Cheukting/mathqa huggingface dataset:
Question (geometry): a rectangular grass field is 60 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1350 , b ) 1200 , c ) 9676 , d ) 1679 , e ) 2691
Rationale: "area = ( l + b + 2 d ) 2 d = ( 60 + 55 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : b"
Answer: b
Question (physics): a clock shows the time as 9 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 5 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 40 min , e ) 55 min
Rationale: "there are 8 hours in between 9 a . m . to 5 p . m . 8 * 5 = 40 minutes . answer : d"
Answer: d
Question (physics): a plant manager must assign 6 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
Options: a ) 24 , b ) 27 , c ) 33 , d ) 45 , e ) 54
Rationale: "whatever : my take selecting team of 2 out of 10 to assign to the shifts = 6 c 2 = 15 ways . now 2 out of 10 means total of 3 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 3 * 2 * 1 = 6 here alt and alt are the same : so 6 / 2 = 3 ways . total ways of selecting = ( selecting 2 out of 6 ) * arranging those teams in shifts = 15 * 3 = 45 ans : d"
Answer: d
Question (general): the average of first four multiples of 4 is :
Options: a ) 3 , b ) 9 , c ) 10 , d ) 15 , e ) 17
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 ) / 4 = 40 / 4 = 10 answer c"
Answer: c
Question (gain): an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 15 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 28 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 60.00
Rationale: without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 43 % , thus he must pay slightly more than $ 57 . only answer choice e fits . answer : e .
Answer: e
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 45 and 125 ?
Options: a ) 1920 , b ) 2201 , c ) 3240 , d ) 1130 , e ) 3840
Rationale: "prime factorization of the given numbers 45 = 3 ^ 2 125 = 5 ^ 3 greatest common factor = 5 lowest common multiple = 3 ^ 2 * 5 ^ 2 * 5 = 1125 sum = 5 + 1125 = 1130 answer d"
Answer: d
Question (probability): the chance of rain on any given day in tel - aviv is 50 % . what is the probability e that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days e = 15 / 64 ans a it is ."
Answer: a
Question (general): you collect pens . suppose you start out with 10 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 59
Rationale: "solution start with 10 pens . mike gives you 22 pens : 10 + 22 = 39 pens . cindy doubles the number of pens you have : 39 ã — 2 = 78 pens . sharon takes 19 pens from you : 78 - 19 = 59 pens . so you have 59 at the end . correct answer : e"
Answer: e
Question (general): how many integer values are there for x such that 1 < 3 x + 5 < 17 ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: the inequality given is 1 < 3 x + 5 < 17 it can further reduced to - 4 < 3 x < 12 finally - 4 / 3 < x < 4 so can only take 5 integer values i . e . - 1 , 0,1 , 2,3 correct answer - d
Answer: d
Question (gain): a portion of the 85 % solution of chemicals was replaced with an equal amount of 30 % solution of chemicals . as a result , 40 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 5 / 11 , b ) 6 / 11 , c ) 7 / 11 , d ) 9 / 11 , e ) 13 / 6
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.85 ( 1 - x ) + 0.3 * x = 0.4 - - > x = 9 / 11 . answer : d ."
Answer: d
Question (general): if the price of a book is first decreased by 20 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 4 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 20 % = 80 then increased 20 % on rs 80 = 80 + 16 = 96 net change in price = 100 - 96 = 4 answer : c"
Answer: c
Question (general): a basketball is dropped from a height of 30 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 3 full bounces .
Options: a ) 50 , b ) 82.5 , c ) 60 , d ) 75 , e ) 80
Rationale: "initial distance = 30 feet first bounce = 15 feet up + 15 feet down = 30 feet second bouche = 7.5 feet up + 7.5 feet down = 15 feet third bounce = 375 feet up and 3.75 feet down = 7.5 feet total distance covered = 30 + 30 + 15 + 7.5 = 82.5 answer is b"
Answer: b
Question (physics): two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 600 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 50 sec , e ) 40 min
Rationale: "they meet every 600 / 7 + 8 = 40 sec answer is e"
Answer: e
Question (general): praveen age after 10 years will be 3 times his age 3 years back . what is the present age of chris ?
Options: a ) 20 , b ) 25 , c ) 10 , d ) 30 , e ) 15
Rationale: chris present age = x after 10 years = x + 10 3 years back = x - 3 x + 10 = 3 ( x - 3 ) x = 20 answer is a
Answer: a
Question (general): how many multiples of 2 are there between 10 and 52 , 10 and 52 inclusive ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 21 , e ) 22
Rationale: "2 multiples are . . . 10,12 , 14,16 , 18,20 , 22,24 , 26,28 , 30,32 , 34,36 , 38,40 , 42,44 , 46,48 , 50,52 , . . . , the answer is = 22 answer is e"
Answer: e
Question (general): what is the next number 12 13 15 17 111 113 117 119 123 129 ?
Options: a ) 154 , b ) 220 , c ) 129 , d ) 131 , e ) 224
Rationale: 131 . these are the first 10 prime numbers ( 2 , 3 , 5 . . . ) prefixed with a 1 answer : d
Answer: d
Question (general): david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 2 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 6 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 4 , e ) 1 / 3
Rationale: "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 2 x total tips for all months = 6 * x + 2 x = 8 x tips for august / total tips for all months = 2 x / 8 x = 1 / 4 answer : d"
Answer: d
Question (general): if the average of 10 x and 8 y is greater than 70 , and x is twice y , what is the least integer value of x ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 10 , e ) 20
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 10 x and 4 x is greater than 70 . average of 10 x and 4 x is 7 x . so , 7 x > 70 x > 10 answer : d"
Answer: d
Question (general): when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 35 % water ?
Options: a ) 1.3 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 65 % ( 100 - 35 ) . therefore 0.5 x amount of flower - nectar = 0.65 x amount of honey = 0.65 x 1 kg therefore amount of flower - nectar needed = ( 0.65 / 0.51 ) kg = 1.3 kgs answer : a
Answer: a
Question (general): a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 1205 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 22200 , b ) 31897 , c ) 48799 , d ) 50000 , e ) 52782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 1205 p = 50000 answer : 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 $ 61.2 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 ) $ 4.50 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 61.2 - - > { original price } = $ 72 . { final price } = $ 61.2 * 1.25 = $ 76.5 . the difference = $ 76.5 - $ 72 = $ 4.5 answer : b ."
Answer: b
Question (general): the smallest number which when diminished by 12 , is divisible 12 , 24 , 36 , 48 and 56 is :
Options: a ) 1008 , b ) 1015 , c ) 1020 , d ) 1032 , e ) 1048
Rationale: "required number = ( l . c . m . of 12 , 24 , 36 , 48,56 ) + 12 = 1008 + 12 = 1020 answer : option c"
Answer: c
Question (general): there are 100 students in 3 sections a , b and c of a class . the average marks of all the 3 sections was 84 . the average of b and c was 87.5 and the average marks of students in a section was ?
Options: a ) 20 , b ) 99 , c ) 28 , d ) 27 , e ) 12
Rationale: numbers of students in section a = x numbers of students in section b and c = ( 100 – x ) x 70 + ( 100 – x ) 87.5 = 84 100 70 x + 87.5 100 – 87.5 x = 8400 8750 – 17.5 x = 8400 17.5 x = 8750 – 8400 = > x = 20 . answer : a
Answer: a
Question (gain): a trader bought a car at 5 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 52 % , d ) 19 % , e ) 22 %
Rationale: original price = 100 cp = 95 s = 95 * ( 160 / 100 ) = 152 100 - 152 = 52 % answer : c
Answer: c
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 . 275 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 275 + x ) / 2 on solving , x = 425 . answer : 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 18 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 8 , b ) 16 , c ) 11 , d ) 12 , e ) 21
Rationale: "relative speed = ( 18 + 72 ) * 5 / 18 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec . answer : b"
Answer: b
Question (general): if x : y = 1 : 3 , find the value of ( 2 x + 3 y ) : ( 5 x – y )
Options: a ) 11 : 3 , b ) 11 : 2 , c ) 3 : 2 , d ) 7 : 2 , e ) 9 : 5
Rationale: "explanation : given : x / y = 1 / 3 ( 2 x + 3 y ) / ( 3 x – y ) = ( 2 * 1 + 3 * 3 ) : ( 5 * 1 – 3 ) = 11 : 2 answer : b"
Answer: b
Question (general): if x # y is defined to equal x ^ 3 / y for all x and y , then ( - 1 # 2 ) # 3 =
Options: a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 12 , d ) - 1 / 12 , e ) 1 / 24
Rationale: "( - 1 ) ^ 3 / 2 = 1 / 2 ( 1 / 2 ) ^ 3 / 3 = 1 / 24 so e is my answer"
Answer: e
Question (gain): in a restaurant , the profit is 150 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 55 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 150 , s . p . = rs . 250 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 250 . profit = rs . ( 250 - 112 ) = rs . 138 . required percentage = ( 138 / 250 * 100 ) % = 55 % appox answer : b"
Answer: b
Question (other): a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter e of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) e = 7 * 3 = 21 . c"
Answer: c
Question (physics): a can do a piece of work in 14 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 14
Rationale: "8 / 14 + 6 / x = 1 x = 14 days answer : e"
Answer: e
Question (general): 8 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 66 , b ) 52 , c ) 58 , d ) 55 , e ) 56
Rationale: "though 2 * ( 8 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 7 , so he ' ll play 14 matches . similarly , second guy has to play with the rest of 6 as his 2 games with the first guy are already played . so he plays 12 matches . this continues like this and the total matches are 14 + 12 + 10 . . . + 2 14 + 12 + . . . + 2 = 2 ( 7 + 6 + . . . + 1 ) = 2 ( ( 7 * 8 ) / 2 ) = 7 * 8 = 56 . answer : e"
Answer: e
Question (gain): a small college reduced its faculty by approximately 14 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 227 , d ) 254 , e ) 302
Rationale: if x is the original number of faculty members , then after 14 % reduction in faculty members number is . 86 x but we are given . 86 x = 195 x = 227 so the original number of faculty members is 227 correct answer - c
Answer: c
Question (gain): one fourth of one third of two fifth of a number is 16 . what will be 40 % of that number
Options: a ) 140 , b ) 150 , c ) 180 , d ) 192 , e ) 250
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 16 then x = 16 * 30 = 480 40 % of 480 = 192 answer : option d"
Answer: d
Question (other): hree number are in the ratio of 3 : 4 : 5 and their l . c . m . is 2400 . their h . c . f . is :
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: let the numbers be 3 x , 4 x and 5 x . then , their l . c . m . = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 x 40 ) , ( 4 x 40 ) and ( 5 x 40 ) . hence , required h . c . f . = 40 . answer : a
Answer: a
Question (geometry): the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 625 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 99 , c ) 100 , d ) 72 , e ) 12
Rationale: "given that the area of the square = 625 sq . units = > side of square = √ 625 = 25 units the radius of the circle = side of the square = 25 units length of the rectangle = 2 / 5 * 25 = 10 units given that breadth = 10 units area of the rectangle = lb = 10 * 10 = 100 sq . units answer : c"
Answer: c
Question (general): if x + y = 250 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 225 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 250 x - y = 200 2 x = 50 x = 25 y = 225 answer is b"
Answer: b
Question (geometry): if the area of a circle is 36 pi square feet , find its circumference .
Options: a ) 65 pi feet , b ) 43 pi feet , c ) 12 pi feet , d ) 18 pi feet , e ) 64 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 81 pi r * r = 36 ; hence r = 36 feet the circumference is given by 2 * pi * r = 2 * pi * 6 = 128 pi feet correct answer c"
Answer: c
Question (physics): to fill a tank , 42 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifths of its present ?
Options: a ) 102 , b ) 103 , c ) 104 , d ) 105 , e ) 106
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 42 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 42 x ) / ( 2 x / 5 ) = ( 42 x ) x 5 / 2 x = 210 / 2 = 105 answer is d ."
Answer: d
Question (other): a factory produces 1 defective bulb out of 10 bulbs a yr . if it produces 870 bulbs a yr , how many defective bulbs are produced ?
Options: a ) 84 , b ) 85 , c ) 86 , d ) 87 , e ) 88
Rationale: 10 out of 1 is defective 20 out of 2 is defective 100 out of 10 is defective and so on 800 out of 80 is defective 70 out of 7 is defective 80 + 7 = 87 answer : d
Answer: d
Question (geometry): the area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is ?
Options: a ) 48 , b ) 40 , c ) 52 , d ) 54 , e ) 58
Rationale: "isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 16 will be divided into 3 parts = 10 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 26 * 4 = 52 c is the answer"
Answer: c
Question (gain): find the principal which yields a simple interest of rs . 20 and compound interest of rs . 25 in two years , at the same percent rate per annum ?
Options: a ) s . 40 , b ) s . 48 , c ) s . 49 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 25 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 25 – 20 ) / 20 ] * 100 = 25 % p . a . let the principal be rs . x time = t = 2 years % rate = 25 % p . a . si = ( prt / 100 ) 20 = ( x * 25 * 2 ) / 100 x = rs . 40 answer : a"
Answer: a
Question (gain): a shopkeeper sells 400 metres of cloth for $ 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) $ 20 , b ) $ 43 , c ) $ 50 , d ) $ 70 , e ) $ 40
Rationale: "c $ 50 sp per metre = 18000 / 400 = $ 45 loss per metre = $ 5 cp per metre = 45 + 5 = $ 50"
Answer: c
Question (general): 36 * 36 * 36 = 6 ^ ?
Options: a ) 3 , b ) 2 , c ) 6 , d ) 1 , e ) 5
Rationale: "6 ^ 2 * 6 ^ 2 * 6 ^ 2 = 6 ^ ( 2 + 2 + 2 ) = 6 ^ 6 answer : 6 answer : c"
Answer: c
Question (general): what is the least number which when divided by 5 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 136 , d ) 184 , e ) 196
Rationale: "explanation : lcm of 5 , 9 , 12 and 18 is 180 required number = 180 + 4 = 184 answer : option d"
Answer: d
Question (general): abhinav and bhupathi together have rs . 1210 . if 4 / 15 of abhinav ' s amount is equal to 2 / 5 of bhupathi ' s amount , how much amount does bhupathi have ?
Options: a ) rs 460 , b ) rs 484 , c ) rs 550 , d ) rs 664 , e ) none of these
Rationale: explanation : let a = abhinav , b = bhupathi . 4 / 15 a = 2 / 5 b = > a = ( 2 / 515 / 4 ) b = > a = 3 / 2 b = > a / b = 3 / 2 = > a : b = 3 : 2 b ' s share = rs . ( 12102 / 5 ) = rs . 484 . answer : b
Answer: b
Question (gain): difference of two numbers is 1620 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2430 , 4050 , e ) 4660 , 3000
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1620 5 * y / 3 – y = 1620 2 * y / 3 = 1620 y = [ ( 1620 * 3 ) / 2 ] = 2430 . one number = 2430 , second number = 5 * y / 3 = 4050 . answer d ."
Answer: d
Question (gain): a shirt goes on sale for 60 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 60 then it is marked down by 10 % = 60 - 6 = 52 . hence it is 52 % od the original price . hence answer is c ."
Answer: c
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively the ratio of their speeds is
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none
Rationale: "solution let us name the trains as a and b . = ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 16 : √ 9 = 4 : 3 answer b"
Answer: b
Question (geometry): 61 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 128 , c ) 152 , d ) 155 , e ) 256
Rationale: "61 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 61 = 155 hence , d is the answer ."
Answer: d
Question (physics): pipe a can fill a tank in 5 hr , pipe b in 10 hr and pipe c in 30 hr . if all the pipes are open in how many hours will tank be filled ?
Options: a ) 1 hr , b ) 2 hr , c ) 3 hr , d ) 4 hr , e ) 5 hr
Rationale: "part filled by ( a + b + c ) in 1 hour = 1 / 5 + 1 / 10 + 1 / 30 = 1 / 3 all the 3 pipes together will fill the tank in 3 hours answer is c"
Answer: c
Question (physics): a pipe takes a hours to fill the tank . but because of a leakage it took 5 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 75 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 300 x = 75 min answer : e"
Answer: e
Question (general): the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.7 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.7 - 19 x 15 ) kg = 9 kg . correct option : e"
Answer: e