Cheukting/mathqa huggingface dataset:
Question (gain): a fruit seller sells mangoes at the rate of rs . 12 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 15 % ?
Options: a ) rs . 11.81 , b ) rs . 12 , c ) rs . 15.33 , d ) rs . 12.31 , e ) none
Rationale: "solution 90 : 12 = 115 : x x = ( 12 ã — 115 / 90 ) = rs . 15.33 hence , s . p per kg = rs . 15.33 answer c"
Answer: c
Question (general): working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 20 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 10 / 1 , e ) 11 / 4
Rationale: "p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 20 + 1 / 20 = 1 / 10 therefore they take 10 ratio = 10 / 1 = d"
Answer: d
Question (physics): two numbers have a h . c . f of 20 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 128 , e ) 180
Rationale: l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 20 = 128 . answer : d
Answer: d
Question (geometry): a cylindrical bucket of height 36 cm and radius 21 cm is filled with sand . the bucket is emptied on the ground and a conical heap of sand is formed , the height of the heap being 12 cm . the radius of the heap at the base is :
Options: a ) 63 cm
b ) 53 cm
c ) 56 cm
d ) 66 cm
e ) none of these
Rationale: volume of the bucket = volume of the sand emptied volume of sand = π ( 21 ) 2 × 36 let r be the radius of the conical heap . then , 1 ⁄ 3 π r 2 × 12 = π ( 21 ) 2 × 36 or r 2 = ( 21 ) 2 × 9 or r = 21 × 3 = 63 answer a
Answer: a
Question (general): a man opens a shop . he buys water bottles for 50 cents each , fruit for 25 cents each , and snacks for a dollar each . he wants to start a bundle of selling a bottle a water , 3 snacks and 2 fruits for d dollars . every 5 th bundle sold will be sold for 2 dollars and a complimentary snack at the owner ' s expense . what should he charge at least to not lose any money ?
Options: a ) 4.6 , b ) 3.0 , c ) 4.1 , d ) 3.2 , e ) 2.9
Rationale: w = 0.50 f = 0.25 s = 1.00 b = w + 2 f + 3 s = 4.00 they pay , he pays 4 , net loss 0 fifth bundle = 2 they pay , he pays 5 , net loss 3 dollars 3 / 5 = 60 cents . charging 60 more cents on each bundle will be safe . answer : a
Answer: a
Question (gain): there is 60 % increase in an amount in 6 years at simple interest . what will be the compound interest of $ 12,000 after 3 years at the same rate ?
Options: a ) $ 2160 , b ) # 3120 , c ) $ 3972 , d ) $ 6240 , e ) none of these
Rationale: "let p = $ 100 . then , s . i . $ . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = $ 12000 . t = 3 years and r = 10 % p . a . c . i . = $ 12000 x 1 + 10 3 - 1 100 = $ 12000 x 331 1000 = 3972 answewr : c 3972"
Answer: c
Question (physics): a person is traveling at 75 km / hr and reached his destiny in 4 hr then find the distance ?
Options: a ) 300 km , b ) 200 km , c ) 250 km , d ) 400 km , e ) 220 km
Rationale: "t = 4 hrs d = t * s = 75 * 4 = 300 km answer is a"
Answer: a
Question (physics): a can do a piece of work in 80 days . he works at it for 10 days & then b alone finishes the remaining work in 42 days . in how much time will a and b , working together , finish the work ?
Options: a ) 30 days , b ) 20 days , c ) 25 days , d ) 35 days , e ) 45 days
Rationale: "work done by a in 10 days = 10 / 80 = 1 / 8 remaining work = ( 1 - ( 1 / 8 ) ) = 7 / 8 now , work will be done by b in 42 days . whole work will be done by b in ( 42 x 8 / 7 ) = 48 days therefore , a ’ s one day ’ s work = 1 / 80 b ’ s one day ’ s work = 1 / 48 ( a + b ) ’ s one day ’ s work = 1 / 80 + 1 / 48 = 8 / 240 = 1 / 30 hence , both will finish the work in 30 days . answer : a"
Answer: a
Question (general): a box contains 11 apples , 10 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: p ( choosing a red apple 6 times in a row ) = 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 11 < 0.5 the answer is d .
Answer: d
Question (physics): bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 11 minutes 20 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: "bob ' s time = 680 secs . his sis ' time = 576 secs . percent increase needed = ( 680 - 576 / 680 ) * 100 = 104 / 640 * 100 = 15 % . ans ( e ) ."
Answer: e
Question (general): if the price of a certain computer increased 30 percent from x dollars to 351 dollars , then 2 x =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = x after 30 % price increase price = x + ( 30 / 100 ) * x = 1.3 x = 351 ( given ) i . e . x = 351 / 1.3 = $ 270 i . e . 2 x = 2 * 270 = 540 answer : option a"
Answer: a
Question (general): in the mundane goblet competition , 6 teams compete in a “ round robin ” format : that is , each team plays every other team exactly once . a team gets 3 points for a win , 1 point for a tie ( a draw ) , and 0 points for a loss . what is the difference between the maximum total points and the minimum total points that can be gained by all teams ( added together ) in the mundane goblet competition ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 75
Rationale: no oa yet : my method : max points : a b c d e f 15 12 9 6 3 0 = 45 points min points a b c d e f 5 5 5 5 5 5 = 30 45 - 30 = 15 points = = = = > ( a ) ans
Answer: a
Question (general): how many integers between 324,805 and 458,705 have tens digit 2 and units digit 3 ?
Options: a ) 1,352 , b ) 1,359 , c ) 1,329 , d ) 1,349 , e ) 1,348
Rationale: "there is one number in hundred with 2 in the tens digit and 3 in the units digit : 23 , 123 , 223 , 323 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 134,900 - one number per each hundred gives 133,900 / 100 = 1,349 numbers . answer : d ."
Answer: d
Question (physics): a can do a job in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 8 / 15 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 4 days work = 7 / 60 * 4 = 7 / 15 remaining work = 1 - 7 / 15 = 8 / 15 answer is b"
Answer: b
Question (general): diana is painting statues . she has 3 / 6 of a gallon of paint remaining . each statue requires 1 / 6 gallon of paint . how many statues can she paint ?
Options: a ) 3 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 3 / 6 ÷ 1 / 6 = 3 / 6 * 6 / 1 = 3 / 1 = 3 answer is a ."
Answer: a
Question (general): what is the units digit of ( 6 ! * 4 ! + 6 ! * 5 ! ) / 12 ?
Options: a ) 0 , b ) 3 , c ) 2 , d ) 1 , e ) 4
Rationale: "( 6 ! * 4 ! + 6 ! * 5 ! ) / 12 = 6 ! ( 4 ! + 5 ! ) / 12 = 720 ( 24 + 120 ) / 12 = ( 720 * 144 ) / 12 = 720 * 12 units digit of the above product will be equal to 0 answer a"
Answer: a
Question (physics): jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 5 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 9 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 180 , b ) 210 , c ) 240 , d ) 270 , e ) 300
Rationale: the relative speed of jack and christina is 5 + 3 = 8 feet per second . the distance between them is 240 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 8 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 9 * 30 = 270 feet . answer : d .
Answer: d
Question (general): a slot machine in a las vegas casino has an average profit of $ 600 for each 8 - hour shift for the 5 days sunday through thursday , inclusive . if the average per - shift profit on friday and saturday is 25 % greater than on the other days of the week and the slot machine is in operation every hour of every day , what is the total weekly profit that the casino makes from the slot machine ?
Options: a ) a - 4500 , b ) b - 9000 , c ) c - 13500 , d ) d - 15500 , e ) e - 27000
Rationale: correct answer is c - 13500 . total profit per weekday = $ 600 x 3 ( shifts ) = $ 1800 total profit per week ( apart from saturdaysunday ) = $ 1800 x 5 = $ 9000 total profit per shift on weekends = $ 600 x 125 / 100 = $ 750 total profit on weekends = $ 750 x 3 ( shifts ) x 2 ( saturday , sunday ) = $ 4500 . hence the answer is - $ 4500 + $ 9000 = $ 13500 . ( c )
Answer: c
Question (general): if the price of a certain bond on may 1 st was 3 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 118.5 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 3 / 4 * 12 = 9 ; the price on july 1 st = 9 * 1.25 = 11.25 . the average price of the bond on may 1 st and july 1 st = ( 9 + 11.25 ) / 2 = 10.125 . the price of the bond on june 1 st ( 12 ) is 32 / 27 times ( 118.5 % ) the average price of the bond on may 1 st and july 1 st . answer : c ."
Answer: c
Question (general): the average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 47.55 kg , b ) 48 kg , c ) 48.55 kg , d ) 49.25 kg , e ) 59.25 kg
Rationale: "16 * 50.25 + 8 * 45.15 / 24 = 48.55 answer : c"
Answer: c
Question (general): how much water should be added to 13 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 13 + x ) ) ) 2 = 5 % * ( 13 + x ) - - - - - - - - > x = 27 ans b"
Answer: b
Question (general): when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 40 .
Options: a ) 3 , b ) 4 , c ) 7 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 40 , remainder will be - 4 i . e . n will be 4 less than a multiple of 40 . so you must add 7 to n to make it a multiple of 40 c"
Answer: c
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.7 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 2 : 1 , e ) 4 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.7 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.7 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.9 = 4 / 9 required ratio = 4 / 9 : 1 = 4 : 9 . answer : e"
Answer: e
Question (general): what is the hcf of 2 / 3 , 4 / 10 and 6 / 5
Options: a ) 7 / 45 , b ) 1 / 15 , c ) 4 / 15 , d ) 8 / 45 , e ) 9 / 45
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 10 , 5 ) = 2 / 30 = 1 / 15 answer : option b"
Answer: b
Question (general): at veridux corporation , there are 215 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 135 male associates , how many female managers are there ?
Options: a ) 50 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 215 â € “ 90 = 125 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 215 â € “ 40 = 175 must be associates . now , in the â € œ associate â €  row , 135 + e = 175 , which means e = 40 â € ” the other 40 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 40 = 90 , which means b = 50 . there are fifteen female managers in this company . thus , the answer = 50 ( a ) ."
Answer: a
Question (general): a number when divided by a divisor leaves a remainder of 30 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 43 , e ) 59
Rationale: let the number is n , the divisor = d , i will make the two equations - n = xd + 30 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 43 as d is also integer and 43 is a prime number , the d should be 43 to satisfy the above equation . hence answer is ' d '
Answer: d
Question (general): a student got twice as many sums wrong as he got right . if he attempted 36 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 36 3 x = 36 x = 12 . answer : a"
Answer: a
Question (general): if 6 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 7 , b ) - 4 , c ) - 3 , d ) - 9 , e ) 6
Rationale: the phrase “ 6 is one solution of the equation ” means that one value of x is 6 . thus , we first must plug 6 for x into the given equation to determine the value of k . so we have 6 ^ 2 + ( 3 ) ( 6 ) + k = 10 36 + 18 + k = 10 54 + k = 10 k = - 44 next we plug - 44 into the given equation for k and then solve for x . x ^ 2 + 3 x – 44 = 10 x ^ 2 + 3 x – 54 = 0 ( x + 9 ) ( x - 6 ) = 0 x = - 9 or x = 6 thus , - 9 is the other solution . answer d .
Answer: d
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 8 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 120
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 8 * 180 / 12 = 120 ounces of water e"
Answer: e
Question (other): in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability q this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability of cgd / ( cg ) q - > 3 / 19 answer d"
Answer: d
Question (general): in the youth summer village there are 125 people , 50 of them are not working , 25 of them have families and 75 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 100 , e ) 90
Rationale: "total = 125 not working = 50 having family = 25 like to sing in shower = 75 working = 125 - 50 = 75 not having family = 125 - 25 = 100 like to sing in shower = 100 largest possible number is the lowest possible among the above thus 75 a"
Answer: a
Question (gain): solution y is 20 percent liquid x and 80 percent water . if 2 kilograms of water evaporate from 8 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 20 % , b ) 21 1 / 2 % , c ) 22 % , d ) 24 % , e ) 25 %
Rationale: "in 8 kilograms of solution y there are 0.2 * 8 = 1.6 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.2 * 2 = 0.4 kilograms of solution x are added , so in the new solution of 8 kilograms there are 1.6 + 0.4 = 2 kilograms of solution x , which is 2 / 8 * 100 = 25 % of this new solution . answer : e ."
Answer: e
Question (general): 20.036 divided by 0.04 gives :
Options: a ) 50.09 , b ) 5.06 , c ) 50.06 , d ) 100.9 , e ) 500.9
Rationale: "= 20.036 / 0.04 = 2003.6 / 4 = 500.9 answer is e ."
Answer: e
Question (other): the ratio between the sale price and the cost price of an article is 12 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 3 : 6 , d ) 5 : 7 , e ) 2 : 1
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 12 x . then , gain = rs . 5 x required ratio = 5 x : 7 x = 5 : 7 answer : d"
Answer: d
Question (general): a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6800 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6791 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6800 * 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 . answer : d"
Answer: d
Question (general): when 17 is divided by positive integer x , the remainder is 1 . for how many values of x is this true ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: when 17 is divided by x , the remainder is 1 i . e . 1 orange left over after grouping , so x must be greater than 1 . it also means that 16 is completely divisible by x . factors of 16 are 1 , 2 , 4 , 8 , 16 . out of these , x can be 2 , 4 , 8 , and 16 . answer ( d ) .
Answer: d
Question (physics): sakshi can do a piece of work in 12 days . tanya is 20 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "ratio of times taken by sakshi and tanys = 120 : 100 = 6 : 5 suppose tanya takes x days to do the work . 6 : 5 : : 12 : x = > x = 10 days . hence , tanya takes 10 days to complete the work . answer : a"
Answer: a
Question (physics): a river 4 m deep and 40 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 10666 , b ) 11678 , c ) 12345 , d ) 10678 , e ) 19099
Rationale: "( 4000 * 4 * 40 ) / 60 = 10666 m 3 answer : a"
Answer: a
Question (physics): in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) kmph = 8 kmph . answer c"
Answer: c
Question (general): what least number should be subtracted from 1398 so that the remainder when divided by 7 , 9 , and 11 will leave in each case the same remainder 5 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "the lcm of 7 , 9 , and 11 is 693 . the next multiple is 2 * 693 = 1386 . 1386 + { remainder } = 1386 + 5 = 1391 , which is 7 less than 1398 . answer : b ."
Answer: b
Question (geometry): if the sides of a triangle are 32 cm , 27 cm and 12 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 162 cm 2 , d ) 666 cm 2 , e ) 886 cm 2
Rationale: "the triangle with sides 32 cm , 27 cm and 12 cm is right angled , where the hypotenuse is 32 cm . area of the triangle = 1 / 2 * 27 * 12 = 162 cm 2 answer : c"
Answer: c
Question (general): 9.99 x 9.9 x 9 ÷ 9.9 ÷ 0.3 = ?
Options: a ) 276 , b ) 299 , c ) 310 , d ) 3.33 , e ) 365
Rationale: "explanation : ? = ( 9.99 x 9.9 x 9 ) / ( 9.9 x 0.9 x 0.3 ) = 3.33 answer : option d"
Answer: d
Question (general): a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1233 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 137 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1233 or 9 x = 1233 or x = 137 . required number = 137 . answer : d"
Answer: d
Question (probability): two letters from the word barkhint are selected at random . what is the probability that at least one of the selected letters is a consonant ?
Options: a ) 30 / 28 , b ) 40 / 28 , c ) 25 / 28 , d ) 27 / 28 , e ) 32 / 28
Rationale: there are 6 consonants and 2 vowels in barkhint . probability that at least one of the selected letters is a consonant = 1 - ( probability of both vowels ) probability of both vowels = 2 c 2 / 8 c 2 = 1 / 28 so , answer is 1 - 1 / 28 = 27 / 28 answer : d
Answer: d
Question (general): if ( a + b ) = 4 , ( b + c ) = 8 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 1 .
Rationale: "given a + b = 4 b + c = 8 c + d = 3 then ( a + b ) - ( b + c ) + ( c + d ) = 4 - 8 + 3 = - 1 option e . . ."
Answer: e