regisss/math_qa huggingface dataset:
Problem: free notebooks were distributed in a class among all the students . each student got notebooks which were 1 / 8 th of the number of student . if number of student been half , then each child would have received 16 notebooks in total . find the total number of books distributed among students ?
Options: a ) 430 , b ) 450 , c ) 460 , d ) 480 , e ) 512
Rationale: let suppose total number of students in class are x . then from the question we can conclude it that , x ∗ 18 x = x 2 ∗ 16 = > x = 64 total notebooks , = 18 x 2 = ( 18 ∗ 64 ∗ 64 ) = 512 e
Answer: e
Problem: what is the least number to be subtracted from 990 to make it a perfect square ?
Options: a ) 100 , b ) 90 , c ) 30 , d ) 71 , e ) 80
Rationale: "the numbers less than 990 and are squares of certain number is 900 . the least number that should be subtracted from 990 to make it perfect square = 990 - 900 = 90 . answer : b"
Answer: b
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 36 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 1 / 3 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 36 = ( 2 / 3 ) * ( 2 / 3 ) therefore probability that the next one she draws is pink = 1 / 3 option ( d )"
Answer: d
Problem: if x is a sum of all even integers on the interval 13 . . . 65 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 13 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 64 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 64 ) / 2 * 26 = 39 * 26 . gcd of 26 and 39 * 26 is 26 . answer : c ."
Answer: c
Problem: a child want to buy 5 new toys . if there are 15 toys that satisfy the child ' s criteria , in how many different ways can the child select the 5 new toys if the order of selection does n ' t matter .
Options: a ) 210 , b ) 1365 , c ) 3003 , d ) 5005 , e ) 3030
Rationale: the number of ways of choosing 5 toys out of 15 are counted by = 15 c 5 ways = 3003 answer : option c
Answer: c
Problem: two boys started running simultaneously around a circular track of length 4800 m from the same point at speeds of 60 km / hr and 100 km / hr . when will they meet for the first time any where on the track if they are moving in opposite directions ?
Options: a ) 105 , b ) 106 , c ) 107 , d ) 108 , e ) 109
Rationale: time taken to meet for the first time anywhere on the track = length of the track / relative speed = 4800 / ( 60 + 100 ) 5 / 18 = 4800 * 18 / 160 * 5 = 108 seconds . answer : d
Answer: d
Problem: a contractor is engaged for 30 days on the condition that he receives rs . 25 for each dayhe works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many dayswas he absent ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 17
Rationale: "30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b"
Answer: b
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 28 years later ?
Options: a ) $ 160,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 450,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 28 years , the investment will get doubled 28 / 14 = 2 times . so the amount invested will get doubled thrice . so , 40000 * 2 = 80000 80000 * 2 = 160000 hence , the answer is a ."
Answer: a
Problem: in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each 100 m in length both trains running with a speed of 80 kmph ?
Options: a ) 4.5 sec , b ) 4.8 sec , c ) 4.2 sec , d ) 5.0 sec , e ) 5.2 sec
Rationale: d = 100 m + 100 m = 200 m * 1 / 1000 = 0.2 kms rs = 80 + 80 = 160 kmph t = ( 0.2 / 160 ) * 3600 = 4.5 sec answer : a
Answer: a
Problem: the profit earned by selling an article for 892 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1005 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: let the profit or loss be x and 892 – x = 448 + x or , x = 444 ⁄ 2 = 222 \ cost price of the article = 892 – x = 448 + x = 670 \ sp of the article = 670 × 150 ⁄ 100 = 1005 answer b
Answer: b
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 720 . find the sum ?
Options: a ) s . 7000 , b ) s . 9000 , c ) s . 14000 , d ) s . 12000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 720 = > 30 x / 100 - 24 x / 100 = 720 = > 6 x / 100 = 720 = > x = 12000 . answer : d"
Answer: d
Problem: 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 $ 4 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 ) 45 % , b ) 13 % , 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 $ 4 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 4 or 45 * 18 - 45 * x + 36 * x = 400 or - 9 x = 400 - 45 * 18 or x = 410 / 9 = 45 % = 45 % a"
Answer: a
Problem: in a building there are 5 rooms . each having a equal area . the length of the room is 4 m and breadht is 5 m . the height of the rooms are 2 m . if 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room ?
Options: a ) 320
b ) 340
c ) 300
d ) 330
e ) 360
Rationale: explanation : area of the floor = 4 m x 5 m = 20 m 2 17 bricks are needed to make 1 m 2 area . so to make 20 m 2 no of bricks needed = 17 x 20 = 340 answer : b
Answer: b
Problem: meena wrote all the numbers from 1 to 69,999 inclusive . how many digits did she write in total ?
Options: a ) 278,889 , b ) 308,889 , c ) 338,889 , d ) 368,889 , e ) 398,889
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 69999 = > 5 * 60,000 = 300,000 the answer is 338,889 the answer is c ."
Answer: c
Problem: a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is
Options: a ) 720 , b ) 900 , c ) 1200 , d ) 1800 , e ) none
Rationale: "solution 2 ( 15 + 12 ) × h = 2 ( 15 x 12 ) ‹ = › h = 180 / 27 m = 20 / 3 m volume = ( 15 × 12 × 20 / 3 ) m 3 ‹ = › 1200 m 3 . answer c"
Answer: c
Problem: harkamal purchased 9 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1120 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 9 kg grapes = 70 × 9 = 630 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 630 + 490 = 1120 a"
Answer: a
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 100 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 142
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 100 = > 2 * ( 2 ) ^ 2 + y = 100 = > 8 + y = 100 = > y = 92 f ( 5 ) = 2 * ( 5 ) ^ 2 + 92 = 142 answer e"
Answer: e
Problem: a sum of rs . 2717 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1672 , b ) 1640 , c ) 1677 , d ) 1698 , e ) 1679
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2717 - x ) * 3 * 5 ) / 100 24 x / 100 = 40755 / 100 - 15 x / 100 39 x = 40755 = > x = 1045 second sum = 2717 â € “ 1045 = 1672 answer : a"
Answer: a
Problem: if 35 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 110 , b ) 330 , c ) 572 , d ) 430 , e ) 880
Rationale: "students enrolled in biology are 35 % and therefore not enrolled are 65 % . so of 880 is 880 * . 65 = 572 answer is c 572"
Answer: c
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 28 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 16 , b ) 24 , c ) 32 , d ) 40 , e ) 48
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.28 ( 800 ) = 216 the answer is a ."
Answer: a
Problem: a sum of rs . 1700 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1700 = > 17 x / 12 = 1700 = > 1700 x 12 / 17 = rs . 1200 hence , b ’ s share = rs . ( 1200 / 4 ) = rs . 300 . answer d"
Answer: d
Problem: on a certain island , 5 % of the 10000 inhabitants are one - legged and half of the others go barefooted . what is the least number of shoes needed in the island ?
Options: a ) 10200 , b ) 10000 , c ) 9500 , d ) 9000 , e ) none
Rationale: explanation : = > one - legged = 5 % of 10000 = 500 = > remaining = 10000 - 500 = 9500 = > barefooted = 9500 / 2 = 4750 = > remaining people = 9500 - 4750 = 4750 = > hence required number of shoes = 4750 * 2 + 500 * 1 = 10000 hence ( b ) is the correct answer . answer : b
Answer: b
Problem: a person borrows rs . 9000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 9000 * 6 * 2 ) / 100 ] - [ ( 9000 * 4 * 2 ) / 100 ] 1080 - 720 = 360 gain in 1 year = ( 360 / 2 ) = 180 rs answer : d"
Answer: d
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 7 gallons of water and 14 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 105 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 14 gallons salt is added and 7 gallons of water is added . so salt now becomes - > ( 0.2 x + 14 ) and water - - > ( 0.6 x + 7 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 14 ) = ( 0.6 x + 7 ) / 2 = > 0.2 x = 21 solving , x = 105 answer : c"
Answer: c
Problem: a car takes 12 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 4 th of the previous time ?
Options: a ) 25 kmph , b ) 60 kmph , c ) 100 kmph , d ) 120 kmph , e ) 180 kmph
Rationale: "time = 12 distence = 540 3 / 4 of 12 hours = 12 * 3 / 4 = 9 hours required speed = 540 / 9 = 60 kmph b )"
Answer: b
Problem: a soccer team played 140 games and won 50 percent of them . how many games did it win ?
Options: a ) 140 , b ) 94 , c ) 104 , d ) 70 , e ) 80
Rationale: "50 % of 140 = x 0.50 * 140 = x 70 = x answer : d"
Answer: d
Problem: how many 11 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 12345654321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 900000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the 11 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 10 th 9 th , 8 th , 7 th , 6 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the , 5 th , 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 11 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 900000 ways ) answer : e"
Answer: e
Problem: 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 224 different signs . if the company used 222 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 224 signs ?
Options: a ) 246 , b ) 248 , c ) 892 , d ) 15,128 , e ) 20,256
Rationale: "# of 2 - letter codes possible from 224 different signs = 224 * 224 . # of 2 - letter codes possible from 222 different signs = 222 * 222 . the difference = 224 ^ 2 - 222 ^ 2 = ( 224 - 222 ) ( 224 + 222 ) = 892 . answer : c ."
Answer: c
Problem: a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and captain ) to a nearby port . altogether , these passengers have 15 heads and 42 legs . how many cats does the ship host ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "sa ' s + co + ca + cats = 15 . sa ' s + 1 + 1 + cats = 15 or sa ' s + cats = 13 . sa ' s ( 2 ) + 2 + 2 + cats * 4 = 42 sa ' s * 2 + cats * 4 = 38 or sa ' s + cats * 2 = 19 or 13 - cats + cat * 2 = 19 then cats = 6 b"
Answer: b
Problem: in 6 successive games , a baseball team scored 1 runs once , 4 runs twice , and 5 runs 3 times . what was the average ( arithmetic mean ) number of runs the team scored per game over the 6 - game period ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: 1 runs once ( one game ) 4 runs twice ( two game ) 5 runs three times ( three games ) so we have ( 1 * 1 + 4 * 2 + 5 * 3 ) / 6 = 24 / 6 = 4 . ans : e .
Answer: e
Problem: what is theleast number should be added to 410 , so the sum of the number is completely divisible by 20 ?
Options: a ) 1 , b ) 2 , c ) 10 , d ) 6 , e ) 8
Rationale: "( 410 / 20 ) gives remainder 10 10 + 10 = 20 , so we need to add 10 answer : c"
Answer: c
Problem: the surface of a cube is 54 sq cm . find its volume ?
Options: a ) 8 cc , b ) 27 cc , c ) 2 cc , d ) 4 cc , e ) 6 cc
Rationale: "6 a 2 = 54 = 6 * 9 a = 3 = > a 3 = 27 cc answer : b"
Answer: b
Problem: a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.2 hrs , e ) 30 hrs
Rationale: "net part filled in 1 hour = 1 / 5 - 1 / 6 = 1 / 30 therefore the cistern will be filled in 30 hours . answer : e"
Answer: e
Problem: one hour before john started walking from p to q , a distance of 23 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 15 miles
Rationale: ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 23 - 3 = 20 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 20 miles so it will take them 20 / 5 = 4 hours to meet . in 4 hrs , ann would have covered 4 hrs * 3 miles per hour = 12 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 12 = 15 miles . answer ( e )
Answer: e
Problem: ( 128.5 x 60 ) + ( 13.8 x 65 ) = ? x 25
Options: a ) 524.48 , b ) 344.28 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 60 ) + ( 13.8 x 65 ) / 25 = 7710 + 897 / 25 = 344.28 answer : option b"
Answer: b
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 11 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 1 to 5 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 11 k waiters . the new ratio is 1 : 5 which equals 3 : 15 . 15 k = 11 k + 12 k = 3 there are 9 cooks . the answer is c ."
Answer: c
Problem: on a certain day , tim invested $ 600 at 10 percent annual interest , compounded annually , and lana invested 1,000 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5.5 , b ) $ 15.5 , c ) $ 23.5 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 600 ( 1.10 ) ^ 2 = 600 ( 1.21 ) = 726 and lana would have 1,000 ( 1.05 ) ^ 2 = 1,000 ( 1.1025 ) = 1102.5 thus , tim earned 126 dollars , while lana earned 102.5 dollars the difference is $ 23.5 and the answer is c ."
Answer: c
Problem: john has 10 pairs of matched socks . if he loses 9 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "because we have to maximize the pair of matched socks , we will remove 4 pairs ( 8 socks ) out of 10 pairs 1 sock from the 5 th pair . thus the no of matching socks pair remaining = 10 - 5 = 5 answer c"
Answer: c
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 8.5 ) = ( 500 ∗ 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 9 % ( option a ) answer : a"
Answer: a
Problem: a trader bought a car at 30 % discount on its original price . he sold it at a 70 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 18 % , b ) 13 % , c ) 12 % , d ) 32 % , e ) 19 %
Rationale: "original price = 100 cp = 70 s = 70 * ( 170 / 100 ) = 119 100 - 119 = 19 % answer : e"
Answer: e
Problem: in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 4 ohms and y is 5 ohms ?
Options: a ) 7 / 9 , b ) 20 / 9 , c ) 7 / 20 , d ) 9 / 20 , e ) 11 / 20
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 5 = 9 / 20 r = 20 / 9 the answer is b ."
Answer: b
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 14 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 23.56 , b ) 23.59 , c ) 23.55 , d ) 18.86 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 14 + 10 ) = 48 cm parameter of the square = 48 cm i . e . 4 a = 48 a = 12 diameter of the semicircle = 12 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 12 ) = 1 / 2 ( 22 / 7 ) ( 12 ) = 264 / 14 = 18.86 cm to two decimal places answer : d"
Answer: d
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 6 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 6 / 100 x 12000 ) = rs . 720 . answer d"
Answer: d
Problem: calculate the circumference of a circular field whose radius is 5 centimeters .
Options: a ) 30 π cm
b ) 80 π cm
c ) 70 π cm
d ) 50 π cm
e ) 10 π cm
Rationale: circumference c is given by c = 2 π r = 2 π * 5 = 10 π cm correct answer e
Answer: e
Problem: two friends plan to walk along a 43 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 15 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ?
Options: a ) 21 , b ) 21.5 , c ) 22 , d ) 22.5 , e ) 23
Rationale: "if q complete x kilometers , then p completes 1.15 x kilometers . x + 1.15 x = 43 2.15 x = 43 x = 43 / 2.15 = 20 then p will have have walked 1.15 * 20 = 23 km . the answer is e ."
Answer: e
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 588 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 1190 , d ) s . 3468 , e ) s . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 588 : n & there n = 289 x 588 / 49 = rs . 3468 answer : d"
Answer: d
Problem: a person travels equal distances with speeds of 4 km / hr , 8 km / hr , 12 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 600 mts , d ) 2 km , e ) 1200 mts
Rationale: let the each distance be x km total distance = 3 x then total time , ( x / 4 ) + ( x / 8 ) + ( x / 12 ) = 11 / 60 x = 0.4 total distance = 3 * 0.4 = 1.2 km = 1200 meters correct option is e
Answer: e
Problem: a man drives at a speed of 40 miles / hr . his wife left 30 mins . late with 50 miles / hr speed . when will they meet ?
Options: a ) 1 hours , b ) 2 hours , c ) 3 hours , d ) 4 hours , e ) 5 hours
Rationale: in 30 minutes the man would have droven 20 miles , when his wife starts . now both are driving in the same direction . so speed of wife related to man is 10 ( 50 - 40 ) miles / hr . so wife will cover 20 miles in 2 hours to meet the man . answer : b
Answer: b
Problem: a and b together can complete work in 8 days . a alone starts working and leaves it after working for 6 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 5 , d ) 12 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 8 now a does half of the work in 6 day so a can complete the whole work in 12 days a ’ s one day work = 1 / 12 b ’ s one day work = 1 / 8 - 1 / 12 = 1 / 24 b alone can complete the work in 24 days so half of the work in 12 days answer : option d"
Answer: d
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 63 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 450 , c ) 150 , d ) 35 , e ) 350
Rationale: since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 63 , so 0.14 * { total } = 63 - - > { total } = 450 . answer : b .
Answer: b
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 78 kmph , find the speed of the stream ?
Options: a ) 15 , b ) 19 , c ) 14 , d ) 18 , e ) 26
Rationale: the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 78 / 3 = 26 kmph . answer : e
Answer: e
Problem: angelina walked 960 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 13 , c ) 24 , d ) 36 , e ) 42
Rationale: "let the speed be x . . . so time taken from home to grocery = 960 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 960 / x - 240 / x = 40 . . 720 / x = 40 . . x = 18 m / secs . . so grocery to gym = 2 * 18 = 36 m / s . . . d"
Answer: d
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 3500 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 31,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 3500 triples to $ 10500 , in 28 years , it will again triple to $ 10500 * 3 = $ 31,500 answer e"
Answer: e
Problem: the ratio of the ages of 3 people is 4 : 6 : 7 . 8 years ago , the sum of their ages was 44 . find their present ages .
Options: a ) 28 , 42,49 , b ) 24 , 36,42 , c ) 20 , 30,35 , d ) 16 , 24,28 , e ) 12 , 18,21
Rationale: let the present ages be 4 x , 6 x , 7 x . ( 4 x - 8 ) + ( 6 x - 8 ) + ( 7 x - 8 ) = 44 17 x = 68 x = 4 their present ages are 16 , 24 , and 28 . the answer is d .
Answer: d
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 72 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 25 sec , d ) 18 sec , e ) 12.5 sec
Rationale: "d = 100 + 150 = 250 s = 72 * 5 / 18 = 20 mps t = 250 / 20 = 12.5 sec answer : e"
Answer: e
Problem: a meal cost $ 35.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 35.5 ) = 3.55 15 % ( 35.5 ) = 5.325 total amount could have been 35.5 + 3.55 and 35.5 + 5.325 = > could have been between 39.05 and 40.625 = > approximately between 39 and 41 answer is b ."
Answer: b
Problem: find the area of trapezium whose parallel sides are 20 cm and 10 cm long , and the distance between them is 10 cm .
Options: a ) 187 cm 2 , b ) 185 cm 2 , c ) 150 cm 2 , d ) 185 cm 2 , e ) 195 cm 2
Rationale: "explanation : area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 10 ) * ( 10 ) = 150 cm 2 answer : option c"
Answer: c
Problem: a rectangular lawn of dimensions 90 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 3988 , b ) s . 3900 , c ) s . 3228 , d ) s . 4200 , e ) s . 3928
Rationale: "area = ( l + b – d ) d ( 90 + 60 – 10 ) 10 = > 1400 m 2 1400 * 3 = rs . 4200 answer : d"
Answer: d
Problem: a soccer team played 158 games and won 40 percent of them . how many games did it win ?
Options: a ) 84 , b ) 63.2 , c ) 104 , d ) 50.8 , e ) 15.8
Rationale: 40 % of 158 = x 0.40 * 158 = x 63.2 = x answer : b
Answer: b
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 70 kmph its consumption is 1 litre per hour . if each litre costs $ 70 and other expenses per hous is $ 70 , then what would be the minimum expenditure required to cover a distance of 700 km ?
Options: a ) 1000 , b ) 1500 , c ) 1240 , d ) 1630 , e ) 1400
Rationale: "70 kmph consumption is 1 lt / hr so 700 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 70 so 10 lt costs $ 700 extra expenses for 1 hr - $ 70 10 hrs - $ 700 total expense - $ 700 + $ 700 = $ 1400 answer : e"
Answer: e
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 80 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 76.6
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover this distance at regular speed is 45 + 2 = 47 seconds = 47 / 3,600 hours = 5 / 383 hours ; so , we get that to cover 1 kilometer 1 / ( 5 / 383 ) hours is needed - - > regular speed 76.6 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e"
Answer: e
Problem: 15 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 3 = 18 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 18 = 50 / 3 = 16.67 % answer is a"
Answer: a
Problem: total number of people attending a party is 600 . 70 % of the men are wearing black shirt and rest are wearing red . if 60 % of the total people are women then how many men are wearing red shirts ?
Options: a ) 168 , b ) 72 , c ) 56 , d ) 170 , e ) 60
Rationale: number of woman in the party = 0.60 * 600 = 360 number of men in the party = 600 - 360 = 240 % of men wearing red shirts = 100 - 70 = 30 % number of men wearing red shirt = 0.30 * 240 = 72 . b is the correct answer
Answer: b
Problem: the mall charges 60 cents for the first hour of parking and $ 4 for each additional hour until the customer reaches 4 hours , after that the parking fee is $ 2 per hour . if edward parked his car in the mall for 7 hours and 30 minutes , how much is he going to pay ?
Options: a ) $ 25.2 , b ) $ 22 . , c ) $ 13 . , d ) $ 14.5 . , e ) $ 15.5
Rationale: "0.60 + 4 * 4 + 2 * 4 + 0.60 = $ 25.2 answer : $ 25.2"
Answer: a
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 650 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 760 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) $ 2.50 , b ) $ 5.00 , c ) $ 5.50 , d ) $ 7.50 , e ) $ 15.00
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 650 . . . eq 1 8 x + 32 y = 760 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1300 8 x = 760 . 36 x = 540 = > x = 15 . sub x in eq 2 . . . . we get 120 + 32 y = 760 . . . then we get 32 y = 640 then y = 20 difference between x and y is 5 . answer : option b is correct answer ."
Answer: b
Problem: ( 17 ) 5.5 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 5.5 * ( 17 ) x = 178 . then , ( 17 ) 5.5 + x = ( 17 ) 8 . ∴ 5.5 + x = 8 ⇔ x = ( 8 - 5.5 ) ⇔ x = 2.5 answer e"
Answer: e
Problem: in a fort , there are 1200 soldiers . if each soldier consumes 3 kg per day , the provisions available in the fort will last for 30 days . if some more soldiers join , the provisions available will last for 25 days given each soldier consumes 2.5 kg per day . find the number of soldiers joining the fort in that case .
Options: a ) 627 , b ) 528 soldiers , c ) 626 , d ) 657 , e ) 673
Rationale: assume x soldiers join the fort . 1200 soldiers have provision for 1200 ( days for which provisions last them ) ( rate of consumption of each soldier ) = ( 1200 ) ( 30 ) ( 3 ) kg . also provisions available for ( 1200 + x ) soldiers is ( 1200 + x ) ( 25 ) ( 2.5 ) k as the same provisions are available = > ( 1200 ) ( 30 ) ( 3 ) = ( 1200 + x ) ( 25 ) ( 2.5 ) x = [ ( 1200 ) ( 30 ) ( 3 ) ] / ( 25 ) ( 2.5 ) - 1200 = > x = 528 . answer : b
Answer: b
Problem: what least value should be replaced by * in 483 * 4312 so the number become divisible by 6
Options: a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7
Rationale: "explanation : trick : number is divisible by 6 , if sum of all digits is divisible by 3 and 2 , last digit is 2 so it is dividable by 2 so ( 4 + 8 + 3 + * + 4 + 3 + 1 + 2 ) = 25 + * should be divisible by 6 , 15 + will be divisible by , so that least number is 2 . answer : option d"
Answer: d
Problem: calculate the standard deviation of each data set { 10 , 1010 , 1010 }
Options: a ) 8.05 , b ) 9 , c ) 10 , d ) 15 , e ) 15.5
Rationale: standard deviation data set a = √ [ ( ( 9 - 10 ) 2 + ( 10 - 10 ) 2 + ( 11 - 10 ) 2 + ( 7 - 10 ) 2 + ( 13 - 10 ) 2 ) / 5 ] = 2 standard deviation data set b = √ [ ( ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 ) / 5 ] = 0 standard deviation data set c = √ [ ( ( 1 - 10 ) 2 + ( 1 - 10 ) 2 + ( 10 - 10 ) 2 + ( 19 - 10 ) 2 + ( 19 - 10 ) 2 ) / 5 ] = 8.05 option a
Answer: a
Problem: the ratio of three numbers is 3 : 4 : 7 and their product is 18144 . the numbers are
Options: a ) 9 , 12,21 , b ) 15 , 20,25 , c ) 18 , 24,42 , d ) 24 , 15,17 , e ) 30 , 12,7
Rationale: "let the numbers be 3 x , 4 x and 7 x 3 x x 4 x x 7 x = 18144 x 3 = 216 x = 6 the numbers are 18 , 24,42 answer c 18 , 24,42"
Answer: c
Problem: john and david can finish a job together in 3 hours . if john can do the job by himself in 4 hours , what percent of the job does david do ?
Options: a ) 35 % , b ) 28 % , c ) 26 % , d ) 20 % , e ) 25 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 12 donuts which is the job ( i picked this as a smart number ) . john on his own works 12 / 4 = 3 donuts per hour . john and david work 12 / 3 = 4 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 3 hours = 3 donuts per hour . therefore 3 donuts / 12 donuts = 1 / 4 = 25 % answer : e"
Answer: e
Problem: the length of the longest tape in cm which can be used to measure exactly , the length 6 m ; 5 m ; and 12 m is :
Options: a ) 200 , b ) 100 , c ) 50 , d ) 1200 , e ) 500
Rationale: the three lengths in cm are 600,500 & 1200 . hcf of 600 , 500 & 1200 is 100 hence , the answer is 100 cm . answer : b
Answer: b
Problem: a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 84 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 84 / 21 = 4 hours answer is a"
Answer: a
Problem: 7.007 / 2.002 =
Options: a ) 3.05 , b ) 3.50035 , c ) 3.501 , d ) 3.5035 , e ) 3.5
Rationale: "7.007 / 2.002 = 7007 / 2002 = 7 ( 1001 ) / 2 ( 1001 ) = 7 / 2 = 3.5 the answer is e ."
Answer: e
Problem: the average of first 40 prime numbers is ?
Options: a ) 15.41 , b ) 16.41 , c ) 15.61 , d ) 15 , e ) 16.91
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) / 12 = 197 / 12 = 16.41 ( approx ) answer is b"
Answer: b
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 198 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1650 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 198 . ∴ x 16 x 9 / 12 x 1 / 100 } = 198 or x = 1650 . ∴ p . w . = rs . 1650 . answer c"
Answer: c
Problem: find the number , difference between number and its 3 / 5 is 56 .
Options: a ) 140 , b ) 143 , c ) 144 , d ) 145 , e ) 150
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 56 , = > ( 2 / 5 ) x = 56 = > 2 x = 56 * 5 , = > x = 140 answer : option a"
Answer: a
Problem: how many seconds will a 600 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 22 , b ) 36 , c ) 99 , d ) 77 , e ) 12
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 600 * 3 / 50 = 36 sec . answer : b"
Answer: b
Problem: nicky and cristina are running a 200 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 35 , b ) 30 , c ) 45 , d ) 40 , e ) 50
Rationale: the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . b
Answer: b
Problem: a train 200 m long is running with a speed of 54 kmph . in what will it pass a car whose speed at 36 kmph in the direction opposite to that in which the train is going
Options: a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 15 sec
Rationale: "explanation : speed of the train relative to man = ( 54 + 36 ) kmph = 90 × 5 / 18 m / sec = 25 m / sec . time taken by the train to cross the car = time taken by it to cover 200 m at 25 m / sec = ( 200 × 1 / 25 ) sec = 8 sec answer : option a"
Answer: a
Problem: a sum of 12,500 amounts to 15,500 in 4 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 6 % , d ) 5 % , e ) 8 %
Rationale: c 6 % s . i . = ( 15500 - 12500 ) = 3000 . rate = ( 100 x 3000 ) / ( 12500 x 4 ) % = 6 %
Answer: c
Problem: car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 72 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 12 : 7 , c ) 13 : 7 , d ) 65 : 36 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 65 ã — 8 = 520 km distance travelled by car b = 72 ã — 4 = 288 km ratio = 520 / 288 = 65 : 36 d"
Answer: d
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 85 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 85 * 3 = 255 jerry wants the average to be = 87 hence total score on 4 tests should be = 87 * 4 = 348 score required on the fourth test = 348 - 255 = 93 option d"
Answer: d
Problem: a number exceeds by 20 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45
Rationale: "x – 3 / 8 x = 20 x = 32 answer : a"
Answer: a
Problem: the radius of the two circular fields is in the ratio 3 : 5 the area of the first field is what percent less than the area of the second ?
Options: a ) 23 % , b ) 62 % , c ) 92 % , d ) 64 % , e ) 22 %
Rationale: "r = 3 π r 2 = 9 r = 5 π r 2 = 25 25 π – 16 π 100 - - - - ? = > 64 % answer : d"
Answer: d
Problem: find the lowest common multiple of 25 , 35 and 50 .
Options: a ) 350 , b ) 420 , c ) 510 , d ) 320 , e ) 280
Rationale: lcm = 2 * 5 * 5 * 7 = 350 . answer is a
Answer: a
Problem: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 580 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 892 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 580 = > x = ( 580 * 100 ) / 65 = 892 answer d"
Answer: d
Problem: country x imported approximately $ 1.20 billion of goods in 1996 . if country x imported $ 288 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 24 million , b ) $ 120 million , c ) $ 144 million , d ) $ 240 million , e ) $ 528 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.20 bill = $ 1200 mill i . e . 1200 / 12 = $ 100 mill / month 1997 imports = $ 288 mill / 2 month i . e . $ 144 mill / month difference / month = 144 - 100 = 44 difference / year = $ 44 mill * 12 = $ 528 mill answer : e"
Answer: e
Problem: a man goes from a to b at a speed of 21 kmph and comes back to a at a speed of 21 kmph . find his average speed for the entire journey ?
Options: a ) 23.3 kmph , b ) 25.3 kmph , c ) 22.5 kmph , d ) 22.3 kmph , e ) 22.9 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 21 ) + ( d / 24 ] = ( 2 d ) / [ 15 d / 168 ) = > 22.3 kmph . answer : d"
Answer: d
Problem: a man rows his boat 72 km downstream and 30 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 5 kmph , c ) 2 kmph , d ) 8 kmph , e ) 7 kmph
Rationale: "speed downstream = d / t = 72 / ( 3 ) = 24 kmph speed upstream = d / t = 30 / ( 3 ) = 10 kmph the speed of the stream = ( 24 - 10 ) / 2 = 7 kmph answer : e"
Answer: e
Problem: a certain fruit stand sold apples for $ 0.70 each and bananas for $ 0.60 each . if a customer purchased both apples and bananas from the stand for a total of $ 5.60 , what total number of apples and bananas did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let ' s start with 1 apple for $ 0.70 . let ' s subtract $ 0.70 from $ 5.60 until we get a multiple of $ 0.60 . $ 5.60 , $ 4.90 , $ 4.20 = 7 * $ 0.60 the customer purchased 7 bananas and 2 apples . the answer is b ."
Answer: b
Problem: 25 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 5 : 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let x be the amount of liquid q to be added . ( 2 / 5 ) * 25 + x = ( 4 / 9 ) * ( 25 + x ) 450 + 45 x = 500 + 20 x 25 x = 50 x = 2 the answer is b ."
Answer: b
Problem: an amount of rs . 1560 was divided among a , b and c in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) rs . 278 , b ) rs . 361 , c ) rs . 369 , d ) rs . 360 , e ) rs . 363
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 a : b : c = 6 / 12 : 4 / 12 : 3 : 12 = 6 : 4 : 3 share of c = 3 / 13 * 1560 = rs . 360 . answer : d"
Answer: d
Problem: elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.20 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c .
Answer: c
Problem: walking at 5 / 6 th of its usual speed a cab is 6 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 30 m , c ) 32 m , d ) 50 m , e ) 62 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 6 m ut / 5 = 6 m ut = 30 m answer is b"
Answer: b
Problem: on the number line , if x is halfway between - 6 and 4 , and if y is halfway between - 2 and 6 , what number is halfway between x and y ?
Options: a ) - 2.5 , b ) - 1.5 , c ) - 0.5 , d ) 0.5 , e ) 1.5
Rationale: "x = - 1 and y = 2 . the answer is d ."
Answer: d
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 50 - 50 )
Options: a ) 337 , b ) 437 , c ) 457 , d ) 537 , e ) 412
Rationale: "there are 51 digits in 10 ^ 50 when we subtract 50 from it , there will be 50 digits left . 10 ^ 50 can be written as 9999999 . . . . ( 50 times ) + 1 so , 10 ^ 50 - 50 = 9999999 . . . . ( 50 times ) + 1 - 50 = 9999999 . . . . ( 50 times ) - 49 consider the last 2 digits , 99 - 49 = 50 the last 2 digits will be 50 . and our number would be 99999 . . . . . . 99950 with 2 less 9 s after subtraction . number of 9 s left are 48 and the last two digits are 50 the sum of the digits will be ( 48 * 9 ) + 5 + 0 = 437 answer : - b"
Answer: b
Problem: what is the least number which when divided by 6 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 30 , b ) 40 , c ) 36 , d ) 56 , e ) 66
Rationale: "explanation : lcm of 6 , 9 , 12 and 18 is 36 required number = 36 + 4 = 40 answer : option b"
Answer: b
Problem: the population of a town increased from 1 , 75,000 to 2 , 80,000 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 280000 - 175000 ) = 105000 . increase % = ( 105000 / 175000 ã — 100 ) % = 60 % . required average = ( 60 / 10 ) % = 6 % . answer c"
Answer: c
Problem: a bullet train 200 m long is running with a speed of 69 kmph . in what time will it pass a man who is running at 3 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 10 sec , b ) 15 sec , c ) 12 sec , d ) 11 sec , e ) 16 sec
Rationale: "a 10 sec speed of the bullet train relative to man = ( 69 + 3 ) kmph = 72 * 5 / 18 m / sec = 60 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 200 m at ( 60 / 3 ) m / sec = ( 200 * 3 / 60 ) sec = 10 sec"
Answer: a
Problem: in what time will a railway train 90 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 1 sec , c ) 9 sec , d ) 6 sec , e ) 2 sec
Rationale: "t = 90 / 36 * 18 / 5 = 9 sec answer : c"
Answer: c
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6800 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9942 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6800 1 = 6800 / 68.4 100 = ( 6800 * 100 ) / 68.4 = rs . 9942 . answer : option d"
Answer: d