % of the attendees registered at least two weeks in advance and paid their conference fee in full . if 10 % of the attendees who paid their conference fee in full did not register at least two weeks in advance , what percent of conference attendees registered at least two weeks in advance ?
Options: a ) 18.0 % , b ) 62.0 % , c ) 79.2 % , d ) 86.67 % , e ) 82.0 %
Rationale: i do not think that venn will be helpful here . a table will make more sense . but here is my approach . 78 % regestered at least 2 weeks and paid full fee . 10 % paid full fee and did not registered at least 2 weeks in advance . then 90 % paid full fee and registered at least 2 weeks before . 90 % * x = 78 % where x is the number of people who registerd 2 weeks in advance and paid full fee . ( answer d )
Answer: d
Question (physics): a can do a piece of work in 22 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 11 days , d ) 8.5 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 22 ∗ 1 / 2 = 11 days option c"
Answer: c
Question (geometry): if the volume of two cubes are in the ratio 8 : 1 , the ratio of their edges is :
Options: a ) 2 : 1
b ) 3 : 2
c ) 3 : 5
d ) 3 : 7
e ) none of these
Rationale: explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 8 / 1 = > ( a / b ) 3 = ( 2 / 1 ) 3 a / b = 2 / 1 = > a : b = 2 : 1 option a
Answer: a
Question (general): what is the dividend . divisor 15 , the quotient is 8 and the remainder is 5
Options: a ) a ) 145 , b ) b ) 148 , c ) c ) 150 , d ) d ) 125 , e ) e ) 158
Rationale: "d = d * q + r d = 15 * 8 + 5 d = 120 + 5 d = 125 answer : d"
Answer: d
Question (physics): x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 20 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 25 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 20 days whole work will be done by y in 20 * 5 / 4 = 25 days answer is c"
Answer: c
Question (gain): the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 5 years ?
Options: a ) 14300 , b ) 24883 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 5 = 24883 b )"
Answer: b
Question (gain): by selling an article at rs . 500 , a profit of 25 % is made . find its cost price ?
Options: a ) 400 , b ) 267 , c ) 287 , d ) 480 , e ) 811
Rationale: "sp = 500 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 500 * [ 100 / ( 100 + 25 ) ] = 500 * [ 100 / 125 ] = rs . 400 answer : a"
Answer: a
Question (other): in a class of 32 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "total = english + german - both + neither - - > 40 = english + 22 - 12 + 0 - - > english = 22 - - > only english = english - both = 22 - 12 = 10 . answer : b ."
Answer: b
Question (geometry): the ratio of radius of a circle and the side of a square is 2 : 5 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 25 , c ) 8 : 77 , d ) 4 : 121 , e ) none
Rationale: "radius / side = 2 / 5 â ‡ ’ area of circle / area of square = 4 / 25 answer : b"
Answer: b
Question (physics): a lion chases a pony 7 hours after the pony runs . lion takes 8 hours to reach the pony . if the average speed of the lion is 49 kmph , what s the average speed of the pony ?
Options: a ) 28.3 kmph , b ) 29.8 kmph , c ) 28.4 kmph , d ) 29.5 kmph , e ) 29.4 kmph
Rationale: pony take 15 hours and lion take 8 hours . . . then distance chased by them is 49 * 8 . so speed of pony is ( 49 * 8 ) / 15 = 29.4 kmph . answer is e
Answer: e
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 360 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 287 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 360 ) = 2 + 2 ( extra ) = > 2 x - 720 = x = > x = 720 . answer : e"
Answer: e
Question (general): the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 102 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b"
Answer: b
Question (gain): a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 900 , what is the reduced price for kg ?
Options: a ) 45 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 900 * ( 25 / 100 ) = 225 - - - - 5 ? - - - - 1 = > rs . 45"
Answer: a
Question (geometry): rectangular tile each of size 80 cm by 55 cm must be laid horizontally on a rectangular floor of size 210 cm by 330 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 ) 26 , b ) 16 , c ) 18 , d ) 19 , e ) 20
Rationale: "area of tile = 80 * 55 = 4400 area of floor = 210 * 330 = 72600 no of tiles = 72600 / 4400 = 16.5 so , the no of tile = 16 answer : b"
Answer: b
Question (general): sowdharya had 90 currency notes in all , some of which are of rs 95 denomination and the remaining of rs 45 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 45 ?
Options: a ) 75 , b ) 72 , c ) 71 , d ) 76 , e ) 73
Rationale: let the number of 45 - rupee notes = x then , the number of 95 - rupee notes = ( 90 – x ) 45 x + 95 ( 90 – x ) = 5000 : x = 71 answer : c
Answer: c
Question (gain): if an investor puts $ 700 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 769.75 , b ) $ 771.75 , c ) $ 773.75 , d ) $ 775.75 , e ) $ 777.75
Rationale: "1.05 * 1.05 * 700 = $ 771.75 the answer is b ."
Answer: b
Question (general): a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12002 , b ) 12000 , c ) 12028 , d ) 12020 , e ) 12013
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer : b"
Answer: b
Question (physics): to deliver an order on time , a company has to make 25 parts a day . after making 25 parts per day for 3 days , the company started to produce 5 more parts per day , and by the last day of work 100 more parts than planned were produced . find how many parts the company made and how many days this took .
Options: a ) 600 , b ) 500 , c ) 575 , d ) 655 , e ) 675
Rationale: let x be the number of days the company worked . then 25 x is the number of parts they planned to make . at the new production rate they made : 3 ⋅ 25 + ( x − 3 ) ⋅ 30 = 75 + 30 ( x − 3 ) therefore : 25 x = 75 + 30 ( x − 3 ) − 100 25 x = 75 + 30 x − 90 − 100 190 − 75 = 30 x − 25 115 = 5 x x = 23 so the company worked 23 days and they made 23 ⋅ 25 + 100 = 675 pieces . so answer is e .
Answer: e
Question (general): how many positive integers less than 100 have a reminder 5 when divided by 7 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "take the multiples of 7 and add 5 0 x 7 + 5 = 5 . . . . 13 x 7 + 5 = 96 there are 14 numbers answer d"
Answer: d
Question (general): what is the 10 th digit of ( 5 ! * 4 ! * 4 ! - 5 ! * 4 ! * 3 ! ) / 2880 ?
Options: a ) 4 , b ) 1 , c ) 6 , d ) 7 , e ) 8
Rationale: "( 5 ! * 4 ! * 4 ! - 5 ! * 4 ! * 3 ! ) / 2880 ? = 5 ! * 4 ! ( 4 ! - 3 ! ) / 4 ! * 5 ! = 4 ! - 3 ! = 18 sum of digits = 1 answer b"
Answer: b
Question (physics): a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weights 8 g / cm cube , then find the weight of the pipe .
Options: a ) 3.696 kg
b ) 3.686 kg
c ) 2.696 kg
d ) 2.686 kg
e ) none of these
Rationale: explanation : in this type of question , we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow . oh ! line become a bit complicated , sorry for that , lets solve it . external radius = 4 cm internal radius = 3 cm [ because thickness of pipe is 1 cm ] volume of iron = π r 2 h = 22 / 7 ∗ [ 42 − 32 ] ∗ 21 cm 3 = 22 / 7 ∗ 1 ∗ 21 cm 3 = 462 cm 3 weight of iron = 462 * 8 = 3696 gm = 3.696 kg option a
Answer: a
Question (general): village x has a population of 72000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 72000 - 1200 p = 42000 + 800 p 2000 p = 30000 p = 15 answer is a ."
Answer: a