Cheukting/mathqa huggingface dataset:
Question (gain): a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 33 per litre so as to make a profit of 30 % on cost when he sells the resulting milk and water mixture for rs . 36 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 23 : 120 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.33 m = = > revenue = price x quantity = 0.36 ( m + w ) = = > profit = 0.36 ( m + w ) - 0.33 m = 0.3 * ( 0.33 m ) [ 30 % of cost ] = = > 0.36 m + 0.36 w - 0.33 m = 0.099 m = = > 0.069 m = 0.36 w = = > m / w = 0.36 / 0.069 = 120 / 23 - - or - - w / m = 23 / 120 b is correct ."
Answer: b
Question (general): carol is 5 times alice ’ s age but only twice as old as betty . alice is 12 years younger than carol . how old is betty ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 18 , e ) 24
Rationale: given that c = 5 a = 2 b . . and a = c - 12 = 5 a - 12 - - > 4 a = 12 - - > a = 3 substituting the values a = 3 , c = 15 and b = 6 . . ans a = 6 . .
Answer: a
Question (geometry): a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 5 cubic feet . if a large block has twice the width , twice the depth , and the same length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 15 , b ) 30 , c ) 20 , d ) 18 , e ) 25
Rationale: "volume of cube = lbh = 5 new cube l , b , h are increases of l , 2 b , 2 h new volume of cube = l * 2 b * 2 h = 4 * lbh = 4 * 5 = 20 answer : c"
Answer: c
Question (general): in a box of 10 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 7 / 12 , b ) 11 / 20 , c ) 17 / 30 , d ) 28 / 45 , e ) 51 / 90
Rationale: "# defective pens = 2 # good pens = 8 probability of the 1 st pen being good = 8 / 10 probability of the 2 nd pen being good = 7 / 9 total probability = 8 / 10 * 7 / 9 = 28 / 45 the answer is d ."
Answer: d
Question (general): if the sum of the 4 th term and the 12 th term of an arithmetic progression is 30 , what is the sum of the first 15 terms of the progression ?
Options: a ) 250 , b ) 275 , c ) 260 , d ) 225 , e ) 230
Rationale: 4 th term + 12 th term = 30 i . e . , ( a + 3 d ) + ( a + 11 d ) = 30 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 30 - - - - - - - - - - - - - - - from ( 1 ) = 225 answer : d
Answer: d
Question (general): if x and y are numbers such that ( x + 5 ) ( y - 5 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 4 , c ) 9 , d ) 25 , e ) 16
Rationale: "from ( x + 5 ) ( y - 5 ) = 0 it follows that either x = - 5 or y = 5 . thus either x ^ 2 = 25 or y ^ 2 = 25 . now , if x ^ 2 = 8125 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 25 + 0 = 25 . similarly if y ^ 2 = 25 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 25 = 25 . answer : d ."
Answer: d
Question (general): find the value of ( 19 + 43 / 151 ) × 151
Options: a ) 2924 , b ) 2916 , c ) 2614 , d ) 2912 , e ) 2215
Rationale: "= ( 19 + 43 / 151 ) × 151 = ( 2869 + 43 ) / 151 × 151 = 2912 / 151 × 151 = 2912 answer is d ."
Answer: d
Question (physics): the lcm of two numbers is 2310 and hcf is 61 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 671 , c ) 330 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 61 / 210 = 11 * 61 = 671 answer : b"
Answer: b
Question (gain): the c . p of 30 books is equal to the s . p of 40 books . find his gain % or loss % ?
Options: a ) 23 % , b ) 24 % , c ) 25 % , d ) 50 % , e ) 40 %
Rationale: "explanation : 30 cp = 40 sp 40 - - - 10 cp loss 100 - - - ? = > 25 % loss answer : c"
Answer: c
Question (physics): a train 280 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 15 , b ) 6 , c ) 7 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 280 * 3 / 55 = 15 sec . answer : a"
Answer: a
Question (physics): a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 30 paise per sq m is
Options: a ) rs . 223.20 , b ) rs . 323.20 , c ) rs . 423.20 , d ) rs . 523.20 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 30 / 100 ) = rs . 223.20 answer : a"
Answer: a
Question (physics): 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 5 men and 2 women will do that task .
Options: a ) 6 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 3 / 16 , e ) 3 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 5 m + 2 w = 12 w answer is 12 / 14 = 6 / 7 answer : a"
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 824 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 500 , b ) 698 , c ) 780 , d ) 910 , e ) 725
Rationale: "sol . s . i . for 1 year = rs . ( 854 - 824 ) = rs . 30 . s . i . for 3 years = rs . ( 30 * 3 ) = rs . 90 . â ˆ ´ principal = rs . ( 815 - 90 ) = rs . 725 answer e"
Answer: e
Question (physics): 6 boysand 8 girls can do job in 10 days , 26 boys & 48 women do work in 2 days find time taken by 15 boys and 20 girls to do same work
Options: a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: 6 b + 8 g = 1 / 10 ( 1 day work ) - - - - - - > ( i ) 26 b + 48 w = 1 / 2 - - - - - - - - > ( ii ) divide both sides by 2 in ( i ) and multiply both sides by 5 now we get 15 b + 20 b = 1 / 4 so ans . is 4 days . answer : a
Answer: a
Question (general): a , b and c have rs . 250 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 300 , b ) b ) 290 , c ) c ) 280 , d ) d ) 270 , e ) e ) 66
Rationale: "a + b + c = 250 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 250 - - - - - - - - - - - - - - - - c = 300 answer : a"
Answer: a
Question (general): a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1947 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 118
Rationale: "factorise 1947 . . 3 * 11 * 59 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 59 = 118 . . ans : e"
Answer: e
Question (physics): a boat can travel with a speed of 14 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 72 km downstream .
Options: a ) 4.25 hr , b ) 3.6 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 14 km / hr speed of the stream = 6 km / hr speed downstream = ( 14 + 6 ) = 20 km / hr time taken to travel 72 km downstream = 72 â  „ 20 = 3.6 hours answer is b"
Answer: b
Question (general): if x is equal to the sum of the integers from 40 to 60 , inclusive , and y is the number of even integers from 40 to 60 , inclusive , what is the value of x + y ?
Options: a ) 1021 , b ) 1041 , c ) 1061 , d ) 1081 , e ) 1101
Rationale: "x = 40 + 41 + . . . + 60 = 21 ( 50 ) = 1050 y = 11 x + y = 1061 the answer is c ."
Answer: c
Question (general): the average age of 36 students in a group is 15 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 52 years , d ) 54 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 37 * 16 - 36 * 15 ) years = 52 years . answer : c"
Answer: c
Question (physics): how many paying stones , each measuring 4 m * 2 m are required to pave a rectangular court yard 40 m long and 20 m board ?
Options: a ) 99 , b ) 18 , c ) 100 , d ) 17 , e ) 12
Rationale: "40 * 20 = 4 * 2 * x = > x = 100 answer : c"
Answer: c
Question (physics): convert the 12 / 36 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 1.9 kmph .
Rationale: "15 / 36 m / s = 12 / 36 * 18 / 5 = 1 ( 1 / 5 ) = 1.2 kmph . answer : c"
Answer: c
Question (general): a two digit number is 18 less than the sum of the squares of its digits . how many such numbers are there ?
Options: a ) 22 , b ) 67 , c ) 200 , d ) 288 , e ) 111
Rationale: "option 2 only 47 and 67 satisfy the condition answer : b"
Answer: b
Question (general): what is the sum of all remainders obtained when the first 100 natural numbers are divided by 7 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 364
Rationale: a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 364 . answer : e .
Answer: e
Question (geometry): rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 4 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 3 / 4 , b ) 9 / 16 , c ) 16 / 3 , d ) 4 / 3 , e ) 3 / 16
Rationale: "the area of rectangle a is ab . c = 4 a / 3 and d = 4 b / 3 . the area of rectangle b is cd = 16 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 16 ab / 9 ) = 9 / 16 . the answer is b ."
Answer: b
Question (physics): to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 7 / 10 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 35.71429 , e ) 64.5
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 7 x / 10 hence , number of buckets needed = 25 x / ( 7 x / 10 ) = ( 25 × 10 ) / 7 = 35.71429 answer is d ."
Answer: d
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 46 kg , then the weight of b is :
Options: a ) 17 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 37 kg
Rationale: "let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 46 = 92 hence 80 + 92 - 144 = 37 ans = 37 answer : e"
Answer: e
Question (other): two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 2 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 9 : 5
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 4 and 2 parts , respectively . this will give us in the final mixture ( 5 + 4 ) : ( 3 + 2 ) , which means 9 : 5 answer e ."
Answer: e
Question (physics): in covering a distance of 30 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "abhay speed = x sameer speed = y ( 30 / x ) - ( 30 / y ) = 2 . . . . 1 - ( 30 / 2 x ) + ( 30 / y ) = 1 . . . - 2 solving 1 and 2 we get 6 x = 30 x = 5 answer e"
Answer: e
Question (general): a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.05 ?
Options: a ) 980 , b ) 1130 , c ) 1440 , d ) 1610 , e ) 1820
Rationale: the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.05 - $ 0.65 = $ 1.40 the charge for the next 1300 grams is $ 1.30 which leaves a charge of $ 0.10 the weight is somewhere between 1550 and 1650 . the answer is d .
Answer: d
Question (geometry): the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 14.25 , what is the perimeter of the garden , in feet ?
Options: a ) 38
b ) 36
c ) 40
d ) 56
e ) 64
Rationale: perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 14.25 ( p ^ 2 ) / 16 = 2 p + 9 p ^ 2 = 32 p + 228 p ^ 2 - 32 p - 228 = 0 p ^ 2 - 38 p + 6 p - 228 = 0 p ( p - 38 ) + 6 ( p + 38 ) = 0 ( p - 38 ) ( p + 6 ) = 0 p = 38 or - 6 discarding negative value , p = 38 answer is a
Answer: a
Question (gain): a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 1 / 2 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 223.78 , b ) 37.78 , c ) 24.6 , d ) 278.88 , e ) 123.0
Rationale: "explanation : capital = rs . x , then 1 / 2 x = 61.5 x = 123.00 answer : e ) rs . 123.00"
Answer: e
Question (gain): a fruit seller had some oranges . he sells 20 % oranges and still has 380 oranges . how many oranges he had originally ?
Options: a ) 475 , b ) 700 , c ) 220 , d ) 400 , e ) none of these
Rationale: explanation : he sells 20 % of oranges and still there are 380 oranges remaining = > 80 % of oranges = 380 ⇒ ( 80 × total oranges ) / 100 = 380 ⇒ total oranges / 100 = 4.75 ⇒ total oranges = 4.75 × 100 = 475 answer : option a
Answer: a
Question (general): find the mean proportional between 25 & 36 ?
Options: a ) a ) 59 , b ) b ) 30 , c ) c ) 63 , d ) d ) 65 , e ) e ) 67
Rationale: "formula = √ a × b a = 25 and b = 36 √ 25 × 36 = 5 × 6 = 30 b"
Answer: b
Question (other): the compound ratio of 2 / 5 , 6 / 7 , 1 / 3 and 1 / 8 is given by ?
Options: a ) 7 / 98 , b ) 1 / 70 , c ) 1 / 98 , d ) 1 / 96 , e ) 1 / 68
Rationale: "2 / 5 * 6 / 7 * 1 / 3 * 1 / 8 = 12 / 840 = 1 / 70 answer : b"
Answer: b
Question (physics): p , q and r can do a work in 5 , 7 and 10 days respectively . they completed the work and got rs . 310 . what is the share of q and r respectively ?
Options: a ) 100 and 80 , b ) 100 and 90 , c ) 100 and 110 , d ) 70 and 100 , e ) 100 and 70
Rationale: the ratio of their working rates = 1 / 5 : 1 / 7 : 1 / 10 = 14 : 10 : 7 . since , they work together , the share of q = 10 / 31 * 310 = rs . 100 the share of r = 7 / 31 * 310 = rs . 70 the share of q and r respectively is rs . 100 and rs . 70 answer : e
Answer: e
Question (general): what is the average ( arithmetic mean ) of the numbers 16 , 17 , 18 , 19 and 20 ?
Options: a ) 14.2 , b ) 16.5 , c ) 17 , d ) 17.5 , e ) 18
Rationale: "{ 16 , 17 , 18 , 19 , 20 } = { 18 - 2,18 - 1 , 18 , 18 + 1,18 + 2 } - - > the average = 18 . answer : e ."
Answer: e
Question (general): a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 267 , d ) 261 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 841 = 261 answer : d"
Answer: d
Question (gain): a reduction of 21 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.66 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1
Rationale: "100 * ( 21 / 100 ) = 21 - - - 10 ? - - - 1 = > rs . 2.1 100 - - - 79 ? - - - 2.1 = > rs . 2.66 answer : a"
Answer: a
Question (general): a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 500 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 500 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 1000 n = 10 satisfies this . a"
Answer: a
Question (general): what is the least number should be added to 1156 , so the sum of the number is completely divisible by 25 ?
Options: a ) 19 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "( 1156 / 25 ) gives remainder 6 6 + 19 = 25 , so we need to add 19 answer : a"
Answer: a
Question (general): the youngest of 4 children has siblings who are 4 , 5 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: x + ( x + 4 ) + ( x + 5 ) + ( x + 7 ) = 84 4 x + 16 = 84 4 x = 68 x = 17 the answer is d .
Answer: d
Question (general): a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 500 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 7799 , c ) 2500 , d ) 2772 , e ) 6250
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 500 b capital = 37500 * 1 / 6 = 6250 . answer : e"
Answer: e
Question (physics): in a kilometer race , a beats b by 50 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 50 sec , b ) 190 sec , c ) 287 sec , d ) 74 sec , e ) 697 sec
Rationale: "explanation : time taken by b run 1000 meters = ( 1000 * 10 ) / 50 = 200 sec . time taken by a = 200 - 10 = 190 sec . answer b"
Answer: b
Question (physics): two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 6 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 8 1 / 8 km , d ) 9 km , e ) 5 km
Rationale: rs = 5 ¾ - 4 ½ = 1 ¼ t = 6 ½ h . d = 5 / 4 * 13 / 2 = 65 / 8 = 8 1 / 8 km answer : c
Answer: c
Question (general): the average of 8 numbers is 25 , that of the first 2 is 20 and of the next 3 is 26 . the sixth number is less than the seventh by 4 , and less than the eighth by 6 . the last number is
Options: a ) 30 , b ) 32 , c ) 40 , d ) 36 , e ) 38
Rationale: explanation : sum of all the numbers = 25 * 8 = 200 sum of first two numbers = 40 sum of next three numbers ( i . e . , 3 rd , 4 th and 5 th ) = 78 so , sum of first five numbers = 118 and sum of 6 th , 7 th and 8 th number = 82 assuming sixth number to be x , we get 7 th number = x + 4 and 8 th number = x + 6 . so , x + ( x + 4 ) + ( x + 6 ) = 82 = > x = 24 . hence , last number ( 8 th number ) = 30 . answer : a
Answer: a
Question (physics): 18 : 12 seconds : : ? : 6 minutes
Options: a ) 10 , b ) 9 , c ) 20 , d ) 25 , e ) 30
Rationale: 18 * 6 = 12 * x x = 9 answer : b
Answer: b
Question (physics): a ship going at the speed of 18 km / hr crosses a light house in 20 seconds . what is the length of the train ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 240 , e ) 200
Rationale: speed = ( 18 x 5 / 18 ) = 5 m / sec . length of the train = ( speed x time ) . length of the train = 5 x 20 m = 100 m . answer : c
Answer: c
Question (physics): matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days peter stops and peter completes the remaining work in 10 days . in how many days matt complete the work separately .
Options: a ) 28 , b ) 27 , c ) 26 , d ) 25 , e ) 29
Rationale: together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 8 / 20 ) = 25 d
Answer: d
Question (general): set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 7 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 7 , e ) e ) 16
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
Answer: d
Question (general): a number is increased by 30 % and then decreased by 30 % . find the net increase or decrease per cent .
Options: a ) 9 % , b ) 8 % , c ) 7 % , d ) 3 % , e ) 6 %
Rationale: "let the number be 100 . increase in the number = 30 % = 30 % of 100 = ( 30 / 100 ã — 100 ) = 30 therefore , increased number = 100 + 30 = 130 this number is decreased by 30 % therefore , decrease in number = 30 % of 130 = ( 30 / 100 ã — 130 ) = 3900 / 100 = 39 therefore , new number = 130 - 39 = 91 thus , net decreases = 100 - 91 = 9 hence , net percentage decrease = ( 9 / 100 ã — 100 ) % = ( 900 / 100 ) % = 9 % answer : a"
Answer: a
Question (general): if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 27 , find the value of ab .
Options: a ) 5 , b ) 9 , c ) 4 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 27 - 9 = 18 ab = 9 . answer is b ."
Answer: b
Question (gain): a man can row his boat with the stream at 19 km / h and against the stream in 11 km / h . the man ' s rate is ?
Options: a ) 4 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 19 us = 11 s = ? s = ( 19 - 11 ) / 2 = 4 kmph answer : a"
Answer: a
Question (general): kamal ' s salary was decreased by 50 % and subsequently increased by 30 % . how much percent does he lose ?
Options: a ) 30 % , b ) 37 % , c ) 65 % , d ) 35 % , e ) 45 %
Rationale: explanation : solution : let original salary = rs . 100 . new final salary = 130 % of ( 50 % of rs . 100 ) = rs . ( 130 / 100 * 50 / 100 * 100 ) = rs . 65 . . ' . decrease = 35 % answer : d
Answer: d
Question (gain): a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 10 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 9 / 10 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 6 / 100 * 1 + ( 20000 - x ) * 10 / 100 * 1 = 1440 6 x - 8 x = 144000 - 200000 = > - 2 x = - 4000 = > x = 2000 so 18000 / 20000 = 9 / 10 answer - b"
Answer: b
Question (general): the ratio of a to b to c is 2 to 3 to 4 , and a , b , c are positive integers . if the average ( arithmetic mean ) of the 3 numbers is 42 , what is the value of a ?
Options: a ) 24 , b ) 25 , c ) 28 , d ) 30 , e ) 32
Rationale: let a = 2 k , b = 3 k , and c = 4 k . a + b + c = 2 k + 3 k + 4 k = 9 k since the average is 42 : 9 k / 3 = 42 3 k = 42 k = 14 then a = 28 . the answer is c .
Answer: c
Question (general): what is the dividend . divisor 18 , the quotient is 9 and the remainder is 4
Options: a ) a ) 166 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158
Rationale: "d = d * q + r d = 18 * 9 + 4 d = 166 answer : a"
Answer: a