Cheukting/mathqa huggingface dataset:
Question (general): what is the units digit of 17 ^ 83 × 13 ^ 52 × 11 ^ 87 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 5 correct option : b"
Answer: b
Question (general): during a certain two - week period , 50 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 9 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 10 a , c ) 20 a , d ) 25 a , e ) 28 a
Rationale: "movies : 50 % comedies . 50 % remaining genre . now in this 50 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 9 x . total 10 x . 10 x = 50 ; x = 5 action movies : 5 % drama movies : 45 % we can say that out of 100 z , : comedies : 50 z action : 5 z drama : 45 z now action movies were a this means : a = 5 z . z = ( a / 5 ) comedies : 50 z = 50 * ( a / 5 ) 10 a b is the answer ."
Answer: b
Question (geometry): a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 200 , b ) 276 , c ) 230 , d ) 240 , e ) 250
Rationale: "let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b"
Answer: b
Question (physics): a and b can do a work in 4 hours and 12 hours respectively . a starts the work at 6 am and they work alternately for one hour each . when will the work be completed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 78
Rationale: "work done by a and b in the first two hours , working alternately = first hour a + second hour b = 1 / 4 + 1 / 12 = 1 / 3 . total time required to complete the work = 2 * 3 = 6 days . answer : d"
Answer: d
Question (gain): john had a stock of 1300 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 69.0 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1300 - n = 1300 - 402 = 898 percentage books not sold / total number of books = 898 / 1300 = 0.69 = 69 % correct answer d"
Answer: d
Question (general): a farm is made up of brown and white goats . the number of male brown goats is 35 % less than the total number of brown goats . the total number of female goats is 20 times more than the number of female brown goats . if the total population of male goats is half the population of the female goats , what percentage of male goats are brown ?
Options: a ) 30.1 , b ) 20.5 , c ) 15.2 , d ) 10.2 , e ) 28.6
Rationale: since we are dealing in percentage let us pick 100 as the number of brown male goats . that means that the total number of brown goats is = 135 ( number of male brown goats is 35 % less than the total number of brown goats ) , therefore the number of brown female goats is 35 . the total number of female goats is 15 x the number of brown female goats = 35 * 20 = 700 female goats . male goats total population is half the population of the female goats = 700 / 2 = 350 therefore percentage of male horses goats that are brown = 100 / 350 * 100 = 28.6 correct option is e
Answer: e
Question (general): for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 4 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 4 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 4 = 3 / 4 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 3 / 4 = 3 / 8 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 3 / 4 * 5 / 8 = 1 / 2 ans d"
Answer: d
Question (general): the average of 7 consecutive numbers is 20 . the largest of these numbers is
Options: a ) 12 , b ) 27 , c ) 23 , d ) 28 , e ) 11
Rationale: let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c
Answer: c
Question (general): ( 128.5 x 25 ) + ( 13.8 x 50 ) = ? x 50
Options: a ) 78.05 , b ) 556.02 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 25 ) + ( 13.8 x 50 ) / 50 = 3212.5 + 690 / 50 = 78.05 answer : option a"
Answer: a
Question (gain): a bookseller sells his books at a 15 % markup in price . if he sells a book for $ 23.00 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 21.00 , d ) $ 19.60 , e ) $ 20.00
Rationale: "let the cost price of book = x selling price of book = 23 $ markup % = 15 ( 115 / 100 ) x = 23 = > x = 20 answer e"
Answer: e
Question (physics): there are 20 poles with a constant distance between each pole . a car takes 24 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 41.4543 , b ) 41.4545 , c ) 41.45128 , d ) 41.41288 , e ) 41.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 24 seconds 1 pole ( 24 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 24 / 11 ) seconds = 41.4545 seconds answer : b"
Answer: b
Question (physics): a person walks from one end to the other of a 100 - meter long moving walkway at a constant rate in 50 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 63 , b ) 66 , c ) 69 , d ) 72 , e ) 75
Rationale: let v be the speed of the person and let x be the speed of the walkway . 50 ( v + x ) = 100 then 150 ( v + x ) = 300 150 ( v - x ) = 100 when we add the two equations : 300 v = 400 v = 4 / 3 time = 100 / ( 4 / 3 ) = 75 seconds the answer is e .
Answer: e
Question (gain): what will be the compound interest on a sum of rs . 23,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 9313.34 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 23000 * ( 1 + 12 / 100 ) 3 ] = 23000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 32313.34 c . i . = ( 32313.34 - 23000 ) = rs . 9313.34 answer : a"
Answer: a
Question (physics): the radius of a wheel is 16.8 cm . what is the distance covered by the wheel in making 300 resolutions ?
Options: a ) 754 m , b ) 316.512 m , c ) 311.512 m , d ) 311.518 m , e ) 313.512 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 300 resolutions . = 300 * 2 * 22 / 7 * 16.8 = 31651.2 cm = 316.512 m answer : b"
Answer: b
Question (general): evaluate : 6302.5 + 630.25 + 63.025 + 6.3025 + 0.63025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 7002.70775
Rationale: "6302.5 630.25 63.025 6.3025 + 0.63025 - - - - - - - - - - - - - - - 7002.70775 answer is e ."
Answer: e
Question (general): what is the sum of all the prime numbers from 20 to 40 ?
Options: a ) 279 , b ) 100 , c ) 278 , d ) 120 , e ) 191
Rationale: "explanation : 23 + 29 + 31 + 37 = 120 answer : d"
Answer: d
Question (other): evaluate 30 ! / 28 !
Options: a ) 720 , b ) 600 , c ) 870 , d ) 910 , e ) 650
Rationale: "we have 30 ! / 28 ! = 30 * 29 * 28 ! / 28 ! = 30 * 29 = 870 answer is c"
Answer: c
Question (other): at present the ratio between the ages of arun and deepak is 2 : 5 . after 10 years arun ' s age will be 30 years . what is the age of the deepak ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 45
Rationale: "let the present age of arun and deepak be 4 x and 3 x 2 x + 10 = 30 2 x = 20 x = 10 deepak ' s age = 5 x = 50 years answer is c"
Answer: c
Question (other): 100 liters of a mixture contains milk and water in the ratio 4 : 1 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 7 : 5 , b ) 9 : 2 , c ) 6 : 1 , d ) 5 : 4 , e ) 11 : 4
Rationale: "quantity of milk in 100 liters if mix = 100 * 4 / 5 = 80 liters quantity of milk in 110 liters of new mix = 80 + 10 = 90 liters quantity of water in it = 110 - 90 = 20 liters ratio of milk and water in new mix = 90 : 20 = 9 : 2 answer is b"
Answer: b
Question (general): there are 8 baskets numbered from 1 to 8 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 640 , b ) 680 , c ) 720 , d ) 760 , e ) 800
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 8 * 9 / 2 = 36 apples . the total number of apples taken by 10 children is 10 * 36 = 360 the number of apples left in the end is 1000 - 360 = 640 apples . the answer is a ."
Answer: a
Question (geometry): a rectangular floor that measures 6 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 15 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 225 , e ) $ 1,920
Rationale: "the width of the rectangular floor ( 6 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 10 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 6 / 2 ) * ( 10 / 2 ) = 15 . the total cost is 15 * 15 = $ 225 . the answer is , therefore , d ."
Answer: d
Question (other): on multiplying a numberz by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number z is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Question (general): the average age of 40 passengers in a ferry is 35 . what is the average age of the new group formed when combining the passengers with the 5 crew members of ferry whose average age is 25 ?
Options: a ) 36.45 , b ) 38.89 , c ) 39.67 , d ) 40.12 , e ) 41.88
Rationale: sum of ages of passengers = 40 x 35 = 1400 sum of ages of crew = 25 x 5 = 125 sum of ages of new group formed = 1525 average = 1525 / 45 = 38.89 answer : b
Answer: b
Question (geometry): one side of the bottom layer of a triangular pyramid has 12 balls . how many are there in the whole pyramid ? note that the pyramid is equilateral and solid .
Options: a ) 286
b ) 364
c ) 504
d ) 164
e ) 165
Rationale: as there are 12 balls along one side , it means that there are 12 layers of balls . the top most layer has 1 ball . the second layer has 3 ( 1 + 2 ) balls . the third layer has 6 ( 1 + 2 + 3 ) balls . the fourth layer has 10 ( 1 + 2 + 3 + 4 ) balls . the fifth layer has 15 ( 1 + 2 + 3 + 4 + 5 ) balls . similarly , there are 21 , 28 , 36 , 45 , 55 , 66 and 78 balls in the remaining layers . hence , the total number of balls are = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 balls answer : b
Answer: b
Question (general): in a company of 15 employees , 6 employees earn $ 37,000 , 5 employees earn $ 42,000 , and the 4 highest - paid employees earn the same amount . if the average annual salary for the 15 employees is $ 45,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 56,250 , b ) $ 57,750 , c ) $ 59,250 , d ) $ 60,750 , e ) $ 62,250
Rationale: "6 * 37,000 + 5 * 42,000 + 4 x = 15 * 45,000 4 x = 675,000 - 222,000 - 210,000 4 x = 243,000 x = 60,750 the answer is d ."
Answer: d
Question (general): what is the units digit of ( 493 ) ( 915 ) ( 381 ) ( 756 ) ( 22 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 1 . imo b ."
Answer: b
Question (gain): a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 25 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) 40 % , b ) 38 % , c ) 36 % , d ) 33.33 % , e ) 35 %
Rationale: "anyway , in this question , there is no discount but the mark up is given as 25 % of the selling price . so it is not 25 % of $ 150 but instead , 40 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 25 % of s = s s = 200 profit = 50 which is calculated on cost price in % terms . so 50 / 150 * 100 = 33.33 % is profit . d"
Answer: d
Question (physics): two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 90 kmph and 108 kmph . in how much time will the trains cross each other ?
Options: a ) 80 / 8 , b ) 80 / 7 , c ) 80 / 5 , d ) 80 / 3 , e ) 80 / 11
Rationale: "relative speed = ( 90 + 108 ) * 5 / 18 = 11 * 5 = 55 mps . the time required = d / s = ( 100 + 100 + 200 ) / 55 = 400 / 55 = 80 / 11 sec . answer : e"
Answer: e
Question (general): how many 4 digit odd numbers do not use any digit more than once
Options: a ) 1720 , b ) 2160 , c ) 224 , d ) 2460 , e ) none of these
Rationale: the way i solved it is a b c d ( thousand , hundreds , tens , units ) d can be 1 3 5 7 9 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities c can be anything execpt a and b so 8 possibilities b can be anything execpt ( a d c ) so 7 possibilities total ways are 8 * 7 * 8 * 5 = 2240 ans e
Answer: e
Question (geometry): how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 9 inches than that of a rectangular sheet of paper measuring 4.5 inches by 11 inches ?
Options: a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
Rationale: "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 9 is twice 4.5 then the area will be double which means 100 % greater . the answer is c ."
Answer: c
Question (general): a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 36 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 19 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 36 pints will require 9 / 17 * 36 = 19 pints . . c"
Answer: c
Question (gain): a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3000 . if the price of the car in 1996 was $ 22000 , what is the car ' s price in 2002 ?
Options: a ) $ 21,700 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 3000 = $ 21700 correct option : a
Answer: a
Question (physics): the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 850 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 18,700
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 850 ã — 22 ) = rs . 18700 answer : option e"
Answer: e
Question (probability): at a conference table , 6 employees gather around a table . one of the employees is the manager and he sits at the head of the table . two of the employees sit on either side of the table . how many different seating arrangements can be made with these 6 employees ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: head ' s sit is fixed . now 5 people is left with 5 seats . 5 people can sit on 5 seats in 5 ! ways or 120 ways . ans is d
Answer: d
Question (general): if q and t are positive integers , qt + q + t can not be
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let qt + t + q = x add 1 on both sides : qt + t + q + 1 = x + 1 tq + 1 ) + q + 1 = x + 1 ( q + 1 ) ( t + 1 ) = x + 1 minimum value of ( q + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > qt + t + s can not be 6 answer : b
Answer: b
Question (probability): an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 1 red and 2 green balls ?
Options: a ) 70 / 323 , b ) 50 / 323 , c ) 52 / 969 , d ) 60 / 323 , e ) 25 / 321
Rationale: "sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue and 1 red and 2 green balls were drawn from bag = 6 c 1 * 5 c 1 * 8 c 2 = 840 probability = 840 / 3876 = 70 / 323 ans - a"
Answer: a
Question (general): a toy factory stores its toys in either a big box or a small box . the big box can store 35 toys while the small box can store 14 toys . if the factory is to store 86 newly manufactured toys , what is the least number of toys that will be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 4
Rationale: total toys to be stored 86 the big box can store 35 small box can store 14 storing 85 toys in big box 85 / 35 = 2 r 16 store remainder in small box 16 / 14 = 1 r 2 least number of toys that will be left unboxed = 2 answer : a
Answer: a
Question (gain): a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 3,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6.43 % , b ) 6.89 % , c ) 7.69 % , d ) 8.21 % , e ) 8.75 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 6500 = 1 / 13 which is about 7.69 % the answer is c ."
Answer: c
Question (physics): a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 35 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 1050 km , b ) 1150 km , c ) 1250 km , d ) 1550 km , e ) 850 km
Rationale: "d = 30 * 5 = 150 rs = 35 – 30 = 5 t = 150 / 5 = 30 d = 35 * 30 = 1050 km answer : a"
Answer: a
Question (general): total dinning bill for 9 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 26.96 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 9 = 26.96 answer : d"
Answer: d
Question (gain): a sum of money at simple interest amounts to rs . 805 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 688 , d ) s . 700 , e ) s . 718
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 805 - 117 ) = rs . 688 . answer : option c"
Answer: c
Question (gain): a shopkeeper fixes the marked price of an item 25 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 11.59 % , b ) 12.59 % , c ) 13.59 % , d ) 14.59 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 125 required gain = 8 % , so selling price = rs 108 discount = 125 - 108 = 17 discount % = ( 17 / 135 ) * 100 = 12.59 % option b"
Answer: b
Question (general): a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 550.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 7.85 , b ) $ 11.30 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 550 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 550 / 70 ~ 7.85 a
Answer: a
Question (gain): a candidate got 30 % of the votes polled and he lost to his rival by 1760 votes . how many votes were cast ?
Options: a ) 4000 , b ) 4100 , c ) 4200 , d ) 4300 , e ) 4400
Rationale: "let x be the total number of votes . 0.3 x + 1760 = 0.7 x 0.4 x = 1760 x = 1760 / 0.4 = 4400 the answer is e ."
Answer: e
Question (general): if 4 / p = 8 & 4 / q = 18 then p - q = ?
Options: a ) 5 / 18 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 4 / 8 , q = 4 / 18 = > q = 2 / 9 therefore p - q = ( 1 / 2 ) - ( 2 / 9 ) = 5 / 18 answer : a"
Answer: a