Cheukting/mathqa huggingface dataset:
Question (gain): one fourth of a solution that was 15 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 16 % , e ) 8.5 %
Rationale: "instead of using complex calculations and remembering formulae , why dont u directly get to weighted average . 3 parts of 15 % + 1 part of x ( unknown ) % = 4 parts of 16 % = > x % = 64 % - 45 % = 16 % ans d it is ."
Answer: d
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 1600 ?
Options: a ) 3000 , b ) 4200 , c ) 2025 , d ) 1205 , e ) 3251
Rationale: "1800 * 9 / 8 * 9 / 8 = 2025 answer : c"
Answer: c
Question (general): how many unique positive odd integers less than 110 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 6 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 110 are odd multiples of 5 so we have 5 , 15,25 , 35,45 , . . and 105 = 11 ans c"
Answer: c
Question (geometry): if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 186 m , what is its area ?
Options: a ) 2510 , b ) 2535 , c ) 2530 , d ) 2030 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 186 m ⇒ breadth = 35 m length = 35 + 23 = 58 m area = 58 × 35 = 2030 m 2 answer is d ."
Answer: d
Question (general): every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 72 , how many more green disks than blue disks are in the bag ?
Options: a ) 20 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 72 - - > x = 4 . g - b = 8 x - 3 x = 5 x = 20 . the answer is a ."
Answer: a
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 40.5 meters . how many times did the ball bounce ?
Options: a ) 3 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "division of total distance travelled will be 16 + 16 + 8 + 0.5 ans : a"
Answer: a
Question (probability): what is the probability of getting atmost one head when two unbiased coin are tossed ?
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 1 / 2 , e ) 2 / 6
Rationale: "here s = { hh , ht , th , tt } let ee = event of getting one head e = { tt , ht , th } p ( e ) = n ( e ) / n ( s ) = 3 / 4 option a"
Answer: a
Question (general): if 5 x + 3 = 10 x – 22 , what is the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: solve for x : 5 x + 3 = 10 x - 22 25 = 5 x 5 = x correct answer e ) 5
Answer: e
Question (general): a jogger running at 9 km / hr along side a railway track is 270 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 39 sec , d ) 87 sec , e ) 45 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 270 + 120 = 390 m . time taken = 390 / 10 = 39 sec . answer : c"
Answer: c
Question (physics): the speed of a boat in still water in 26 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 20 minutes is :
Options: a ) 10.4 km , b ) 10.66 km , c ) 11.4 km , d ) 11.22 km , e ) 12 km
Rationale: "explanation : speed downstream = ( 26 + 6 ) = 32 kmph time = 20 minutes = 20 / 60 hour = 1 / 3 hour distance travelled = time × speed = ( 1 / 3 ) × 32 = 10.66 km answer : option b"
Answer: b
Question (general): find the average of all the numbers between 6 and 39 which are divisible by 5 ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 23
Rationale: "average = ( 10 + 15 + 20 + 25 + 30 + 35 ) 6 = 135 / 6 = 23 answer is e"
Answer: e
Question (general): add : + 47 and - 27
Options: a ) - 30 , b ) + 30 , c ) 0 , d ) 27 , e ) 47
Rationale: the absolute values of + 47 and - 27 are 47 and 27 respectively ; and their difference = 47 – 27 = 30 . ( + 47 ) + ( - 27 ) = + 30 answer : b
Answer: b
Question (geometry): a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet . what is its area , in square feet ?
Options: a ) 76,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 400 , you can deduce the following a = 240 b = 320 240 x 320 = 76,800 a is the answer ."
Answer: a
Question (general): last year , for every 100 million vehicles that traveled on a certain highway , 40 vehicles were involved in accidents . if 2 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 800 , b ) 900 , c ) 100 , d ) 1000 , e ) 950
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 40 accidents as 2 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 2,000 million rather than 2 billion . creating a proportion we have : 100 / 40 = 2,000 / x cross multiplying gives us : 100 x = 2,000 * 40 x = 20 * 40 = 800 answer : a"
Answer: a
Question (general): find the value of ( √ 1.21 ) / ( √ 0.64 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 3.089 , e ) 185 / 63
Rationale: "( √ 1.21 ) / ( √ 0.64 ) + ( √ 1.44 ) / ( √ 0.49 ) 11 / 8 + 12 / 7 = > 3.089 answer is d"
Answer: d
Question (physics): a and b together can do a piece of work in 5 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
Rationale: "b = 1 / 5 – 1 / 20 = 0.15 days answer : e"
Answer: e
Question (physics): a boat moves upstream at the rate of 1 km in 25 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 2 kmph , c ) 3 kmph , d ) 1.3 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 25 * 60 ) = 2.4 kmph rate dowm stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 2.4 ) = 1.3 kmph answer : d"
Answer: d
Question (gain): the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 50 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 960 , d ) $ 870 , e ) $ 660
Rationale: "c $ 960 let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 150 % of $ 640 = 150 / 100 * 640 = $ 960 ."
Answer: c
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 56 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 58
Rationale: "amount earned by james = 40 * x + 16 * 2 x = 72 x therefore , amount earned by harry = 72 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 72 x ] ] so x * ( 1.5 y - 45 + 30 ) = 72 x or x * ( 1.5 y - 15 ) = 72 x so 1.5 y - 15 = 72 so 1.5 y = 87 so y = 58 answer is e"
Answer: e
Question (general): simplify : 100 x 100 - 50 x 50
Options: a ) 7612 , b ) 7614 , c ) 7500 , d ) 7615 , e ) none of them
Rationale: "( 100 ) ^ 2 - ( 50 ) ^ 2 = ( 100 + 50 ) ( 100 - 50 ) = 150 x 50 = 7500 . answer is c ."
Answer: c
Question (physics): a worker ' s daily wage is increased by 40 % and the new wage is $ 28 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 18 , b ) $ 20 , c ) $ 22 , d ) $ 24 , e ) $ 25
Rationale: "let x be the daily wage before the increase . 1.4 x = $ 28 x = $ 20 the answer is b ."
Answer: b
Question (physics): two pipes can fill a tank in 15 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 15 + 1 / 15 - 1 / 45 = 1 / 9 so , the tank becomes full in 9 minutes . answer : d"
Answer: d
Question (general): set r is composed of 9 numbers , labeled r 1 through r 9 . set s is also composed of 9 numbers , labeled s 1 through s 9 . set s is defined as follows : s 1 = 1 + r 1 ; s 2 = 2 + r 2 ; and so on , including s 9 = 9 + r 9 . how much larger is the sum of set s ' s mean and range than the sum of set r ' s mean and range ?
Options: a ) 8 , b ) can not be determined , c ) 4 , d ) 6 , e ) 9
Rationale: yes , the correct answer is b
Answer: b
Question (general): the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 60 * 5 = 300 lowest is 45 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 45 = 180 . on the fifth day it is 300 - 180 = 120 range is therefore 120 - 45 = 75 answer e"
Answer: e
Question (other): at a certain organisation , the number of male members went up by 12 % in the year 2001 from year 2000 , and the number of females members went down by 5 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 7
Rationale: "men increase by 12 % = = > 1.12 m = males in 2001 women decrease by 5 % = = > 0.95 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.12 m + 0.95 f = 1.012 * ( m + f ) 1.12 m + 0.95 f = 1.012 m + 1.012 f 1.12 m - 1.012 m = 1.012 f - 0.95 f 0.108 m = 0.062 f m / f = ( 0.062 ) / ( 0.108 ) = 62 / 108 = 4 / 7 answer = ( e )"
Answer: e
Question (general): if the average of 9 digits is 18 and the average of 4 of them is 8 , calculate the average of the remaining 5 numbers ?
Options: a ) 21 , b ) 26 , c ) 27 , d ) 22 , e ) 29
Rationale: explanation : total of the 9 digits - 9 * 18 = 162 total of the 4 digits - 4 * 8 = 32 total of the remaining 5 digits - 162 - 32 = 130 average of the remaining 3 numbers = 130 / 5 = 26 answer : b
Answer: b
Question (general): the units digit of ( 35 ) ^ ( 87 ) + ( 3 ) ^ ( 45 ) is :
Options: a ) 2 , b ) 8 , c ) 6 , d ) 9 , e ) 0
Rationale: "any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . 2 nd part 3 ^ 45 has a units digit of 3 therefore , the second term has a units digit of 3 . of course 5 + 3 = 8 , so something with a units digit of 5 plus something with a units digit of 3 answer = b"
Answer: b
Question (other): in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 20 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 75 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 20 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 20 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 20 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 20 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 20 ) ( 1 ) 11 x = 7 x + 20 4 x = 20 x = 5 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 5 ) = 75 final answer : a
Answer: a
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 60 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 59 , b ) 57 , c ) 59.5 , d ) 58 , e ) 55.5
Rationale: "d 75 * t = 1 km = > t = 1 / 60 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 60 + 2 / 3600 ) = 1 = > v = 58 km / h"
Answer: d
Question (general): the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 17 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 17 a – d = 3 a + d = 17 2 d = 14 d = 7 anser e"
Answer: e
Question (general): mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24624 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 2052 , d ) 4845.6 , e ) none of these
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 24624 ⁄ 12 = 2052 answer c"
Answer: c
Question (physics): a train 210 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 18 sec , e ) 12 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 210 * 2 / 35 = 18 sec answer : d"
Answer: d
Question (general): drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 2 / 5 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 4 / 5 , b ) 8 / 15 , c ) 11 / 15 , d ) 9 / 20 , e ) 13 / 20
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 2 / 5 ) y = ( 13 / 20 ) y the answer is e ."
Answer: e
Question (physics): joe drives 180 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 50 , c ) 50 , d ) 54 , e ) 56
Rationale: "t 1 = 180 / 60 = 3 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 6 hours avg speed = total distance / t = 300 / 6 = 50 mph = b"
Answer: b
Question (general): at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 140 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 140 male associates implies 70 female associates which means the remaining 20 females must be managers b . 20"
Answer: b
Question (physics): a train travels 250 km in 2 hours and 350 km in 4 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 70 kmph , d ) 100 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 250 + 350 = 600 km thus , total speed = 6 hrs or , average speed = 600 / 6 or , 100 kmph . answer : d"
Answer: d
Question (geometry): the difference of the areas of two squares drawn on two line segments in 32 sq . cm . find the length of the greater line segment if one is longer than the other by 2 cm
Options: a ) 9 cm
b ) 8 cm
c ) 7 cm
d ) 6 cm
e ) 5 cm
Rationale: explanation : let the lengths of the line segments be x and x + 2 cm then , ( x + 2 ) 2 − x 2 = 32 x 2 + 4 x + 4 − x 2 = 324 x = 28 x = 7 cm option c
Answer: c
Question (gain): if the cost price of 24 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 50 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 24 articles = rs . 24 . selling price of 16 articles = rs . 24 therefore , selling price of 24 articles is : - = > 24 / 16 ã — 24 = > 36 . therefore , profit = selling price - cost price . = > 36 â ˆ ’ 24 = 12 . hence , the percentage of profit = profit x 100 / c . p . = > 12 / 24 ã — 100 . = > 50 % profit . answer : b"
Answer: b
Question (physics): x and y can do a piece of work in 20 days and 12 days respectively . x started the work alone and then after 4 days y joined him till the completion of the work . how long did the work last ?
Options: a ) 6 days , b ) 10 days , c ) 15 days , d ) 16 days , e ) 20 days
Rationale: work done by x in 4 days = ( 1 / 20 ) * 4 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 . ( x + y ) ' s 1 day ' s work = 1 / 20 + 1 / 12 = 8 / 60 = 2 / 15 . now , 2 / 15 work is done by x and y in 1 day . so , 4 / 5 work will be done by x and y in ( 15 / 2 x 4 / 5 ) = 6 days . hence , total time taken = ( 6 + 4 ) days = 10 days . option b
Answer: b
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 144 ft , b ) 88 ft , c ) 22 ft , d ) 112 ft , e ) 146 t
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 10 x breadth = 680 breadth = 68 feet area to be fenced = 2 b + l = 2 ( 68 ) + 20 = 146 feet answer : e ) 146 ft"
Answer: e
Question (other): a study group consists of 4 english majors , 6 biological sciences majors , and 5 engineers . in how many ways can 3 english majors , 3 biological science majors and 3 engineers selected from the given group ?
Options: a ) 987 ways , b ) 346 ways , c ) 600 ways , d ) 200 ways , e ) 134 ways
Rationale: the number of ways of selecting three english majors , two biological science majors and three engineers is : = ⁴ c ₃ * ⁶ c ₂ * ⁵ c ₃ = ( 4 * 3 * 2 ) / ( 3 * 2 * 1 ) * ( 6 * 5 ) / ( 3 * 2 * 1 ) * ( 5 * 4 * 3 ) / ( 3 * 2 * 1 ) = 4 * 5 * 10 = 200 ways . answer : d
Answer: d
Question (physics): a man swims downstream 35 km and upstream 20 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 6.5 , b ) 5.5 , c ) 5.2 , d ) 4.6 , e ) 9.7
Rationale: "35 - - - 5 ds = 7 ? - - - - 1 20 - - - - 5 us = 4 ? - - - - 1 m = ? m = ( 7 + 4 ) / 2 = 5.5 answer : b"
Answer: b
Question (other): in the third grade of windblown school there are 90 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 90 failed in math = 90 / 3 = 30 failed in literature = 90 / 6 = 15 the least failed in both can be 0 while max can be 15 answer a"
Answer: a
Question (general): a volunteer organization is recruiting new members . in the fall they manage to increase their number by 9 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.25 % , c ) 14.14 % , d ) 13.33 % , e ) 11.71 %
Rationale: "( 100 % + 9 % ) * ( 100 % - 19 % ) = 1.09 * . 81 = 0.8829 . 1 - 0.8829 = 11.71 % lost = - 11.71 % the answer is e the organization has lost 11.71 % of its total volunteers from fall to spring ."
Answer: e
Question (general): a theater box office sold an average ( arithmetic mean ) of 64 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 76 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 15 : 19 , e ) 64 : 76
Rationale: "deviation from the mean for the daytime staff = 76 - 64 = 12 . deviation from the mean for the evening staff = 64 - 60 = 4 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 4 : 12 = 1 : 3 . the answer is c ."
Answer: c
Question (general): for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.988 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 54 , e ) can not be determined
Rationale: "it can not be determined . as we do not know the actual value of k . however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer k = [ lcm of 80 and 45 ] * ( any integer ) for value of k ( 60 ) * any integer unit value will be always zero . a"
Answer: a
Question (physics): in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is ?
Options: a ) 12 , b ) 27 , c ) 24 , d ) 29 , e ) 11
Rationale: "each row contains 12 plants . there are 11 gapes between the two corner trees ( 11 x 2 ) metres and 1 metre on each side is left . therefore length = ( 22 + 2 ) m = 24 m . answer : c"
Answer: c
Question (general): 5 n + 2 > 12 and 7 n - 5 < 30 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 5 , e ) 2 and 9
Rationale: "5 n > 10 - - > n > 2 7 n < 35 - - > n < 5 2 < n < 5 answer : d"
Answer: d
Question (physics): how long does a train 110 m long traveling at 36 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 28 , b ) 16.0 , c ) 16.4 , d ) 16.8 , e ) 16.1
Rationale: "d = 110 + 170 = 280 m s = 36 * 5 / 18 = 10 t = 280 * 1 / 10 = 28 sec answer : a"
Answer: a
Question (general): how many positive integer solutions does the equation 2 x + 5 y = 100 have ?
Options: a ) 50 , b ) 33 , c ) 16 , d ) 35 , e ) 10
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 5 ) = 10 answer : e"
Answer: e
Question (general): in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 34 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 66.90 % , c ) 68.57 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 34 % of 1100 ) + ( 32 % of 900 ) = 374 + 288 = 662 failed = 2000 - 662 = 1338 failed % = [ ( 1338 / 2000 ) x 100 ] % = 66.9 % . answer : b"
Answer: b
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 88 feet , b ) 86 feet , c ) 84 feet , d ) 82 feet , e ) 83 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 680 = > breadth = 34 feet area to be fenced = 2 b + l = 2 * 34 + 20 = 88 feet answer : option a"
Answer: a