Cheukting/mathqa huggingface dataset:
Question (gain): a started a business with an investment of rs . 10000 and after 7 months b joined him investing rs . 12000 . if the profit at the end of a year is rs . 24000 , then the share of b is ?
Options: a ) 10000 , b ) 8000 , c ) 12000 , d ) 6000 , e ) 14000
Rationale: "ratio of investments of a and b is ( 10000 * 12 ) : ( 12000 * 5 ) = 2 : 1 total profit = rs . 24000 share of b = 1 / 3 ( 24000 ) = rs . 8000 answer : b"
Answer: b
Question (gain): in a certain pond , 30 fish were caught , tagged , and returned to the pond . a few days later , 30 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 750 , c ) 1250 , d ) 2500 , e ) 10 000
Rationale: "if x is total number of fish in the pond : 4 = 30 / x * 100 = > x = 750 so answer is b"
Answer: b
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 9 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 289 m , d ) 799 m , e ) 1000 m
Rationale: speed = 300 / 9 = 100 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 100 / 3 = > x = 1000 m . answer : e
Answer: e
Question (general): the largest 4 digit number exactly divisible by 88 is :
Options: a ) 9944 , b ) 9955 , c ) 9966 , d ) 6677 , e ) 9958
Rationale: "largest 4 - digit number = 9999 88 ) 9999 ( 113 88 - - - - 119 88 - - - - 319 264 - - - 55 - - - required number = ( 9999 - 55 ) = 9944 . answer : a"
Answer: a
Question (gain): a and b ’ s salaries together amount to rs . 4,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) 2777 , b ) 1500 , c ) 3000 , d ) 2776 , e ) 2881
Rationale: ( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 4000 4 b = 4000 = > b = 1000 a = 3000 answer c
Answer: c
Question (general): the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 324 different signs . if the company used 322 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 324 signs ?
Options: a ) 246 , b ) 248 , c ) 1292 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 324 different signs = 324 * 324 . # of 2 - letter codes possible from 322 different signs = 322 * 322 . the difference = 324 ^ 2 - 322 ^ 2 = ( 324 - 322 ) ( 324 + 322 ) = 1292 . answer : c ."
Answer: c
Question (general): the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 3.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 3.50 + 0.50 ( x − 2 ) = 3.50 + . 5 * 3 = 3.5 + 1.5 = 5 $ answer e
Answer: e
Question (physics): a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 4 t seconds , then what is the length of the platform ?
Options: a ) 0.5 l , b ) l , c ) 1.5 l , d ) 2 l , e ) 3 l
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 4 t ( l + p ) / ( l / t ) = 4 t p = 3 l the answer is e ."
Answer: e
Question (geometry): a 45 ° - 45 ° - 90 ° right triangle has hypotenuse of length h . what is the area of the triangle e in terms of h ?
Options: a ) h / √ 2
b ) h / 2
c ) h / 4
d ) ( h ) ^ 2
e ) ( h ) ^ 2 / 4
Rationale: if . . . each of the two shorter sides = 3 , then the hypotenuse = h = 3 ( root 2 ) . the area e = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 3 ) ( 3 ) = 9 / 2 . so we ' re looking for an answer that = 9 / 2 when h = 3 ( root 2 ) . there ' s only one answer that matches . . . e
Answer: e
Question (geometry): the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 675 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "area = l * w = 3 w ^ 2 = 675 w ^ 2 = 225 w = 15 the answer is b ."
Answer: b
Question (general): in feb mrs bil ' s earnings were 70 percent of the bil family ' s total income . in june mrs bil earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs bil ' s earnings were approximately what percent of the bil family ' s total income ?
Options: a ) 72 , b ) 34 , c ) 78 , d ) 37 , e ) 27
Rationale: lets say the family income is 100 in may , bil earned 70 family income is 30 in june , bil earned 10 % more than may , so it is ( 70 + 10 * 70 / 100 = 77 ) family income is same 30 in june bil ' s income percent is 77 * 100 / 107 ~ 72 ans is a
Answer: a
Question (other): find the number of zeroes at the end of 50 !
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "calculate division by 5 and 25 50 / 5 = 10 50 / 25 = 2 total = 12 answer : c"
Answer: c
Question (probability): a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random form this box . the probability that at least one of these is defective is :
Options: a ) 8 / 19 , b ) 7 / 19 , c ) 10 / 19 , d ) 20 / 19 , e ) 22 / 19
Rationale: "p ( none is defective ) = 16 c 2 / 20 c 2 = 12 / 19 p ( at least one is defective ) = 1 - 12 / 19 = 7 / 19 answer b"
Answer: b
Question (physics): john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 2 , 3 , 4 , or 5 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 20 , e ) 7 / 20
Rationale: john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 4 * 2 / 5 = 2 / 20 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 4 * 1 / 5 = 1 / 20 p ( john runs farther ) = 2 / 20 + 1 / 20 = 3 / 20 the answer is d .
Answer: d
Question (gain): john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 40,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 50000 , b ) 55000 , c ) 60000 , d ) 70000 , e ) 80804
Rationale: a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 40,000 ( 1 + 0.04 / 4 ) ^ 4 - 40,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 40,000 ( 1.0201 + 1 ) = 80804 . hence answer is e .
Answer: e
Question (geometry): one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 14 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 10 and 7 , d ) 3 and 10 , e ) 8 and 5
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 14 cm 2 more than the first area . therefore a 1 + 14 = a 2 x ( x − 3 ) + 14 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 14 = x 2 + x − 2 x − 2 2 x = 16 x = 8 . so , the sides of the rectangle are 8 cm and ( 8 − 3 ) = 5 cm long . so answer is e ."
Answer: e
Question (general): if two positive numbers are in the ratio 1 / 10 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 42.8 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .
Rationale: "given ratio = 1 / 10 : 1 / 7 = 7 : 10 let first number be 7 x and the second number be 10 x . the second number is more than first number by 3 x . required percentage = 3 x / 7 x * 100 = 42.8 % . answer : b"
Answer: b
Question (general): if 7125 ¸ 1.25 = 5700 < the value of 712.5 ÷ 12.5 is :
Options: a ) 5.7 , b ) 57 , c ) 570 , d ) 0.57 , e ) 0.057
Rationale: given 7125 / 1.25 = 5700 712.5 / 12.5 = 71.25 / 1.25 = 7125 * 1 / 1.25 * 100 = 5700 / 100 = 57 answer : b
Answer: b
Question (other): how many of the positive factors of 33 are not factors of 45 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 33 - 1 , 3 , 11 , 33 , factors of 45 - 1 , 3 , 5 , 9 , 15 , 45 , comparing both , we have three factors of 33 which are not factors of 45 - 11 , 33 , the answer is c"
Answer: c
Question (gain): find the principle on a certain sum of money at 5 % per annum for 6 years if the amount being rs . 1120 ?
Options: a ) 862 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: 1120 = p [ 1 + ( 5 * 6 ) / 100 ] p = 862 answer : a
Answer: a
Question (other): a certain high school has 500 students . of these students , 40 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 40 y = 20 z = 10 so , we have 40 students taking music , 20 taking art and 10 taking both music and art . 30 student taking just music 10 student taking just art 10 student taking both music and art total = 50 students we ' re asked for the total number of students who are taking neither course . that is 500 - 50 = 450 . c
Answer: c
Question (general): when 1 / 10 percent of 7,000 is subtracted from 1 / 10 of 7,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 693 , e ) 500
Rationale: we can break this problem into two parts : 1 ) what is 1 / 10 percent of 7,000 ? 2 ) what is 1 / 10 of 7,000 ? to calculate 1 / 10 percent of 7,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 7,000 = 1 / 1,000 x 7,000 = 7 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 7,000 . to do this we simply multiply 1 / 10 by 7,000 . 1 / 10 x 7,000 = 700 the answer to part 1 is 7 , and the answer to part 2 is 700 . their difference is 700 – 7 = 693 . answer d .
Answer: d
Question (gain): what sum of money will produce rs . 210 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) rs . 2500 , b ) rs . 1500 , c ) rs . 1400 , d ) rs . 1600 , e ) rs . 1300
Rationale: 210 = ( p * 4 * 7 / 2 ) / 100 p = 1500 answer : b
Answer: b
Question (physics): while driving from a - ville to b - town , harriet drove at a constant speed of 90 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 160 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 192
Rationale: 5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . d . t = 162 min * leg a - b - - - > d = 90.192 / 60 = 17280 / 60 * leg b - a - - - - > d = 160 * 108 / 60 = 17280 / 60 so the correct ans . ise
Answer: e
Question (general): the milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5625 , e ) 6000
Rationale: 6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 64 * 25 * 1 / 2 = 800 feet ^ 3 of milk must be removed , which equals to 800 * 7.5 = 6000 gallons . answer : e .
Answer: e
Question (gain): a computer store offers employees a 20 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1000 dollars and marked up the price 20 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 20 % off retail price ) as opposed to the final retail price .
Options: a ) $ 1,000 , b ) $ 960 , c ) $ 240 , d ) $ 200 , e ) $ 150
Rationale: "cost price = 1000 profit = 20 % = 20 % of 1000 = 200 selling price = cp + profit sp = 1200 a discount of 20 % to employees means 20 % off on 1200 so 20 % of 1200 = 240 so a employee thinks he saved 240 . . answer : c"
Answer: c
Question (gain): i sold a book at a profit of 10 % . had i sold it for $ 90 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 1800 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 90 5 % of cost = $ 90 cost = 90 * 100 / 5 = $ 1800 answer is a"
Answer: a
Question (gain): reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 972 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 972 12 r 2 = 972 r 2 = 81 r = 9 . answer : e"
Answer: e
Question (general): 7 , 10 , 8 , 11 , 9 , 12 , ___
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "10 = 7 + 3 8 = 10 - 2 11 = 8 + 3 9 = 11 - 2 12 = 9 + 3 similarly 12 - 2 = 10 answer : a"
Answer: a
Question (gain): how much more would rs . 20000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) a ) rs . 6 , 602.50 , b ) b ) rs . 6 , 601.50 , c ) c ) rs . 6 , 603.50 , d ) d ) rs . 6 , 604.50 , e ) e ) rs . 6 , 605.50
Rationale: "20000 ( 11 / 10 ) 4 - 20000 ( 6 / 5 ) 2 = 6 , 602.50 answer : a"
Answer: a
Question (gain): how much interest will $ 10,000 earn in 9 months at an annual rate of 10 % ?
Options: a ) $ 250 , b ) $ 350 , c ) $ 450 , d ) $ 60 , e ) $ 650
Rationale: "soln : - 9 months = 3 / 4 of year ; 10 % = 10 / 100 = 1 / 10 ; $ 10,000 ( principal ) * 3 / 50 ( interest rate ) * 1 / 10 ( time ) = $ 60 . answer : d"
Answer: d
Question (general): a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 320,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,333 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "making the numbers a little easy looking : monthly payment = 320,000 * ( 80 / 100 * 4 / 100 + 20 / 100 * 9 / 100 ) / 12 = 3200 / 12 * ( 3.2 + 1.8 ) = 16000 / 12 = 1333 answer : a"
Answer: a
Question (other): a dog takes 5 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 4 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 5 : 8 , b ) 5 : 3 , c ) 5 : 2 , d ) 5 : 9 , e ) 2 : 5
Rationale: "explanation : dog : hare = ( 5 * 4 ) leaps of hare : 8 leaps of hare = 20 : 8 - - > 10 : 4 - - > 5 : 2 answer : c"
Answer: c
Question (gain): by selling 200 apples , a fruit - seller gains the selling price of 50 apples . find the gain percent ?
Options: a ) 33.33 % , b ) 35 % , c ) 27.75 % , d ) 35.75 % , e ) 32.25 %
Rationale: sp = cp + g 200 sp = 200 cp + 50 sp 150 sp = 200 cp 150 - - - 50 cp 100 - - - ? = > 33.33 % answer : a
Answer: a
Question (physics): a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 8 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 8 days = 8 * ( 1 / 24 + 1 / 30 ) = 3 / 5 remaining work = 2 / 5 the number of days required for this initial work = 4 days . the total number of days required = 8 + 4 = 12 days . answer : a"
Answer: a
Question (general): a man whose bowling average is 12.4 , takes 4 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Rationale: "12.4 * x + 26 = ( 4 + x ) 12 solve equation x = 55 answer : c"
Answer: c
Question (physics): an engine moves at the speed of 60 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 48 kmph . what will be the speed of train when 25 coaches are attached .
Options: a ) 35 , b ) 28 , c ) 40 , d ) 44 , e ) 42
Rationale: 1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 60 - 20 = 40 c
Answer: c
Question (gain): a survey was sent to 80 customers , 12 of whom responded . then the survey was redesigned and sent to another 63 customers , 10 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "rate of first survey = 12 / 80 rate of second survey = 10 / 63 % response rate increase ( 10 / 63 - 12 / 80 ) / ( 12 / 80 ) = 5 % answer is b = 5 %"
Answer: b
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 , b ) 288 , c ) 120 , d ) 776 , e ) 180
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 9 = 180 m . answer : e"
Answer: e
Question (general): in a mixture of 60 litres the ratio of milk to water is 5 : 1 . additional 20 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 1 : 4 , d ) 3 : 2 , e ) 3 : 1
Rationale: "given that milk / water = 5 x / x and 5 x + x = 60 - - > x = 10 . thus milk = 5 x = 50 liters and water = x = 10 liters . new ratio = 50 / ( 20 + 10 ) = 50 / 30 = 5 / 3 . answer is b"
Answer: b
Question (physics): a train traveling at 72 kmph crosses a platform in 34 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 320 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 34 = 680 m . so , length of platform = 680 - 360 = 320 m imo , answer b"
Answer: b
Question (geometry): square abcd is the base of the cube while square efgh is the cube ' s top face such that point e is above point a , point f is above point b etc . what is the distance between the midpoint of edge ab and the midpoint of edge eh if the area of square abcd is 2 ?
Options: a ) 1 / sqrt 2
b ) 1
c ) sqrt 2
d ) sqrt 3
e ) 2 sqrt 3
Rationale: distance from mid point of ab to ad = sqrt [ ( 1 / sqrt 2 ) ^ 2 + ( 1 / sqrt 2 ) ^ 2 ] = 1 the distance between the midpoint of edge ab and the midpoint of edge eh = sqrt [ 1 ^ 2 + ( sqrt 2 ) ^ 2 ] = sqrt 3 . answer : d
Answer: d
Question (general): in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is :
Options: a ) 12 , b ) 11 , c ) 10 , d ) 27 , e ) 22
Rationale: explanation : total employees = \ inline \ frac { ( 25 - 10 ) \ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c ) 10
Answer: c
Question (general): you have been given a physical balance and 7 weights of 52 , 50 , 48 , 44 , 45 , 46 and 78 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 183 kgs .
Options: a ) 180 , b ) 181 , c ) 182 , d ) 178 , e ) 168
Rationale: "add the max weights 52 + 50 + 78 = 180 answer : a"
Answer: a
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 34 kmph . of how many minutes does the train stop per hour ?
Options: a ) e 982 , b ) 27 , c ) 12 , d ) 14.6 , e ) 28
Rationale: "explanation : t = 11 / 45 * 60 = 14.6 answer : option d"
Answer: d
Question (gain): a , b and c start a business each investing 20,000 . after 5 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 69,900 was recorded . find the share of b
Options: a ) 20,000 , b ) 21,000 , c ) 28,200 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7 = 205000 : 212000 : 282000 = 205 : 212 : 282 . b ’ s share = ( 69900 × 212 ⁄ 699 ) = 21200 ; answer c"
Answer: c
Question (physics): 5 men or 8 women do equal amount of work in a day . a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days .
Options: a ) 10 , b ) 7 , c ) 6 , d ) 12 , e ) 13
Rationale: 1 man can do the work of 8 / 5 = 1.6 women equivalent of 3 * 1.6 + 5 = 9.8 women take 10 days so women needed to do the work in 14 days = [ 10 / 14 ] * 9.8 = 7 answer : b
Answer: b
Question (physics): ajay can walk 10 km in 1 hour . in how many hours he can walk 50 km ?
Options: a ) 5 hrs , b ) 10 hrs , c ) 15 hrs , d ) 20 hrs , e ) 30 hrs
Rationale: 1 hour he walk 10 km he walk 50 km in = 50 / 10 * 1 = 5 hours answer is a
Answer: a
Question (physics): factory x ' s bulbs work for over 5000 hours in 75 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 65 % of cases . it is known that factory x supplies 70 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 76.4 % , b ) 78 % , c ) 77.4 % , d ) 72 % , e ) 73.9 %
Rationale: "for x , 70 % of 75 % will work . for y , 30 % of 65 % will work . * 30 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.70 ( 0.75 ) = . 525 0.30 ( 0.65 ) = 0.195 the combined probability then is 52.5 + 19.5 = 72 % ans d"
Answer: d