Cheukting/mathqa huggingface dataset:
Question (gain): the simple interest on a certain sum of money at the rate of 5 % p . a . for 8 years is rs . 840 . at what rate of interest the same amount of interest can be received on the same sum after 5 years ?
Options: a ) 6 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) none
Rationale: "solution s . i . = rs . 840 , r = 5 % , t = 8 years . principal = rs . ( 800 x 840 / 5 x 8 ) = rs . 2100 . now , p = rs . 2100 , s . i . = rs . 840 , t = 5 years . ∴ rate = ( 100 x 840 / 2100 x 5 ) = 8 % . answer b"
Answer: b
Question (gain): what is the rate percent when the simple interest on rs . 1200 amount to rs . 400 in 4 years ?
Options: a ) 8.33 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 1 %
Rationale: "interest for 4 yrs = 400 interest for 1 yr = 100 interest rate = 100 / 1200 x 100 = 8.33 % answer : a"
Answer: a
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is ?
Options: a ) 24 kg , b ) 62 kg , c ) 34 kg , d ) 31 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 * 3 ) = 135 - - - ( i ) a + b = ( 40 * 2 ) = 80 - - - ( ii ) b + c = ( 43 * 2 ) = 86 - - - ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 - - - ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 b ' s weight = 31 kg . answer : d"
Answer: d
Question (general): what is the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 83 ?
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): 400 students took a mock exam in delhi , 60 % of the boys and 80 % of the girls cleared the cut off in the examination . if the total percentage of students qualifying is 65 % , how many girls appeared in the examination ?
Options: a ) 50 , b ) 100 , c ) 120 , d ) 140 , e ) 180
Rationale: 60 % * x + 80 % * ( 400 - x ) = 65 % * 400 ans = 100 answer : b
Answer: b
Question (general): what is the greater of the two numbers whose product is 2688 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) a ) 84 , b ) b ) 104 , c ) c ) 110 , d ) d ) 72 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2688 / s = 84 . answer : a"
Answer: a
Question (general): the proportion of copper and zinc in the brass is 3 : 7 . how much zinc will there be in 100 kg of brass ?
Options: a ) 70 , b ) 50 , c ) 40 , d ) 270 , e ) 170
Rationale: "7 / 10 * 100 = 70 answer : a"
Answer: a
Question (physics): a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days q will the work get over ?
Options: a ) q = 60 , b ) q = 70 , c ) q = 75 , d ) 80 , e ) 100
Rationale: we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )
Answer: c
Question (general): find the value of c from ( 8 ) ^ 3 x 9 ^ 3 ã · 679 = c .
Options: a ) 249.7 , b ) 529.7 , c ) 549.7 , d ) 594.7 , e ) 119.7
Rationale: given exp . = ( 8 ) ^ 3 x 9 ^ 3 ã · 679 = c = 512 x 729 ã · 679 = 549.7 c
Answer: c
Question (gain): a man has $ 10,000 to invest . he invests $ 4000 at 5 % and $ 3500 at 4 % . in order to have a yearly income of $ 500 , he must invest the remainder at
Options: a ) 6 % , b ) 6.1 % , c ) 6.2 % , d ) 6.3 % , e ) 6.4 %
Rationale: income from $ 4000 at 5 % in one year = $ 4000 of 5 % . = $ 4000 × 5 / 100 . = $ 4000 × 0.05 . = $ 200 . income from $ 3500 at 4 % in one year = $ 3500 of 4 % . = $ 3500 × 4 / 100 . = $ 3500 × 0.04 . = $ 140 . total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340 . remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340 . = $ 160 . total invested amount = $ 4000 + $ 3500 = $ 7500 . remaining invest amount = $ 10000 - $ 7500 = $ 2500 . we know that , interest = principal × rate × time interest = $ 160 , principal = $ 2500 , rate = r [ we need to find the value of r ] , time = 1 year . 160 = 2500 × r × 1 . 160 = 2500 r 160 / 2500 = 2500 r / 2500 [ divide both sides by 2500 ] 0.064 = r r = 0.064 change it to a percent by moving the decimal to the right two places r = 6.4 % therefore , he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year . the answer is ( e )
Answer: e
Question (physics): a train speeds past a pole in 11 seconds and a platform 120 m long in 22 seconds . its length is ?
Options: a ) 128 , b ) 177 , c ) 199 , d ) 120 , e ) 150
Rationale: let the length of the train be x meters and its speed be y m / sec . they , x / y = 11 = > y = x / 11 x + 120 / 22 = x / 11 x = 120 m . answer : d
Answer: d
Question (general): a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 180 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 31 , b ) 33 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 180 = > . 1 x + 3 / 4 x = 180 = > x = 211 211 - 180 = pure gala = 31 . a"
Answer: a
Question (gain): the banker â € ™ s gain on a sum due 3 years hence at 12 % per annum is rs . 90 . the banker â € ™ s discount is
Options: a ) rs . 340 , b ) rs . 840 , c ) rs . 1020 , d ) rs . 760 , e ) none
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 90 x 100 / 12 x 3 ) = rs . 250 . b . d = rs ( 250 + 90 ) = rs . 340 . answer a"
Answer: a
Question (general): in the quadratic equation x 2 - bx + 20 = 0 , if the product of two roots is 20 , what is the sum of the two roots ?
Options: a ) 20 , b ) 12 , c ) 16 , d ) 14 , e ) 18
Rationale: explanation : the sum of the roots of the quadratic equation ax 2 + ax + c = 0 are ( - b / a ) and the product of the roots are ( c / a ) . thus , in the equation x 2 - ax + 20 = 0 , where a = 1 , b = - a and c = 20 . we get , product of the roots = 20 sum of the roots = - ( - 12 ) / 1 = 12 answer : b
Answer: b
Question (physics): a carpenter worked alone for 1 day on a job that would take him 7 more days to finish . he and another carpenter completed the job in 4 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 16 , b ) 7 , c ) 9 , d ) 14 , e ) 24
Rationale: "a carpenter worked only 1 day on something that takes him 7 more days . means ; carpenter finishes his work in 8 days . let his buddy finish the same task in x days . respective rates per day : 1 / 8 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 8 per day . second one worked for 4 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 8 + 4 * 1 / x = 1 5 x + 32 = 8 x 2 x = 32 x = 16 days . ans : a"
Answer: a
Question (gain): in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 55 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 29 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 55 % means total women in company 45 % ( assume total people in company 100 % ) no of men employees attended picnic = 55 x ( 20 / 100 ) = 11 no of women employees attend picnic = 45 x ( 40 / 100 ) = 18 total percentage of employees attend the picnic = 11 + 18 = 29 % answer : a"
Answer: a
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 7 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 3 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 7 or 45 * 18 - 45 * x + 36 * x = 7 * 100 or 9 x = - 7 * 100 + 45 * 18 x = 110 / 9 = 12.2 % e"
Answer: e
Question (other): how many of the positive factors of 42 are not factors of 56 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 42 - 1 , 2,3 , 6,7 , 14,42 factors of 56 - 1,2 , 4,7 , 8,14 , 28,56 comparing both , we have three factors of 42 which are not factors of 56 - 3 , 6,42 . the answer is 3 . pls check your options again - d $ e are same . answer : c"
Answer: c
Question (general): if taxi fares were $ 10.00 for the first 1 / 5 mile and $ 1.00 for each 1 / 5 mile there after , then the taxi fare for a 10 - mile ride was
Options: a ) $ 55.10 , b ) $ 59.20 , c ) $ 59.40 , d ) $ 59.00 , e ) $ 55.00
Rationale: "in 10 miles , initial 1 / 5 mile charge is $ 10 rest of the distance = 10 - ( 1 / 5 ) = 49 / 5 rest of the distance charge = 49 ( 1.00 ) = $ 49.00 ( as the charge is 1.00 for every 1 / 5 mile ) = > total charge for 4 miles = 10 + 49.00 = 59.00 answer is d"
Answer: d
Question (geometry): two cubes of tire sides ratio 2 : 3 . find its cube volumes ratio ?
Options: a ) 2 : 27
b ) 3 : 27
c ) 1 : 27
d ) 8 : 27
e ) 5 : 27
Rationale: a ( power 3 ) : b ( power 3 ) = 2 ( power 3 ) : 3 ( power 3 ) = 8 : 27 answer is d .
Answer: d
Question (gain): the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 7000 , brokerage being 1 / 4 % , is :
Options: a ) 96.97 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 7000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 7000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 97.22 . = market value of rs . 100 stock = rs . 97.22 - re . 0.25 . = market value of rs . 100 stock = rs . 96.97 answer : a"
Answer: a
Question (physics): a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3600 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 450 , c ) s . 600 , d ) s . 800 , e ) s . 850
Rationale: c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 3600 ) = rs . 450 answer = b
Answer: b
Question (gain): in town x , 60 percent of the population are employed , and 15 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 75 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "total employed people 60 % , out of which 15 are employed males , hence 45 % are employed females . ( employed females ) / ( total employed people ) = 45 / 60 = 3 / 4 = 75 % answer : b ."
Answer: b
Question (gain): according to a recent student poll , 5 / 6 out of 30 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 1 / 14 , b ) 4 / 49 , c ) 2 / 7 , d ) 28 / 29 , e ) 13 / 14
Rationale: 25 students are interested , 5 are not interested prob = 1 - 5 c 2 / 30 c 2 = 1 - ( 5 * 4 / ( 30 * 29 ) ) = 1 - 20 / 580 = 1 - 1 / 29 = 28 / 29 answer : d
Answer: d
Question (general): for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 80 ?
Options: a ) 24 , b ) 26 , c ) 20 , d ) 22 , e ) 18
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 80 4 n < 73 n < 18 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 18 ) combining the two - 1.5 < n < 18.25 n = 1 to 18 ( 18 integers ) and n = - 1 and 0 so 20 integers . c is the answer"
Answer: c
Question (physics): three cubes of metal whose edges are 5 , 12 and 15 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 28 , b ) 77 , c ) 17.3 , d ) 18 , e ) 99
Rationale: "53 + 123 + 153 = a 3 = > a = 17.3 answer : c"
Answer: c
Question (geometry): a rectangular pig farm has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 1250 square feet , what is the total length of the fence , in feet ?
Options: a ) 25
b ) 50
c ) 100
d ) 150
e ) 200
Rationale: two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 1250 ie x ^ 2 = 625 ie x = 25 l = 50 w = 25 total length of fence = 2 * 25 + 50 = 100 my answer is c
Answer: d
Question (other): the ratio of pens to pencils is 5 to 6 . there are 6 more pencils than pens . how many pencils are there ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 6 x = 6 the number of pencils is 36 . the answer is b ."
Answer: b
Question (physics): there is a clock which shows false timing ie it shows 10 minutes less for each 1 hour . . . . if the clock shows 12 noon now how many minutes will be lost when it shows 3 pm ?
Options: a ) 16 minutes , b ) 26 minutes , c ) 36 minutes , d ) 46 minutes , e ) 56 minutes
Rationale: for 1 hour , 10 minutes is slower , then for 06 miuntes - 1 minutes is slower 30 minutes - 5 minutes actual time false time 12 12 01 pm 12.50 pm ( 10 minutes slower ) 02 pm 01.40 pm ( 12.50 + 60 min - 10 minutes slower ) 03 pm 02.30 pm ( 01.40 + 60 min - 10 minutes slower ) 03.36 pm 03.00 pm ( 02.30 + 36 min - 6 minutes slower ) so , 36 minutes will be lost when it is showing 3.00 pm . and the actual time is 3.36 pm answer : c
Answer: c
Question (general): in a box of 7 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 2 / 3 , d ) 2 / 7 , e ) 1 / 7
Rationale: "first , there are 5 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 7 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 5 c 3 / 7 c 3 = 10 / 35 = 2 / 7 answer is d"
Answer: d
Question (general): the mean of 50 observations was 36 . it was found later that an observation 90 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 37.3 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 90 - 23 ) = 1867 . correct mean = 1825 / 50 = 37.3 answer : a"
Answer: a
Question (other): how many kilograms of pure water is to be added to 100 kilograms of a 30 % saline solution to make it a 10 % saline solution .
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: let x be the weights , in kilograms , of pure water to be added . let y be the weight , in kilograms , of the 10 % solution . hence x + 100 = y x = 200 kilograms . answer b
Answer: b
Question (general): there is a escalator and 2 persons move down it . a takes 50 steps and b takes 75 steps while the escalator is moving down . given that the time taken by a to take 1 step is equal to time taken by b to take 3 steps . find the no . of steps in the escalator while it is staionary ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: if a takes 1 step in one second , then b takes 3 steps in one second . if a takes t 1 seconds to take 50 steps , then b takes 150 steps in t 1 seconds . for b , to take 150 steps he requires t 1 seconds , then to take 75 steps he requires t 1 / 2 seconds . now use relative velocity l - v * t 1 = 50 ( for first person ) l - v * t 1 / 2 = 75 ( for second person ) s ( escalator w . r . t ground ) - s ( person w . r . t escalator ) = s 1 ( person w . r . t ground ) s , s , s 1 are the steps now put the v * t 1 from 1 into the second equation and u get l - ( l - 50 ) / 2 = 75 l + 50 = 150 l = 100 answer : e
Answer: e
Question (gain): at what price must an article costing rs . 57 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 69.5 , c ) 62.3 , d ) 62.1 , e ) 75
Rationale: "cp = 57 sp = 57 * ( 125 / 100 ) = 71.25 mp * ( 95 / 100 ) = 71.25 mp = 75 answer : e"
Answer: e
Question (general): if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.20 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 2.80
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.2 ) = $ 2.8 ( as the charge is 0.2 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 2.8 = 3.8 answer is c ."
Answer: c
Question (general): if 3 ^ x * 4 ^ y = 59,049 and x – y = 10 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 59,049 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 10 and y = 0 , then x = 10 . the answer is a ."
Answer: a
Question (physics): a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 18 seconds . what is the length of the train in meters ?
Options: a ) 180 meters , b ) 1111 meters , c ) 1777 meters , d ) 1822 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 18 seconds distance = speed * time 36000 * 18 / 3600 = 180 meters . a is the answer ."
Answer: a
Question (gain): from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 11 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 11 x = 45 - - > 10 / 9 * x = 45 - - > x = 45 * 9 / 10 = 1500 / 37 = ~ 41 . answer : d ."
Answer: d
Question (general): when you multiply a number by 4 and then subtract 3 , the result is the same as if you first subtracted 7 from the same number and then multiplied by 9 . what is the number ?
Options: a ) a ) 23 , b ) b ) 13 , c ) c ) 19 , d ) d ) 12 , e ) e ) 10
Rationale: let x equal the number and then change the words into an equation and solve for x : 4 x – 3 = 9 ( x – 7 ) 4 x – 3 = 9 x – 63 60 = 5 x 12 = x correct answer d ) 12
Answer: d
Question (gain): a man can row his boat with the stream at 25 km / h and against the stream in 13 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 2 kmph , c ) 6 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 25 us = 13 s = ? s = ( 25 - 13 ) / 2 = 6 kmph answer : c"
Answer: c
Question (other): an alloy of zinc and copper contains the metals in the ratio 5 : 3 . the quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is :
Options: a ) 2 , b ) 9 , c ) 8 , d ) 7 , e ) 4
Rationale: explanation : in sixteen kg of alloy 10 kg of zinc and 6 kg copper is present to make the ratio 3 : 1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper so answer is 8 . answer : c
Answer: c
Question (gain): what is the cp of rs 100 stock at 5 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 95.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 5 + 1 / 5 95.2 thus the cp is rs 95.2 . answer : c"
Answer: c
Question (physics): a monkey start climbing up a tree 21 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 18 hrs it wil be 18 ft . but since the height of the tree is 21 ft , so if the monkey hops up the tree in the next hr i . e 19 th hr then it reaches at the top of the tree . hence it takes 19 hrs for monkey to reach at the top answer : c"
Answer: c
Question (gain): john makes $ 50 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
Options: a ) 15 % , b ) 16.66 % , c ) 50 % , d ) 19 % , e ) 21 %
Rationale: "increase = ( 25 / 50 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c"
Answer: c
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 . 6400 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 22888
Rationale: "6400 * 9 / 8 * 9 / 8 = 8100 answer : a"
Answer: a
Question (general): oil cans x and y are right circular cylinders and the height and radius of y are each thrice those of x . if the oil in can x filled to capacity sells for $ 4 , how much does the oil in y sell for if y is only 1 / 3 rd filled ?
Options: a ) $ 30 , b ) $ 25 , c ) $ 36 , d ) $ 40 , e ) $ 28
Rationale: "formula for vol of a cyl is pi * r ^ 2 * h so vy = 27 * vy y when 1 / 3 rd filled will cost 9 times x so ans is c"
Answer: c
Question (gain): an alloy weighing 60 ounces is 20 percent copper . how many ounces of copper must be added to create an alloy that is 60 percent copper ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "an alloy of 60 oz which is 20 % copper means there is 12 oz of gold . to get to an alloy that is 60 % copper , let ' s use this expression : ( 12 + x ) / ( 60 + x ) = 0.60 with x representing the amount of pure copper that must be added to get to 60 % . the expression we are using represents the new total weight of pure copper over the new total weight of the alloy and this fraction should represent 60 % or 0.6 . you will see that 60 is the correct answer , as 72 / 120 = 0.6 choose c"
Answer: c
Question (gain): by selling 16 pens for a rupee a woman loses 5 % . how many for a rupee should he sell in order to gain 18 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 13 , e ) 65
Rationale: d 95 % - - - 16 118 % - - - ? 95 / 118 * 16 = 13
Answer: d