regisss/math_qa huggingface dataset:
Problem: if k is the greatest positive integer such that 4 ^ k is a divisor of 16 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "16 / 4 = 4 16 / 16 = 1 4 + 1 = 5 k = 5 answer : c"
Answer: c
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 20 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 767 , e ) 432
Rationale: "1 h - - - - - 4 ? - - - - - - 60 12 h rs = 16 + 20 = 36 t = 12 d = 36 * 12 = 432 answer : e"
Answer: e
Problem: johnny makes $ 8.25 per hour at his work . if he works 2 hours , how much money will he earn ?
Options: a ) $ 30.50 , b ) $ 16.50 , c ) $ 28.50 , d ) $ 12 , e ) $ 9.60
Rationale: 8.25 * 2 = 16.50 . answer is b .
Answer: b
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number t ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = t answer : b"
Answer: b
Problem: how many positive integers less than 5,000 are evenly divisible by neither 18 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 18 5000 / 18 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 18 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 18 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4428 answer d ."
Answer: d
Problem: evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70"
Answer: d
Problem: if xy denotes x is raised to the power y , find the last two digits of 19413844 + 19714181
Options: a ) 154 , b ) 677 , c ) 784 , d ) 148 , e ) 132
Rationale: "1941 ^ 3844 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 4 = 16 = 2 means last two digit = 61 and 1971 ^ 4181 unit digit = 1 10 th digit = 7 * 1 = 7 mean last two digit = 71 hence , 71 + 61 = 132"
Answer: e
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 172 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 172 = > 4 x / 10 = 172 = > 4 x = 1720 = > x = 430 . answer : a"
Answer: a
Problem: 12 buckets of water fill a tank when the capacity of each bucket is 55 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 5 litres ?
Options: a ) 142 , b ) 130 , c ) 132 , d ) 123 , e ) 120
Rationale: "capacity of the tank = ( 12 ã — 55 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 55 / 5 = 12 ã — 11 = 132 answer is c"
Answer: c
Problem: yesterday i noticed that in my clock , there is time when the hour needle and the minute needle are exactly between 1 and 2 . also both the needles lie on top of each other . what time i and talking about ?
Options: a ) 10 : 00 , b ) 11 : 00 , c ) 09 : 00 , d ) 12 : 00 , e ) 07 : 00
Rationale: d 12 : 00 both minute and hour clock lie exactly between the number one and two in the number .
Answer: d
Problem: a watch was sold at a loss of 46 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 280 , b ) 288 , c ) 279 , d ) 277 , e ) 290
Rationale: "54 % 104 % - - - - - - - - 50 % - - - - 140 100 % - - - - ? = > rs . 280 answer : a"
Answer: a
Problem: ( 168 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 354 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 168 x 1265 / 100 ) ÷ 6 = 212520 / 600 = 354 answer : option a"
Answer: a
Problem: there are 15 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 650 , b ) 750 , c ) 850 , d ) 950 , e ) 1050
Rationale: "the number of ways to choose two teams is 15 c 2 = 15 * 14 / 2 = 105 the total number of games in the season is 10 * 105 = 1050 . the answer is e ."
Answer: e
Problem: if 3 : 12 : : x : 16 , then find the value of x
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : treat 3 : 12 as 3 / 12 and x : 16 as x / 16 , treat : : as = so we get 3 / 12 = x / 16 = > 12 x = 48 = > x = 4 option b
Answer: b
Problem: bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 8 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 10 left in his pocket . what was the value of n ?
Options: a ) $ 32 , b ) $ 36 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer b if he had 36 , then he spent 9 at hardware store now he was left with 27 $ he spent 8 dollars on cleaning , thus he remained with 19 $ he then spent 1 / 2 of 19 , or 9.50 , hence , the only option that can be right is a . ans a"
Answer: a
Problem: john can complete a given task in 20 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 4 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 6 , b ) 10 , c ) 8 , d ) 7.5 , e ) 3.5
Rationale: "john 6 * 20 = 120 jane 10 * 12 = 120 in 4 days working alone john did : 4 days * rate = 4 * 6 = 24 , so working together they did 120 - 24 = 96 - - > rate ( a + b ) * t = 96 - > 16 * t = 96 , t = 6 . hence the answer is b ( john worked 4 days + 6 days they worked together = 10 days )"
Answer: b
Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 1 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 45 , c ) 270 , d ) 90 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 1 / 3 ) of total igneous rocks . ( 1 / 3 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 3 ) = 90 total sedimentary rocks = 2 * total igneous rocks = 2 * 90 = 180 total number of rocks = 90 + 180 = 270 answer ( c )"
Answer: c
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 5 / 6 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 4 / 7 , b ) 5 / 9 , c ) 6 / 11 , d ) 7 / 12 , e ) 8 / 13
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 5 x / 6 ) ( 3 y / 4 ) = 5 xy / 8 the total number of boxes is xy + 5 xy / 8 = 13 xy / 8 the fraction loaded by the day crew is xy / ( 13 xy / 8 ) = 8 / 13 the answer is e ."
Answer: e
Problem: a man has some hens and cows . if the number of heads be 50 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 30 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 50 implies , 2 x + 4 y = 140 and x + y = 50 solving these two equations , we get x = 30 and y = 20 therefore , hens are 26 . answer : d"
Answer: d
Problem: the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 4.4 miles in the fifth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 45 , b ) 48 , c ) 51 , d ) 54 , e ) 57
Rationale: "( 4.4 miles / 8 minutes ) * 60 minutes / hour = 33 mph let x be the original speed . x - 4 ( 3 ) = 33 x = 45 mph the answer is a ."
Answer: a
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 9 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 36.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.91 * 150 x = 136.5 x hence total profit = 36.5 % option d"
Answer: d
Problem: if p / q = 6 / 7 , then 2 p + q = ?
Options: a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 19
Rationale: "let p = 6 , q = 7 then 2 * 6 + 7 = 19 so 2 p + q = 19 . answer : e"
Answer: e
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 9 minutes , then the area of the park ( in sq . m ) is
Options: a ) 153200 , b ) 153400 , c ) 153600 , d ) 194400 , e ) 154200
Rationale: "perimeter = distance covered in 9 min . = 12000 x 9 m = 1800 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1800 or x = 180 . length = 540 m and breadth = 360 m . area = ( 540 x 360 ) m 2 = 194400 m 2 . d"
Answer: d
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.08 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fourth day it is overdue ?
Options: a ) $ 0.62 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.08 2 nd day fine - 0.08 * 2 = 0.16 ( as doubling gives lower value ) 3 rd day fine - 0.16 * 2 = 0.32 ( as doubling gives lower value ) 4 th day fine - 0.32 + 0.3 = 0.62 ( as doubling gives higher value we add 0.3 this time ) answer : a ."
Answer: a
Problem: it is currently 7 : 05 pm . what time was it in the morning exactly 51132 minutes ago ?
Options: a ) 6 : 53 , b ) 6 : 55 , c ) 6 : 59 , d ) 7 : 03 , e ) 7 : 09
Rationale: convert 51,132 minutes to hours by dividing by 60 : 51,132 / 60 = 852 r 12 . that is 852 hours , 12 minutes . convert 852 hours to days by dividing by 24 : 852 / 24 = 35 r 12 . that is 35 days , 12 hours . thus 852 hours before 7 : 05 pm is 12 hours before 7 : 05 pm which is 7 : 05 am . 12 minutes before that is 6 : 53 am . a
Answer: a
Problem: mary and mike enter into a partnership by investing $ 800 and $ 200 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1200 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3000 , b ) $ 3500 , c ) $ 4000 , d ) $ 4200 , e ) $ 4500
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 8 : 2 . i . e . , 80 % of 2 x would go to mary and 20 % of 2 x would go to mike . hence , mary would get ( 80 - 20 ) % of 2 x more than mike or 60 % of 2 x = $ 1200 i . e . , ( 60 / 100 ) * 2 x = 1200 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a"
Answer: a
Problem: the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4332 sq cm . what is the ratio of the width and the area of the rectangle ?
Options: a ) 1 : 72 , b ) 1 : 76 , c ) 1 : 80 , d ) 1 : 84 , e ) 1 : 88
Rationale: "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4332 12 x ^ 2 = 4332 x ^ 2 = 361 x = 19 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 76 the answer is b ."
Answer: b
Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 30 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a = 3.1 and b is very small , then a ^ 3 + b ^ 3 can equal 30 . if a > 4 , then a ^ 3 + b ^ 3 > 30 . the answer is b ."
Answer: b
Problem: an owner of a pizza stand sold small slices of pizza for rs . 150 each and large slices for rs . 250 each . one night he sold 5000 slices , for a total of rs . 10.50 lakh . how many small slices were sold ?
Options: a ) 3000 , b ) 2000 , c ) 4000 , d ) 2500 , e ) 3500
Rationale: explanatory answer this question is a word problem in linear equations . the problem is solved by framing two linear equations from the information given in the question and solving them . let ' s ' be the number of small slices and ' b ' the number of large slices sold on that night . therefore , s + b = 5000 . . . eqn ( 1 ) each small slice was sold for rs . 150 . therefore , ' s ' small slices would have fetched rs . 150 s . each large slice was sold for rs . 250 . therefore , ' b ' large slices would have fetched rs . 250 b . total value of sale = 150 s + 250 b = 10 , 50000 ( note the left hand side is in rupees and hence we have to convert right hand also to rupees from lakhs of rupees ) or 150 s + 250 b = 10 , 50000 . . . eqn ( 2 ) multiplying equation ( 1 ) by 150 , we get 150 s + 150 b = 7 , 50000 . . . eqn ( 3 ) subtracting eqn ( 3 ) from eqn ( 2 ) , we get 100 b = 300000 or b = 3000 we know that s + b = 5000 so , s = 5000 - b = 5000 - 3000 = 2000 . 2000 small slices were sold . answer b
Answer: b
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 189 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 189 km time taken = distance / speed = 189 / 27 = 7 hours . answer : option e"
Answer: e
Problem: light glows for every 21 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 236 times , c ) 382 times , d ) 392 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 21 ) = 236 times . answer : b"
Answer: b
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 240 = 600 m required time = 600 * 2 / 25 = 48 sec answer : d"
Answer: d
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 12 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1232 , d ) s . 1202 , e ) s . 1204
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 12 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1232 . answer : c"
Answer: c
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes have only one face coloured ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 24 , e ) 2
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having only one face coloured = ( x - 2 ) 2 x no . of faces = ( 4 - 2 ) ^ 2 x 6 = 24 answer : d"
Answer: d
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 20 percent on clothing , 50 percent on food , and 30 percent on other items . if jill paid a 10 percent tax on the clothing , 15 percent tax on the food , and no tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 12.45 , b ) 12.5 , c ) 12.65 , d ) 12.35 , e ) 12.25
Rationale: "assume she has $ 200 to spend . tax clothing = 20 % = $ 40 = $ 10.00 food = 50 % = $ 100 = $ 15.00 items = 30 % = $ 60 = $ 0.00 total tax = $ 25.00 % of total amount = 25 / 200 * 100 = 12.25 % answer e"
Answer: e
Problem: if there are 26 laborers in a crew , and on a certain day , 10 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 39.5 % , b ) 38.5 % , c ) 36.5 % , d ) 37.5 % , e ) 30.5 %
Rationale: "10 / 26 * 100 = 38.46 38.5 % correct answer b"
Answer: b
Problem: how many 3 - digit numbers can be formed from the digits 2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and if the repetition is allowed ?
Options: a ) 20 , b ) 5 , c ) 10 , d ) 36 , e ) 25
Rationale: "since , each desired number is divisible by 5 , so we must have 5 at the unit place . so , the tens place can now be filled by any of the remaining 6 digits ( 2 , 3 , 6 , 7 , 9 , 5 ) therefore the 3 - digit no can be formed by ( 6 * 6 * 1 ) = 36 ways - - - - - - ( since repetition is allowed ) ans - d"
Answer: d
Problem: the profit obtained by selling an article for rs . 66 is the same as the loss obtained by selling it for rs . 52 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) none of these
Rationale: "s . p 1 - c . p = c . p – s . p 2 66 - c . p = c . p - 52 2 c . p = 66 + 52 ; c . p = 118 / 2 = 59 answer : d"
Answer: d
Problem: if 7 and 9 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 14 , e ) 21
Rationale: "60 n / 7 * 9 should be integer = > 2 * 2 * 3 * 5 * n / 7 * 3 * 3 = 2 * 2 * 5 * n / 21 must be an integer for this to be true n must multiple of 21 , thus min of n = 21 hence e"
Answer: e
Problem: a bag contains 5 red , 4 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 33 , d ) 4 / 27 , e ) 3 / 23
Rationale: "p ( both are red ) , = 5 c 212 c 2 = 5 c 212 c 2 = 10 / 66 = 5 / 33 c"
Answer: c
Problem: in an election between two candidates , the first candidate got 70 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "let v be the total number of votes . 0.3 v = 240 v = 800 the answer is a ."
Answer: a
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 38 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 86.66 % , e ) 66.66 %
Rationale: - - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 38 % 0.4 x + ( m - x ) 0.25 = 0.38 m 0.15 x = 0.13 m x = 0.8666 m x = 86.66 % of m d
Answer: d
Problem: find the product of the localvalue and absolutevalue of 5 in 20568 ?
Options: a ) 1000 , b ) 2500 , c ) 1200 , d ) 5000 , e ) 1600
Rationale: "local value of 5 = 5 x 100 = 500 place value of 5 = 5 there fore = 5 x 500 = 2500 b"
Answer: b
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 9.09 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 10 / 11 = ( 1 + p % ) profit % = 25 % answer : d"
Answer: d
Problem: a 1.5 by 2 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 2.5 π
b ) 3 π
c ) 3.5 π
d ) 4 π
e ) 5.5 π
Rationale: the diagonal of the rectangle will be the diameter of the circle . and perimeter = 2 * pi * r ans : a
Answer: a
Problem: a sum of rs . 2665 is lent into two parts so that the interest on the first part for 5 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 ) rs . 1178.55 , b ) rs . 1978.25 , c ) rs . 1332.5 , d ) rs . 1678 , e ) rs . 1675.55
Rationale: "( x * 5 * 3 ) / 100 = ( ( 2665 - x ) * 3 * 5 ) / 100 15 x / 100 = 39975 / 100 - 15 x / 100 30 x = 39975 = > x = 1332.5 second sum = 2665 – 1025 = 1332.5 answer : c"
Answer: c
Problem: 2 , 3 , 6 , 15 , _ , 123 ?
Options: a ) 42 , b ) 38 , c ) 28 , d ) 29 , e ) 11
Rationale: answer : a
Answer: a
Problem: nitin ranks 15 th in a class of 47 students . what is rank from the last ?
Options: a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19
Rationale: "explanation : number students behind the nitin in rank = ( 47 - 15 ) = 32 nitin is 33 rd from the last answer : a ) 33"
Answer: a
Problem: cole drove from home to work at an average speed of 70 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 70 time from work to home = x / 105 total time = 2 hrs ( x / 70 ) + ( x / 105 ) = 2 solving for x , we get x = 84 time from home to work in minutes = ( 84 ) * 60 / 70 = 72 minutes ans = c"
Answer: c
Problem: what is the least common multiple of 152 and 190 ?
Options: a ) 304 , b ) 14440 , c ) 760 , d ) 28880 , e ) 1520
Rationale: "yes there is a shorter way 152 = 2 * 2 * 2 * 19 190 = 2 * 5 * 19 i think everyone knows how to do this . then choose 2 * 2 * 2 and choose 5 and choose 19 2 * 2 * 2 * 5 * 19 = 760 answer is c"
Answer: c
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 1220 , b ) 1650 , c ) 1920 , d ) 2440 , e ) 2860
Rationale: "there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 30 * 64 = 1920 . the answer is c ."
Answer: c
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 289 cm 2
b ) 285 cm 2
c ) 287 cm 2
d ) 267 cm 2
e ) 207 cm 2
Rationale: area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : b
Answer: b
Problem: canister c is 1 / 2 full of water and canister d , which has twice the capacity of canister c , is 1 / 3 full of water . if the water in canister d is poured in canister c until canister c is completely full of water , canister d will still contain what fraction of its capacity of water ?
Options: a ) 0 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4
Rationale: say canister c has a capacity of 6 liters . it ' s half full , thus there can be poured 3 liters of water . canister b is 12 liters and there are 4 liters of water . we can pour 3 liters from d to c and 1 liter will still be left in d , which is 1 / 12 of its total capacity . answer : c .
Answer: c
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 6000 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 100
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 6000 x = 100 the numbers are 3 * 100 , 4 * 100 , 5 * 100 hence required h . c . f . = 100 answer is e"
Answer: e
Problem: jose is uploading a file to the internet for a college project . the file weighs 160 megabytes . if jose ' s internet speed for uploading tops 8 megabytes per minute , how long will it take until the upload is completed ?
Options: a ) 1 hour , b ) 45 minutes , c ) 20 minutes , d ) 5 minutes , e ) 1 hour and 10 minutes
Rationale: answer is ( c ) . jose calculates that if the files weighs 160 megabytes , and his internet uploads at 8 megabytes per minute , it would take 20 minutes to upload as 160 divided by 8 megabytes per minute equals 20 .
Answer: c
Problem: the average monthly salary of 20 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3700 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 2891
Rationale: "explanation : manager ' s monthly salary rs . ( 1700 * 21 - 1600 * 20 ) = rs . 3700 . answer : a ) 3700"
Answer: a
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 19000 left with him . find salary . .
Options: a ) $ 10900 , b ) $ 19000 , c ) $ 190000 , d ) $ 1900 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 19000 , = [ 1 - 9 / 10 ] * total salary = $ 19000 , total salary = $ 19000 * 10 = $ 190000 , correct answer ( c )"
Answer: c
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 30 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.10 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 30 % of 1100 ) + ( 32 % of 900 ) = 330 + 288 = 618 failed = 2000 - 618 = 1382 failed % = [ ( 1382 / 2000 ) x 100 ] % = 69.1 % . answer : d"
Answer: d
Problem: if 2 x + y = 7 and x + 2 y = 10 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 9 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 7 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 17 divide both sides by 3 to get : x + y = 17 / 3 so , ( x + y ) / 3 = 17 / 9 answer : c"
Answer: c
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 40 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 110 , c ) 120 , d ) 16 , e ) 180
Rationale: "c 120 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 40 mph = 120 miles"
Answer: c
Problem: puzzle ! ! ! 🙂 if 111 = 09 444 = 12 777 = 15 then 888 = ? ? ?
Options: a ) 13 , b ) 17 , c ) 18 , d ) 11 , e ) 15
Rationale: e 15 one + one + one ( 3 + 3 + 3 ) = 09 four + four + four ( 4 + 4 + 4 ) = 12 seven + seven + seven ( 5 + 5 + 5 ) = 15 therefore eight + eight + eight ( 5 + 5 + 5 ) = 15
Answer: e
Problem: town m town n town o town p town q town r ; town a town b town c town d town e town f in the table above , what is the least number of table entries that are needed to show the mileage between each town and each of the other 5 towns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: easy way to go about this problem is we have 6 * 6 = 36 enteries in table the least number of enteries would be ( 36 - 6 ) / 2 since 6 enteries represent the distances between same points . alternatively this can be solved as combination problem . correct answer e
Answer: e
Problem: what is the greatest of 3 consecutive integers whose sum is 33 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "33 / 3 = 11 the three numbers are 10 , 11 , and 12 . the answer is c ."
Answer: c
Problem: a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 45 - sided polygon have ?
Options: a ) 875 , b ) 945 , c ) 1425 , d ) 2025 , e ) 2500
Rationale: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 45 . plugging it in , we get 945 diagonals ! answer ( b ) ."
Answer: b
Problem: divide rs . 1600 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) rs . 800 , b ) rs . 400 , c ) rs . 600 , d ) rs . 500 , e ) rs . 900
Rationale: "a + b + c = 1600 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1600 = > 400 answer : b"
Answer: b
Problem: 112 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 26 , c ) 49 , d ) 27 , e ) 11
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 112 = 49 answer : c"
Answer: c
Problem: a , b and c started a shop by investing rs . 5,000 , rs . 15,000 and rs . 30,000 respectively . at the end of the year , the profits were distributed among them . if c â € ™ s share of profit be rs . 3000 , then the total profit was :
Options: a ) 30,000 , b ) 5,000 , c ) 80,000 , d ) 120,000 , e ) none
Rationale: sol . a : b : c = 5000 : 15000 : 30000 = 1 : 3 : 6 . so , c â € ™ s share : total profit = 6 : 10 let the total profit be rs . x . then , 6 / 10 = 3000 / x or x = 3000 * 10 / 6 = 5000 . answer b
Answer: b
Problem: christine selects an item at a 25 % off ticket price sale . the item is ticket priced at $ 25 . how much should christine expect to pay at the register ?
Options: a ) 22.5 , b ) 20.0 , c ) 18.75 , d ) 12.5 , e ) 10.0
Rationale: r . p . = $ 25.00 sale % = 25 s . p . = r . p . * ( 1 - ( sale % / 100 ) ) = 25 * ( 1 - ( 25 / 100 ) ) = 18.75 answer : c
Answer: c
Problem: two employees x and y are paid a total of rs . 500 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 227 , b ) s . 287 , c ) s . 297 , d ) s . 300 , e ) s . 380
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 500 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 500 ⇒ y [ 12 / 10 + 1 ] = 500 ⇒ 22 y / 10 = 500 ⇒ 22 y = 5000 ⇒ y = 5000 / 22 = rs . 227.77 a )"
Answer: a
Problem: if the perimeter of square region e and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of e
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pe ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pe = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 30 days to complete the same work . then q alone can do it in
Options: a ) 10 , b ) 22 , c ) 25 , d ) 27 , e ) 30
Rationale: work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 30 work done by p , q and r in 1 day = 1 / 10 + 1 / 30 = 4 / 30 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 4 / 30 = > work done by p in 1 day = 4 / 60 = > work done by q and r in 1 day = 4 / 60 hence work done by q in 1 day = 4 / 60 â € “ 1 / 30 = 2 / 60 = 1 / 30 so q alone can do the work in 30 days answer is e .
Answer: e
Problem: calculate the average of all the numbers between 11 and 27 which are divisible by 2 .
Options: a ) 11 , b ) 10 , c ) 18 , d ) 19 , e ) 21
Rationale: "explanation : numbers divisible by 2 are 12,14 , 16,18 , 20,22 , 24,26 , average = ( 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 , ) / 8 = 152 / 8 = 19 answer : d"
Answer: d
Problem: we had $ 3500 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 4600 , b ) $ 4800 , c ) $ 5000 , d ) $ 5200 , e ) $ 5400
Rationale: "let x be the amount of money we started with . 0.7 x = 3500 x = 5000 the answer is c ."
Answer: c
Problem: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 40 million gallons of water . this amount is one fifth of the normal level . if this amount represents 80 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 40 mg = 80 % of total . . total = 40 / . 8 = 50 mg . . normal level = 1 / 5 of 50 = 10 mg . . shortage of normal level = 50 - 10 = 40 mg . . c"
Answer: c
Problem: on a certain farm the ratio of horses to cows is 3 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 5 : 3 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "originally , there were 3 k horses and k cows . 3 ( 3 k - 15 ) = 5 ( k + 15 ) 9 k - 5 k = 75 + 45 4 k = 120 k = 30 the difference between horses and cows is ( 3 k - 15 ) - ( k + 15 ) = 2 k - 30 = 30 the answer is b ."
Answer: b
Problem: what is the total number of integers between 2 and 38 that are divisible by 4 ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 11
Rationale: "4 , 6 , 8 , . . . , 32,36 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 36 - 4 ) / ( 4 ) + 1 = 32 / 4 + 1 = 8 + 1 = 9 answer is b"
Answer: b
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 7 rows or 6 rows or 4 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 84 , c ) 28 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 7 , 6,4 ) = 84 . answer : b"
Answer: b
Problem: the number n is 5 , h 64 , where h represents the 100 ' s digit . if n is divisible by 4 , what is the value of h ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) all the above value
Rationale: if the number is divisible by 4 , the last two digits must be divisible by 4 . all the values yields such a number . answer : e
Answer: e
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 22 } + { 20 } ?
Options: a ) 23 , b ) 20 , c ) 11 , d ) 5 , e ) 2
Rationale: "soln : { 22 } + { 20 } = 22 * { 20 } + { 20 } = 23 * { 20 } answer : a"
Answer: a
Problem: what is the maximum number t of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options: a ) 36
b ) 32
c ) 24
d ) 21
e ) 15
Rationale: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get t = 24 cubes . ans . c
Answer: c
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1480 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 400 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 1480 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 1480 3.7 z = 1480 , z = 400 answer : . d"
Answer: d
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 70 , b ) 25 , c ) 60 , d ) 80 , e ) 55
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 5 years , their ages will be 45 and 25 . sum of their ages = 45 + 25 = 70 . answer a"
Answer: a
Problem: if the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 5 : 6 , d ) 1 : 4 , e ) 3 : 4
Rationale: "the ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6 . the ratio of apples to bananas to cucumbers is 5 to 2 to 6 . the ratio of apples to cucumbers is 5 to 6 . the answer is c ."
Answer: c
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,6 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 6 = 12 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 12 = 2 / 3 the answer is d ."
Answer: d
Problem: the edge of a cube is 4 a cm . find its surface ?
Options: a ) 24 a 8 , b ) 24 a 4 , c ) 96 a 2 , d ) 24 a 2 , e ) 24 a 7
Rationale: "6 a 2 = 6 * 4 a * 4 a = 96 a 2 answer : c"
Answer: c
Problem: the ratio of the present age of two brothers is 1 : 2 and 5 years back , the ratio was 1 : 3 . what will be the ratio of their ages after 5 years ?
Options: a ) 3 : 9 , b ) 3 : 0 , c ) 3 : 5 , d ) 3 : 2 , e ) 3 : 1
Rationale: let the present ages of the two brothers be x and 2 x years respectively . then , ( x - 5 ) / ( 2 x - 5 ) = 1 / 3 3 ( x - 5 ) = ( 2 x - 5 ) = > x = 10 required ratio = ( x + 5 ) : ( 2 x + 5 ) = 15 : 25 = 3 : 5 answer : c
Answer: c
Problem: find the least number must be subtracted from 724946 so that remaining no . is divisible by 10 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "on dividing 724946 by 10 we get the remainder 6 , so 6 should be subtracted d"
Answer: d
Problem: if x is 20 percent more than y and y is 30 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 84 % , e ) 60 %
Rationale: "z = 100 ; y = 70 so x = 84 x as % of z = 84 / 100 * 100 = > 84 % answer will be ( d )"
Answer: d
Problem: a truck covers a distance of 240 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 0 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 240 / 8 = 30 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 30 + 18 ) = 48 kmph distance travelled by car = 240 + 0 = 240 km time taken by car = distance / speed = 240 / 48 = 5 hours . answer – b"
Answer: b
Problem: evaluate : 57 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 49 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 57 - 12 * 3 * 2 = 57 - 8 = 49 correct answer b"
Answer: b
Problem: a mixture of 180 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 4 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 12.5 liters
Rationale: "number of liters of water in 180 liters of the mixture = 20 % of 120 = 20 / 100 * 180 = 36 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 36 + p ) and total volume of mixture is ( 180 + p ) . ( 36 + p ) = 25 / 100 * ( 180 + p ) 96 + 4 p = 180 + p p = 12 liters . answer : d"
Answer: d
Problem: the sum of all the integers k such that – 23 < k < 24 is
Options: a ) 0 , b ) - 43 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "- 22 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 22 - 21 sum of which is - 43 . hence option d . b"
Answer: b
Problem: there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) 10 , b ) 12 , c ) 24 , d ) 60 , e ) 100
Rationale: "there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ? 10 12 24 60 100 soln : total number of patterns is 5 ! since 3 red chips are identical and 2 blue ones are identical thus we have = 5 ! / ( 2 ! * 3 ! ) = 10 such different patterns a"
Answer: a
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 45 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 40 = > v = 40 ( option b ) ."
Answer: b
Problem: what is the sum between the place values of three 7 ' s in the numeral 87953.0727
Options: a ) 21 , b ) 7000.0707 , c ) 7777 , d ) 7014 , e ) 7000.0077
Rationale: "required sum = 7000 + 0.0700 + 0.0007 = 7000.0707 answer is b"
Answer: b
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 18 , d ) d ) 56 , e ) e ) 12
Rationale: "let the total number of workers be x . then , 8000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 2000 x = 36000 = x = 18 . answer : c"
Answer: c
Problem: two good train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none
Rationale: sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 500 + 500 ) m = 1000 m . required time = ( 1000 x 6 / 125 ) sec = 48 sec . answer c
Answer: c
Problem: in a tree , 2 / 5 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 2 / 3 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 3 / 5 , b ) 4 / 15 , c ) 7 / 15 , d ) 8 / 15 , e ) 17 / 30
Rationale: the fraction of birds that are male robins is ( 2 / 3 ) ( 2 / 5 ) = 4 / 15 . the fraction of birds that are male bluejays is ( 1 / 3 ) ( 3 / 5 ) = 1 / 5 . the total fraction of male birds is 4 / 15 + 1 / 5 = 7 / 15 . the answer is c .
Answer: c
Problem: what distance will be covered by a bus moving at 90 kmph in 20 seconds ?
Options: a ) 500 , b ) 600 , c ) 289 , d ) 276 , e ) 207
Rationale: "90 kmph = 90 * 5 / 18 = 25 mps d = speed * time = 25 * 20 = 500 m . answer : a"
Answer: a
Problem: in traveling from a dormitory to a certain city , a student went 1 / 2 of the way by foot , 1 / 4 of the way by bus , and the remaining 6 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 35 , b ) 24 , c ) 14 , d ) 24 , e ) 12
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 1 / 4 x + 6 x - 1 / 2 x - 1 / 4 x = 6 x = 24 km option : d"
Answer: d
Problem: the speed of a car is 80 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 70 kmph , c ) 87 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 80 + 60 ) / 2 = 70 kmph answer : b"
Answer: b
Problem: if a town of 15,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 16000 , b ) b . 17000 , c ) c . 18000 , d ) d . 19000 , e ) e . 20000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Problem: the ratio , by volume , of bleach ( b ) to detergent ( d ) to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 60
b ) 50
c ) 40
d ) 80
e ) 70
Rationale: b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be a
Answer: a
Problem: when 0.232323 . . . . . is converted into a fraction , then the result is
Options: a ) 23 / 99 , b ) 2 / 9 , c ) 1 / 5 , d ) 23 / 100 , e ) 23 / 98
Rationale: 0.232323 . . . = 0.23 = 23 / 99 answer is a .
Answer: a
Problem: in a garden , 26 trees are planted at equal distances along a yard 400 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 12 , d ) 14 , e ) 16
Rationale: 26 trees have 25 gaps between them . length of each gap = 400 / 25 = 16 i . e . , distance between two consecutive trees = 16 answer is e .
Answer: e
Problem: 36 men can complete a piece of work in 18 days . in how many days will 108 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 6 , d ) 29 , e ) 21
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 108 : 36 : : 18 : x x = 6 answer : c ) 6 days"
Answer: c
Problem: the length and breadth of a rectangle is increased by 11 % and 22 % respectively . what is the increase in the area ?
Options: a ) 35.22 , b ) 33.52 , c ) 35.42 , d ) 36.22 , e ) 38.42
Rationale: "100 * 100 = 10000 111 * 122 = 13542 - - - - - - - - - - - - 3542 10000 - - - - - - - 3542 100 - - - - - - - - - - 35.42 answer c"
Answer: c
Problem: the simple interest on a sum of money will be rs . 700 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 2261 , b ) 2888 , c ) 1400 , d ) 2699 , e ) 2771
Rationale: "p - - - 10 - - - - 700 p - - - 5 - - - - - 350 3 p - - - 5 - - - - - 1050 - - - - - - = > 1400 answer : c"
Answer: c
Problem: barbata invests $ 2000 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2000 + 0.05 * 2000 + x + 0.08 x = 2000 + x + 0.06 ( 2000 + x ) 0.05 * 2000 + 0.08 x = 0.06 x + 0.06 * 2000 0.02 x = 2000 ( 0.06 - 0.05 ) x = 2000 * 0.01 / 0.02 = 1000 ans : ` ` c ' '"
Answer: c