Cheukting/mathqa huggingface dataset:
Question (general): the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 100 , then their difference is
Options: a ) 19 , b ) 10 , c ) 28 , d ) 27 , e ) 29
Rationale: "let the numbers be x and ( 100 - x ) . then , \ inline \ fn _ jvn \ rightarrow \ inline \ fn _ jvn x ^ { 2 } - 100 x + 2475 = 0 \ inline \ fn _ jvn \ rightarrow ( x - 55 ) ( x - 45 ) = 0 \ inline \ fn _ jvn \ rightarrow x = 55 or x = 45 \ inline \ fn _ jvn \ therefore the numbers are 45 and 55 required difference = ( 55 - 45 ) = 10 answer : b"
Answer: b
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 48 and 72
Options: a ) 126 , b ) 184 , c ) 168 , d ) 154 , e ) 186
Rationale: "prime factorization of 72 = 2 x 2 x 2 x 3 x 3 prime factorization of 48 = 2 x 2 x 2 x 2 x 3 gcf = 24 lcm = 144 sum = 168 ans : c"
Answer: c
Question (geometry): the area of a square is 4225 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 41 : 130
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4225 a = 65 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 41 : 130 answer : e"
Answer: e
Question (physics): jisha walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: jisha walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e
Answer: e
Question (physics): the spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls . the diameters of two of these are 1 1 / 2 cm and 2 cm respectively . the diameter of third ball is ?
Options: a ) 2.8 , b ) 2.5 , c ) 2.2 , d ) 2.0 , e ) 2.1
Rationale: "4 / 3 π * 3 * 3 * 3 = 4 / 3 π [ ( 3 / 2 ) 3 + 23 + r 3 ] r = 1.25 d = 2.5 answer : b"
Answer: b
Question (gain): thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 21 have taken the preparatory course and 42 have not taken the course . how many members are there in the swim club ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 90 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 42 + 21 = 63 members have not passed the test , thus 0.7 * total = 63 - - > total = 90 . answer : d ."
Answer: d
Question (gain): ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) 228 , b ) 288 , c ) 500 , d ) 200 , e ) 881
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 500 was made . answer : c"
Answer: c
Question (physics): on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 28 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 12.2 , c ) 14.8 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 28 inch = ( 136 ã — 28 ) / 312 = 12.2 km answer : b"
Answer: b
Question (general): positive integer y is 50 percent of 25 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?
Options: a ) 50 , b ) 125 , c ) 200 , d ) 1,000 , e ) 2,000
Rationale: y = 50 % of 25 % 0 f x = x / 8 and y / 100 of x = 100 y / 100 * 8 y = 100 y = 125 answer - b
Answer: b
Question (general): in simple interest what sum amounts of rs . 1120 / - in 4 years and rs . 1200 / - in 5 years ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 800 , d ) rs . 900 , e ) rs . 700
Rationale: for 1 year interest = 1200 - 1120 = 80 for 4 year 320 then sum = 1120 - 320 = 800 answer : c
Answer: c
Question (general): if 9 a - b = 10 b + 50 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: this implies 9 a - b = 10 b + 50 , 9 a - b = - 12 b - 2 a , 10 b + 50 = - 12 b - 2 a manipulating the second equation gives us 9 a - b = - 12 b - 2 a = = > 11 a + 11 b = 0 answer is c
Answer: c
Question (physics): the current of a stream runs at the rate of 4 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 4 , e ) 1
Rationale: s = 4 m = x ds = x + 4 us = x - 4 6 / ( x + 4 ) + 6 / ( x - 4 ) = 2 x = 8 answer : c
Answer: c
Question (physics): cathy and jim begin running at the same time and they start at the same place on a straight path . cathy runs at 10 miles per hour , and jim runs at 6 miles per hour . after 18 minutes , cathy stops to stretch . if it takes cathy 27 minutes to stretch and jim continues to run during this time , how many minutes will it take cathy to catch up to jim ?
Options: a ) 20.5 , b ) 21.5 , c ) 22.5 , d ) 23.5 , e ) 24.5
Rationale: in 18 minutes , cathy runs 3 miles . in 45 minutes , jim runs 4.5 miles . cathy can catch jim at a rate of 4 miles per hour . since jim is ahead by 1.5 miles , it will take cathy 1.5 / 4 hours = 22.5 minutes to catch jim . the answer is c .
Answer: c
Question (physics): the speed of a car is 65 km in the first hour and 45 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 55 kmph , c ) 50 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "s = ( 65 + 45 ) / 2 = 55 kmph answer : b"
Answer: b
Question (general): set x consists of all two - digit primes and set y consists of all positive multiples of 4 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 93 , c ) 90 , d ) 92 , e ) 95
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 4 , 8 , 12 , . . . . . . . . . . . . . . . , 88 , 92 , 96 } combining two sets , say set z set z = { 4,8 , 11 , 12,13 , 17 , . . . . . . . . . . . . . . . . . . . , 83 , 88 , 89 , 92 , 96 , 97 } range = max value - min value range ( z ) = 97 - 4 = 93 oa b is the answer ."
Answer: b
Question (gain): car z travels 50 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 375.2 , c ) 400 , d ) 408.3 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 50 miles / hour , the car will run 40 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40 miles / gallon * 10 gallons = 400 miles . answer c ."
Answer: c
Question (gain): 30 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 75
Rationale: "i came up with ( e ) 75 think of 100 people total : from the first fact , 30 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 30 equals the number of fair haired men , which is 45 men with fair hair . add this 45 to the 30 women and get 75 fair haired men and women out of 100 total men and women . 75 % e"
Answer: e
Question (gain): the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 255 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 445 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 255 + x ) / 2 on solving , x = 445 . answer : b"
Answer: b
Question (geometry): a rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares . through how many of the squares does a diagonal of the rectangle pass ?
Options: a ) 6
b ) 8
c ) 10
d ) 12
e ) 16
Rationale: 1 ) if the two sides are co - prime , sum of sides - 1 . . 2 ) and if not co - prime , sum of sides - hcf of sides . . the difference is related to the diagonal passing through a vertex of squares at some place . . here 6 and 8 are not co - primes , so ans = 6 + 8 − hcf ( 6,8 ) = 14 − 2 = 12 answer : d
Answer: d
Question (general): if x + y = 3 and x 2 y 3 + y 2 x 3 = 27 , what is the value of xy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "xy = 3 as x + y = 3 x 2 y 3 + y 2 x 3 = 27 x 2 y 2 ( y + x ) = 27 substituting x + y x 2 y 2 = 9 xy = 3 answer : c"
Answer: c
Question (gain): the balance of a trader weighs 10 % less than it should . still the trader marks up his goods to get an overall profit of 20 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 9 %
Rationale: "original cost before weight adjustment : x cost after 90 % weight adjustment : 9 / 10 x 20 % profit on 9 / 10 x : ( 120 / 100 ) ( 9 / 10 ) ( x ) or 108 x / 100 mark up on original cost of x : ( 108 x / 100 ) / x - 1 = 8 / 100 answer : b"
Answer: b
Question (physics): water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 16 meters . what is value of the radius in meters ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 8
Rationale: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 16 ) which is about 1 / 16 r = 1 / 4 the answer is c ."
Answer: c
Question (physics): working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel six times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 7 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 6 and w = 6 s then we have 1 / ( 6 * s ) + 1 / s = 1 / 6 < = > 7 / ( 6 * s ) = 1 / 6 < = > s = 7 ans : d"
Answer: d
Question (physics): a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 7.2 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 3 min
Rationale: "s = 600 / 40 = 15 mps s = 7200 / 15 = 480 sec = 8 min . answer : c"
Answer: c
Question (probability): a bag contains 6 black and 7 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 7 / 13
Rationale: "let number of balls = ( 6 + 7 ) = 13 . number of white balls = 7 . p ( drawing a white ball ) = 7 / 13 hence answer is e"
Answer: e
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 100 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 94.7
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 100 kilometers per hour is 1 / 100 hours = 3,600 / 100 seconds = 36 seconds ; time to cover this distance at regular speed is 36 + 2 = 38 seconds = 38 / 3,600 hours = 4 / 379 hours ; so , we get that to cover 1 kilometer 1 / ( 4 / 379 ) hours is needed - - > regular speed 94.7 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e ."
Answer: e
Question (general): how many multiples of 4 are there between 4 and 64 ?
Options: a ) 12 , b ) 64 , c ) 14 , d ) 16 , e ) 60
Rationale: "it should be mentioned whether 4 and 64 are inclusive . if 4 and 64 are inclusive , then the answer is ( 64 - 4 ) / 4 + 1 = 16 . if 4 and 64 are not inclusive , then the answer is ( 60 - 8 ) / 4 + 1 = 14 . since oa is c , then we have not inclusive case ."
Answer: c
Question (physics): points a , b , c , and d , in that order , lie on a line . if ab = 3 cm , ac = 4 cm , and bd = 8 cm , what is cd , in centimeters ?
Options: a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 3 ( ab = 3 ) c - 4 ( ac = 4 ) d - 11 ( bd = 8 ) cd is 11 - 4 = 7 . ans a"
Answer: a
Question (physics): a can do a piece of work in 5 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 30 , b ) 20 , c ) 10 , d ) 6 , e ) 5
Rationale: "a ' s 1 hour ' s work = 1 / 5 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 5 + 1 / 3 ) = 8 / 15 . b ' s 1 hour ' s work = ( 8 / 15 - 1 / 2 ) = 1 / 30 . therefore a alone will take 30 hours to do the work . a"
Answer: a
Question (probability): there is a 10 % chance that tigers will not win at all during the whole season . there is a 20 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %
Rationale: "there is a 10 % chance that tigers will not win at all during the whole season we can infer that there is 90 % chance tigers will win . similarly there is a 20 % chance that federer will not play at all in the whole season we can also infer that there is 80 % chance that federer will play . answer e"
Answer: e
Question (physics): lally ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning lally makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?
Options: a ) 15 , b ) 24 , c ) 25 , d ) 26 , e ) 13
Rationale: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now lally can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional payments i . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c
Answer: c
Question (gain): a retailer bought a machine at a wholesale price of $ 108 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 144
Rationale: "my solution : wholesale price = 108 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 108 + 1 / 5 ( 108 ) x = 144 ; answer : e"
Answer: e
Question (geometry): if n is the smallest integer such that 72 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "72 can written as = 2 * 2 * 2 * 3 * 3 - - > 2 ^ 3 * 3 ^ 2 - - - ( 1 ) so for 72 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 3 to make the power of 2 in ( 1 ) even option a is correct"
Answer: a
Question (general): in one day , juan sends keith 8 times as many messages as he sends laurence , and laurence sends missy 4.5 times as many messages as he receives from juan . if missy received 18 messages from laurence , how many messages does keith receive from juan ?
Options: a ) 13 , b ) 26 , c ) 32 , d ) 48 , e ) 56
Rationale: juan - - > laurence = x messages ; juan - - > keith = 8 x messages ( juan sends keith eight times as many messages as he sends laurence ) ; laurence - - > missy = 4.5 x = 18 ( laurence sends missy 4.5 times as many messages as he receives from juan ) . 4.5 x = 18 - - > x = 4 - - > 8 x = 32 . answer : c .
Answer: c
Question (geometry): the area of a triangle will be when a = 1 m , b = 2 m , c = 3 m , a , b , c being lengths of respective sides .
Options: a ) 0 sq m
b ) 7 sq m
c ) 2 sq m
d ) 3 sq m
e ) 6 sq m
Rationale: s = ( 1 + 2 + 3 ) / 2 = 3 = > no triangle exists answer : a
Answer: a
Question (physics): edward earns $ 7.00 per hour for the first 40 hours he works per week , and twice this rate for overtime . if michael earned $ 210 last week , how many hours did he work ?
Options: a ) 43 , b ) 44 , c ) 45 , d ) 46 , e ) 47
Rationale: $ 7 * 40 + $ 12 * x = $ 210 - - > x = 5 hours . total working hours = 40 + 5 = 45 answer : c .
Answer: c
Question (gain): i bought two books ; for rs . 470 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 274.17 , b ) 280.17 , c ) 299.17 , d ) 266.17 , e ) 279.17
Rationale: "x * ( 85 / 100 ) = ( 470 - x ) 119 / 100 x = 274.17 answer : a"
Answer: a
Question (physics): 18 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 8 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 1 days
Rationale: "1 women ' s 1 day work = 1 / 126 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 126 + 10 / 140 ) = 1 / 9 5 women and 10 children will complete the work in 9 days . answer : d"
Answer: d
Question (general): when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.45 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 20 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.45 and remainder is 9 so . 45 x y = 9 hence y = 20 ans d"
Answer: d
Question (general): an employee ’ s annual salary was increased $ 5000 . if her new annual salary now equals $ 25000 what was the percent increase ?
Options: a ) 15 % , b ) 80 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5000 . = $ 20000 % increase = ( $ 15000 / $ 75000 ) * 100 = 80 % hence b .
Answer: b
Question (physics): it takes avery 3 hours to build a brick wall while tom can do it in 4 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 25 minutes . , b ) 55 minutes . , c ) 1 hour and 41 minutes , d ) 1 hour and 35 minutes , e ) 1 hour and 20 minutes
Rationale: "avery ' s efficiency is 100 / 3 = 33 % tom ' s = 100 / 4 = 25 % they worked together for 1 hour and finished 58 % of the job remaining = 42 % tom will complete 25 % in 60 minutes , and 17 % in 60 * 17 / 25 minutes = 40.8 minutes time taken by tom to finish the remaining on his own = 60 + 40.8 = 100.8 minutes ( adjusting for 0.2 ) ~ 101 minutes answer : c"
Answer: c
Question (gain): of the 200 employees in a certain company , 30 percent will be relocated to city x and the remaining 70 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 115 , b ) 120 , c ) 140 , d ) 152 , e ) 165
Rationale: 120 prefer x ( group 1 ) ; 80 prefer y ( group 2 ) . city y needs 140 people : letall 80 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 60 people : 120 - 60 = 60 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 80 + 60 = 140 . answer : c .
Answer: c
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.7 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.1 , d ) 12 , e ) 12.5
Rationale: "mean = 14.5 two standard deviations is 1.7 + 1.7 = 3.4 there could be two calues for this . mean + two standard deviations = 17.9 mean - two standard deviations = 11.1 answer choice has 11.1 and so c is the answer ."
Answer: c
Question (general): divide rs . 1700 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 346 , b ) 425 , c ) 375 , d ) 337 , e ) 639
Rationale: "a + b + c = 1700 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1700 = > 425 answer : b"
Answer: b
Question (physics): the sector of a circle has radius of 24 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 11.5 cm , c ) 104.6 cm , d ) 92.5 cm , e ) 99.5 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 24 ) + 2 ( 24 ) = 56.6 + 48 = 104.6 cm answer : c"
Answer: c
Question (general): what is the x - intercept of a line that passes through the point ( 3 , 4 ) and has a slope of 2 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: first , plot the point ( 3 , 4 ) on a graph . a slope of 2 means “ up 2 , over 1 , ” so plot this point on a graph , too . here ’ s the resulting graph : y over 1 up 2 ( 1 , 0 ) ( 2 , 2 ) ( 3 , 4 ) ( 4 , 6 ) x the line passes through the x - axis at 1 , making the correct answer d ) 1
Answer: d
Question (gain): raja spends 35 % of his monthly income on household items , 20 % of his monthly income on buying cloths , 5 % of his monthly income on medicines and saves the remaining amount which is rs . 15000 . find his monthly income .
Options: a ) rs . 40000 , b ) rs . 36000 , c ) rs . 37500 , d ) rs . 45000 , e ) none of these
Rationale: savings 40 % - 15000 expenditure 60 % - 22500 total - 37500 answer : c
Answer: c
Question (general): what least number should be subtracted from 13600 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13600 ÷ 87 = 156 , remainder = 28 hence 28 is the least number which can be subtracted from 13600 such that the remainder is divisible by 87 answer is c"
Answer: c