regisss/math_qa huggingface dataset:
Problem: a certain pair of used shoes can be repaired for $ 11.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 28.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 20.8 , b ) 21.46 , c ) 21.74 , d ) 22.3 , e ) 21.4
Rationale: "1 ) cost of repairing = 11.5 ( for one year ) , therefore for 2 years it would be $ 23 . 2 ) cost of new pair which will last for 2 years is $ 28 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe . i . e ( 28 - 23 ) / ( 23 ) * 100 = 21.74 % . ans is c"
Answer: c
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 80 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 40 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 80 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 80 / 10 = 8 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 8 = 40 kms . . . answer - c"
Answer: c
Problem: renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 4 days . in what time suma can do it alone ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu ’ s one day ’ s work = 1 / 6 suma ’ s one day ’ s work = 1 / 4 - 1 / 6 = 1 / 12 suma can do it alone in 12 days . answer : b"
Answer: b
Problem: working at their respective constant rates , machine a makes 100 copies in 8 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 675 , d ) 825 , e ) 750
Rationale: "machine a can produce 100 * 30 / 8 = 375 copies and , machine b can produce 150 * 30 / 10 = 825 copies total producing 700 copies . d is the answer"
Answer: d
Problem: q - 1 ) of the 84 parents who attended a meeting at a school , 25 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic . if the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments , how many of the parents volunteered to bring refreshments ?
Options: a ) 25 , b ) 36 , c ) 38 , d ) 45 , e ) 42
Rationale: i used the following formula : total = group 1 + group 2 + neither - both using the information from the question stem , we have : 84 total people 25 who supervise ( group 1 ) x who neither supervise nor bring refreshments 1.5 x people who bring refreshments ( group 2 ) 11 who supervise and bring refreshments ( both ) therefore . . . 84 = 25 + 1.5 x + x - 11 solving , we get x = 28 since we want the value of those who bring refreshments and supervise : 1.5 ( 28 ) = 42 answer is e
Answer: e
Problem: in a mayoral election , candidate x received 1 / 4 more votes than candidate y , and candidate y received 1 / 6 fewer votes than z . if z received 24,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22000 , c ) 24000 , d ) 25000 , e ) 32000
Rationale: "z = 24 - - > y received 1 / 4 fewer votes than z - - > y = z - 1 / 6 * z = 20 ; x received 1 / 4 more votes than y - - > x = y + 1 / 4 * y = 25 . answer : d ."
Answer: d
Problem: excluding stoppages , the speed of a bus is 72 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 8 min , c ) 9 min , d ) 10 min , e ) 55.8 min
Rationale: "due to stoppages , it covers 9 km less . time taken to cover 67 km = ( 67 / 72 ) x 60 = 55.8 min answer : e"
Answer: e
Problem: two cars are driving toward each other . the first car is traveling at a speed of 60 km / h , which is 25 % slower than the second car ' s speed . if the distance between the cars is 770 km , how many hours will it take until the two cars meet ?
Options: a ) 4 , b ) 4.5 , c ) 5 , d ) 5.5 , e ) 6
Rationale: "the speed of the first car is 60 km / h . the speed of the second car is 60 / 0.75 = 80 km / h . the two cars complete a total of 140 km each hour . the time it takes the cars to meet is 770 / 140 = 5.5 hours . the answer is d ."
Answer: d
Problem: in 15 year ’ s time the combined age of my 4 brothers will be 107 . what will it be in 6 year ’ s time ?
Options: a ) 65 , b ) 87 , c ) 71 , d ) 60 , e ) 66
Rationale: c 71 combined age in 15 years = 107 . 4 × 15 = 60 , therefore combined age now is 107 – 60 = 47 . in 6 years time , therefore , combined age will be 47 + 24 ( 4 × 6 ) = 71 .
Answer: c
Problem: if sharon ' s weekly salary increased by 10 percent , she would earn $ 330 per week . if instead , her weekly salary were to increase by 8 percent , how much would she earn per week ?
Options: a ) rs . 424 , b ) rs . 524 , c ) rs . 324 , d ) rs . 350 , e ) rs . 354
Rationale: "soln : - ( 330 / 110 ) 108 = 324 in this case long division does not take much time . ( 330 / 110 ) 108 = 324 answer : c"
Answer: c
Problem: the compound interest on $ 27,000 at 11 % p . a is $ 11,000 . find out the period ( in years ) ?
Options: a ) 2.5 , b ) 3 1 / 4 , c ) 3 , d ) 2 3 / 4 , e ) 4
Rationale: "amount = 27,000 + 11,000 = 38,000 . . . . . . . . . now by using compound interest formula we get , 27,000 * ( 111 / 100 ) ^ n = 38000 = = = = > n = = 3 1 / 4 years ans - b"
Answer: b
Problem: 1,5 , 13,25 , __
Options: a ) 26 , b ) 30 , c ) 31 , d ) 41 , e ) 43
Rationale: "series increased by 1 1 + ( 4 * 1 ) = 1 + 4 = 5 5 + ( 4 * 2 ) = 5 + 8 = 13 13 + ( 4 * 3 ) = 13 + 12 = 25 25 + ( 4 * 4 ) = 25 + 16 = 41 answer : d"
Answer: d
Problem: ages of two persons differ by 18 years . if 4 years ago , the elder one was 4 times as old the younger one , find their present age
Options: a ) 6,24 , b ) 9,27 , c ) 10,28 , d ) 18,36 , e ) 19,37
Rationale: explanation : let the age of younger person be x , then elder person ' s age is ( x + 18 ) = > 4 ( x - 4 ) = ( x + 18 - 4 ) [ 4 years before ] = > 4 x - 16 = x + 14 = > x = 10 . so elder person ' s age is x + 18 = 28 answer : option c
Answer: c
Problem: if 13 = 13 w / ( 1 - w ) , then ( 4 w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 4
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 4 w = 2 4 w * 2 = 2 * 2 = 4 answer : e"
Answer: e
Problem: in a recent head - to - head run - off election , 10,000 absentee ballets were cast . 2 / 3 of the absentee ballets were thrown out and 2 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
Rationale: "1 / 3 * 3 / 5 ( total absentee votes ) = 1 / 5 ( total votes ) = 1 / 5 * 10000 = 2000 answer is a"
Answer: a
Problem: a bicycle wheel has a diameter of 0.61 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 522 , c ) 1408 , d ) 710 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.61 m ) = 522.1 . hence 522 complete revolutions . answer b"
Answer: b
Problem: nitin borrowed some money at the rate of 6 % p . a . for the first 3 years , 9 % p . a . for the next 5 years and 13 % p . a . for the period beyond 8 years . if the total interest paid by him at the end of 11 years is rs . 8160 , how much money did he borrow ?
Options: a ) 8000 , b ) 2787 , c ) 27766 , d ) 9976 , e ) 21671
Rationale: let the sum be rs . x . then , [ ( x * 6 * 3 ) / 100 ] + [ ( x * 9 * 5 ) / 100 ] + [ ( x * 13 * 3 ) / 100 ] = 8160 18 x + 45 x + 39 x = ( 8160 * 100 ) 102 x = 816000 = > x = 8000 . answer : a
Answer: a
Problem: the ratio between the sale price and the cost price of an article is 6 : 2 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 2 : 1
Rationale: "c . p . = rs . 2 x and s . p . = rs . 6 x . then , gain = rs . 4 x required ratio = 4 x : 2 x = 2 : 1 e"
Answer: e
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1200 in total compensation , how many total hours did he work that week ?
Options: a ) 60 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1200 - 640 = 560 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 560 / 28 = 20 total hrs = 40 + 20 = 60 answer a 60"
Answer: a
Problem: if 5 ^ 29 * 4 ^ 15 = 2 * 10 ^ n , what is the value of n ?
Options: a ) 11 , b ) 21 , c ) 22 , d ) 29 , e ) 32
Rationale: my attempt : 5 ^ ( 29 ) * 4 ^ ( 15 ) = 2 * 10 ^ p 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 * ( 2 * 5 ) ^ p 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 * 2 ^ ( p ) * 5 ^ ( p ) 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 ^ ( p + 1 ) * 5 ^ ( p ) = > ( p + 1 ) = 30 = > p = 29 answer : 29 ( d )
Answer: d
Problem: a man is standing on a railway bridge which is 180 m long . he finds that a train crosses the bridge in 20 seconds but himself in 8 seconds . find the length of the train and its speed .
Options: a ) 10 m / sec , b ) 15 m / sec , c ) 18 m / sec , d ) 19 m / sec , e ) 25 m / sec
Rationale: if length of train is l and speed of train is s , then l / s = 8 ( l + 180 ) / s = 20 ( l + 180 ) / l = 20 / 8 = 5 / 2 2 l + 360 = 5 * l 3 * l = 360 l = 120 mtrs s = l / 8 = 120 / 8 = 15 m / sec answer : b
Answer: b
Problem: if 2 ^ k = 4 , then 2 ^ ( 2 k + 2 ) =
Options: a ) 29 , b ) 45 , c ) 81 , d ) 64 , e ) 18
Rationale: "2 ^ k = 4 2 ^ 2 k = 4 ^ 2 2 ^ 2 k = 16 2 ^ ( 2 k + 2 ) = 2 ^ 2 k * 2 ^ 2 = 16 * 4 = 64 answer : d"
Answer: d
Problem: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 60 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 60
Rationale: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 60 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 30 cents . fraction of spirit is 1 / 2 . 30 = k * ( 1 / 2 ) k = 60 cost per liter = 60 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 60 * ( 1 / 3 ) * 3 = 50 cents e . 60 cents"
Answer: e
Problem: the average marks of a class of 28 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 52.1
Rationale: "sum of the marks for the class of 28 students = 28 * 40 = 1120 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 78 students = 1120 + 3000 = 4120 average marks of all the students = 4120 / 78 = 52.8 answer : c"
Answer: c
Problem: free notebooks were distributed equally among children of a class . the number of notebooks each child got was one - eighth of the number of children . had the number of children been half , each child would have got 16 notebooks . total how many notebooks were distributed ?
Options: a ) 256 , b ) 512 , c ) 432 , d ) 352 , e ) 640
Rationale: let total number of children be x . then , x * ( 1 / 8 ) x = ( x / 2 ) x 16 x = 64 . number of notebooks = ( 1 / 8 ) x ^ 2 = ( 1 / 8 ) x 64 x 64 = 512 . answer is b .
Answer: b
Problem: if 7800 / 3.25 = 2400 , then 780.0 / 32.5 is equal to ?
Options: a ) 21 , b ) 28 , c ) 26 , d ) 25 , e ) 24
Rationale: "answer given expression 780.0 / 32.5 = 7800 / 325 = 7800 / ( 3.25 x 100 ) = 2400 / 100 = 24 correct option : e"
Answer: e
Problem: tim and é lan are 120 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 45 miles . , d ) 60 miles . , e ) 80 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice e meet the 2 : 1 ( tim : elan = 80 : 40 ) ratio of maintaining total distance traveled 120 miles so correct answer e"
Answer: e
Problem: the sum of the first 40 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 6,500 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 40 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 4000 + 2500 = 6500 a is the answer ."
Answer: a
Problem: the diagonals of a rhombus are 14 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 190 , c ) 140 , d ) 278 , e ) 292
Rationale: "1 / 2 * 14 * 20 = 140 answer : c"
Answer: c
Problem: what is the perimeter of a triangle with sides 7 and 5 that has the maximum possible area ?
Options: a ) 12 + √ 7
b ) 12 + 4 √ 7
c ) 12 + √ 47
d ) 12 + 4 √ 47
e ) 12 + √ 74
Rationale: we can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle . then the third side is the hypotenuse with a length of √ ( 49 + 25 ) = √ 74 the perimeter is 12 + √ 74 the answer is e .
Answer: e
Problem: if x and y are positive integers and 20 x = 10 y what is the least possible value of xy ?
Options: a ) 14 , b ) 28 , c ) 63 , d ) 84 , e ) 100
Rationale: "20 x = 10 y = > x / y = 1 / 2 = > 2 x = y 2 ( 3 ) = 1 ( 3 ) = > x * y = 9 but it is not given 2 ( 10 ) = 1 ( 10 ) = > x * y = 100 e"
Answer: e
Problem: find the greatest number which on dividing 1661 and 2045 , leaves a reminder of 10 and 13 respectively
Options: a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 150
Rationale: explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1661 - 10 ) and ( 2045 - 13 ) = hcf ( 1651 , 2032 ) = 127 option b
Answer: b
Problem: the price of a t . v . set worth rs . 40000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 22678 , b ) 26699 , c ) 26788 , d ) 19000 , e ) 39000
Rationale: "money paid in cash = rs . 1000 balance payment = ( 40000 - 1000 ) = rs . 39000 answer : e"
Answer: e
Problem: 3 candidates in an election and received 2136 , 7636 and 11628 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45 % , b ) 49 % , c ) 54 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 2136 + 7636 + 11628 ) = 21260 so , required percentage = 11628 / 21260 * 100 = 54 % c"
Answer: c
Problem: find the number of terms in an arithmetic progression with the first term 2 and the last term being 62 , given that common difference is 2 .
Options: a ) 31 , b ) 40 , c ) 22 , d ) 27 , e ) 25
Rationale: the n th term = a + ( n - 1 ) * d 62 = 2 + ( n - 1 ) * 2 , 62 – 2 = ( n - 1 ) * 2 , n = 60 / 2 + 1 = 31 . answer : a
Answer: a
Problem: a , b , c , d , and e are positive consecutive integers and a < b < c < d < e . if the sum of a + b is one less than e , and the product of ab is one more than d , then what is the value of c ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: since the integers are consecutive , we can write each as the previous integer + 1 . for example , b = a + 1 , and c = b + 1 . we can also reverse this : a + 1 = b , and b + 1 = c . since ab = d + 1 , we can also write this ab = e . since a + b = e - 1 , then a + b = ab - 1 . find the pair of consecutive integers whose sum is one less than its product . these numbers are 2 and 3 ( sum : 5 ; product : 6 ) . now that we know how the series starts , we can find the value of c . if the first two numbers are 2 and 3 , the third number is 4 ( option b ) .
Answer: b
Problem: a train is 360 meter long is running at a speed of 36 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 50 seconds , b ) 29 seconds , c ) 40 seconds , d ) 11 seconds , e ) 12 seconds
Rationale: "speed = 36 km / hr = 36 * ( 5 / 18 ) m / sec = 10 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 10 ) = 50 seconds answer : a"
Answer: a
Problem: 15 times a positive integer is more than its square by 56 , then the positive integer is
Options: a ) 13 , b ) 8 , c ) 11 , d ) 12 , e ) 14
Rationale: explanation : let the number be x . then , 15 x = x 2 + 56 = > x 2 - 15 x + 56 = 0 = > ( x - 7 ) ( x - 8 ) = 0 = > x = 7 or 8 answer : option b
Answer: b
Problem: a shopkeeper has 280 kg of apples . he sells 35 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 35 x 20 % + 60 x 30 % = 25 this profit will remain same for any total quantity unless the % of products remains the same . hence ' b ' is the answer"
Answer: b
Problem: a train running at 1 / 5 of its own speed reached a place in 10 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "new speed = 1 / 5 of usual speed new time = 5 / 1 of usual time 5 / 1 of usual time = 10 hrs usual time = 10 * 1 / 5 = 2 hrs time saved = 10 - 2 = 8 hrs answer is a"
Answer: a
Problem: a number exceeds 20 % of itself by 40 . the number is
Options: a ) 50 , b ) 60 , c ) 80 , d ) 320 , e ) none
Rationale: "explanation : let the answer be ' a ' then a − 20 / 100 a = 40 ⇒ 5 a − a = 200 ⇒ a = 50 ⇒ a = 50 correct option : a"
Answer: a
Problem: a line that passes through ( – 1 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "this is a considerably more difficult one , which will involve some algebra . let ’ s say that the “ first ” point is ( – 1 , – 4 ) and the “ second , ” ( 3 , k ) . the rise = k + 4 , which involves a variable . the run = 3 – ( – 1 ) = 4 . there the slope is ( k + 4 ) / 4 , and we can set this equal to k and solve for k . { { k + 4 } / 4 } = k k + 4 = 4 k 4 = 3 k k = 4 / 3 answer = c"
Answer: c
Problem: in a class of 94 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 40
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 94 54 + not = 94 not = 94 - 54 = 40 so answer is e"
Answer: e
Problem: the faces of storage box are to be painted by 6 different colors . in how many ways can be this be done ?
Options: a ) a . 720 , b ) b . 256 , c ) c . 1 , d ) d . 12 , e ) e . 36
Rationale: if i have to paint 6 sides with 6 different colour . . . first face can have 6 c 1 options , 2 nd would have 5 c 1 , and subsequent ones would have 4 c 1 , 3 c 1 , 2 c 1 and 1 options respectively . total options = 6 c 1 x 5 c 1 x 4 c 1 x 3 c 1 x 2 c 1 x 1 = 720 distinct ways correct answer - a
Answer: a
Problem: john had a stock of 1000 books in his bookshop . he sold 20 on monday , 120 on tuesday , 200 on wednesday , 250 on thursday and 300 on friday . what percentage of the books were not sold ?
Options: a ) 68 % , b ) 74 % , c ) 76 % , d ) 62 % , e ) 89 %
Rationale: "let n be the total number of books sold . hence n = 20 + 120 + 200 + 250 + 300 = 890 let m be the books not sold m = 1000 - n = 1200 - 890 = 798 percentage books not sold / total number of books = 890 / 1000 = 0.89 = 89 % correct answer e"
Answer: e
Problem: if a lends rs . 1000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 112.5 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 45
Rationale: "( 1000 * 1.5 * 3 ) / 100 = > 45 answer : e"
Answer: e
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors r ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have r = 2 * 3 * 5 * 7 = 840 thus , answer b
Answer: b
Problem: a can finish a work in 24 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done by a in 24 * 5 / 12 = 10 days answer is a"
Answer: a
Problem: a reduction of 50 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 80 , e ) s . 34
Rationale: "800 * ( 50 / 100 ) = 400 - - - - 5 ? - - - - 1 = > rs . 80 answer : d"
Answer: d
Problem: if x / 4 + 24 / x = 5 , what are the values of 3 x - 4 ?
Options: a ) 8 and 9 , b ) 20 and 32 , c ) 17 and 19 , d ) 12 and 29 , e ) 17 and 29
Rationale: i got the same thing b is the answer 20 or 32
Answer: b
Problem: a candidate who gets 30 % of the marks fails by 50 marks . but another candidate who gets 45 % marks gets 25 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 150 , b ) 200 , c ) 250 , d ) 275 , e ) 285
Rationale: 30 % - - - - - - - - - - - - 50 45 % - - - - - - - - - - - - 25 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 75 30 % - - - - - - - - - - - - - - ? 150 + 50 = 200 marks answer : b
Answer: b
Problem: if two integers x , y ( x > y ) are selected from - 6 to 6 ( inclusive ) , how many cases are there ?
Options: a ) 70 , b ) 74 , c ) 78 , d ) 82 , e ) 86
Rationale: "there are 13 integers from - 6 to 6 inclusive . 13 c 2 = 78 . the answer is c ."
Answer: c
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 2 months , find for how much time did q invest the money ?
Options: a ) 8 , b ) 10 , c ) 18 , d ) 4 , e ) 12
Rationale: "7 * 5 : 2 * x = 7 : 10 x = 4 answer : 4 answer is d"
Answer: d
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 14 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 12 , b ) 14 , c ) 10 , d ) 11 , e ) 13
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 8 no . of days when b works = 6 → 8 x + 6 y = 1 when b starts : no . of days when a works = 7 no . of days when a works = 7 → 7 x + 7 y = 1 solving the above two equations for xy x = 1 / 14 y = 1 / 14 → total work done by ab in a day = 1 / 14 + 1 / 14 = 2 / 28 = 1 / 14 → no . of days to complete the work when both work together = 14 answer : b"
Answer: b
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 15500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 120,000
Rationale: answer equals e in 48 years . i thought by 50 th year it would reach 120,000 . options should have been separated more widely for clarity .
Answer: e
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 55 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 35 = > 20 = x - 35 = > x = 20 + 35 = 55 answer is c ."
Answer: c
Problem: a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 15 . if he got 170 marks in two subjects together how many marks did he got in english ?
Options: a ) 120,50 , b ) 180,60 , c ) 180,90 , d ) 120,40 , e ) none of them
Rationale: let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 15 2 x - 3 y = 90 â € ¦ â € ¦ > ( 1 ) x + y = 170 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 120 and y = 50 answer is a .
Answer: a
Problem: in the manufacture of a certain product , 4 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.2 % , c ) 0.16 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 4 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 4 / 100 ) * 100 % = ( 16 / 10000 ) * 100 % = ( 16 / 100 ) % = . 16 % answer c"
Answer: c
Problem: if you roll a fair - sided die twice , what is the probability of getting a ( 4.4 ) double ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 12 , d ) 1 / 3 ! , e ) 1 / 24
Rationale: total no . in two dice ( 1,1 ) , ( 2,2 ) . . . . . ( 6 , ) total number of events = 6 * 6 total events of getting same pair ( 4 , 4 ) = 6 probability = 6 / 6 * 6 = 1 / 6 = 1 / 3 ! d
Answer: d
Problem: how many seconds will a 770 m long train take to cross a man walking with a speed of 2.5 km / hr in the direction of the moving train if the speed of the train is 46.5 km / hr ?
Options: a ) 63 , b ) 88 , c ) 66 , d ) 44 , e ) 35
Rationale: "speed of train relative to man = 46.5 - 2.5 = 44 km / hr . = 44 * 5 / 18 = 110 / 9 m / sec . time taken to pass the man = 770 * 9 / 110 = 63 sec . answer : a"
Answer: a
Problem: buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 30 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 70 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 122 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 122 min c"
Answer: c
Problem: at a certain zoo , the ratio of sea lions to penguins is 4 to 11 . if there are 84 more penguins than sea lions at the zoo , how many sea lions are there ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 72 , e ) 132
Rationale: the ratio as mentioned = 4 / 11 also sea lion + 84 = penguins or , 4 x + 84 = 11 x x = 84 / 7 = 12 number of sea lions = 12 * 4 = 48 answer : c
Answer: c
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 36 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 19 sec , d ) 7.2 sec , e ) 13 sec
Rationale: rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 36 d = 36 * 100 / 18 = 200 rs = 60 + 40 = 100 * 5 / 18 t = 200 * 18 / 500 = 7.2 sec answer : d
Answer: d
Problem: if x + y = 2 x + z , x - 2 y = 4 z and x + y + z = 21 , what is the value of y / z ?
Options: a ) - 4.5 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 6 .
Rationale: x + y = 2 x + 2 z y = x + 2 z - - - - - - - - - - 1 x - 2 y = 4 z x - 4 z = 2 y - - - - - - - - - 2 subtracting equation 1 from equation 2 - 6 z = y y / z = - 6 e is the answer
Answer: e
Problem: the bankers discount of a certain sum of money is rs . 36 and the true discount on the same sum for the same time is rs . 30 . the sum due is :
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 36 * 30 ) / 36 - 30 ; 180 answer : e"
Answer: e
Problem: 12 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 190 , b ) 132 , c ) 210 , d ) 220 , e ) 225
Rationale: "though 2 * ( 12 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 11 , so he ' ll play 22 matches . similarly , second guy has to play with the rest of 10 as his 2 games with the first guy are already played . so he plays 20 matches . this continues like this and the total matches are 22 + 20 + 18 . . . + 2 22 + 20 + . . . + 2 = 2 ( 11 + 10 + . . . + 1 ) = 2 ( ( 11 * 12 ) / 2 ) = 11 * 12 = 132 . answer : b"
Answer: b
Problem: one hour after adrienne started walking the 60 miles from x to y , harold started walking from x to y as well . adrienne walks 3 miles per hour and harold walks 1 mile per hour faster than adrienne . how far from x will harold be when he catches up to adrienne ?
Options: a ) 8 miles , b ) 12 miles , c ) 10 miles , d ) 11 miles , e ) 14 miles
Rationale: first , determine how far adrienne has walked in the one hour . she has walked three miles which means she is three miles ahead of harold when he sets off . harold walks at four miles / hour which means that every hour , harold will get one mile closer to adrienne . if he gets one mile closer every hour , it will take him three hours to catch up to her which means he travels 3 hours * 4 miles / hour = 12 miles and she travels 4 hours * 3 miles / hour = 12 miles . he will be 12 miles from x when he catches up to her . a slightly different way to solve . . . we do n ' t know how long they will walk before they catch up to one another but we do know that a walks for one hour more than j . j = t and a = t + 1 . we are looking for the distance at which they meet up which means the distance will be the same . d = r * t so , r * t ( harold ) = r * t ( adrienne ) r * ( t ) = r * ( t + 1 ) 4 t = 3 t + 3 t = 3 d = r * t d = 4 * 3 d = 12 b ) 12 miles
Answer: b
Problem: in a division , a student took 48 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
Rationale: "x / 48 = 24 . x = 24 * 48 . so correct answer would be , ( 24 * 48 ) / 36 = 32 . answer : b"
Answer: b
Problem: a man can row upstream at 20 kmph and downstream at 60 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 34 kmph , c ) 30 kmph , d ) 45 kmph , e ) 40 kmph
Rationale: "us = 20 ds = 60 m = ( 20 + 60 ) / 2 = 40 answer : e"
Answer: e
Problem: two family reunions are happening at the same hotel , the dates reunion and the hall reunion . all 50 guests at the hotel attend at least one of the reunions . if 50 people attend the dates reunion and 60 people attend the hall reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 60
Rationale: no of people in dates reunion = 50 no of people in hall reunion = 60 attending both = x all guests attend at least one . therefore , 50 = 50 + 60 - ( both ) both = 60 answer e
Answer: e
Problem: a person travels equal distances with speeds of 6 km / hr , 12 km / hr , 18 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 1500 mts , c ) 1800 mts , d ) 2 km , e ) 1250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 6 ) + ( x / 12 ) + ( x / 18 ) = 11 / 60 x = 0.6 total distance = 3 * 0.6 = 1.8 km = 1800 meters correct option is c"
Answer: c
Problem: working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 5 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 10 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 5 x / 5 x * 10 = 10 min ans : e"
Answer: e
Problem: the volume of a cube is 1331 cc . find its surface .
Options: a ) 864 , b ) 726 , c ) 255 , d ) 287 , e ) 267
Rationale: "a 3 = 1331 = > a = 11 6 a 2 = 6 * 11 * 11 = 726 answer : b"
Answer: b
Problem: if ( a – b ) is 11 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 11 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 11 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 11 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 11 = ( c – a ) – 3 = > 2 ( a – c ) = 8 = > ( a – c ) = 4 answer : d"
Answer: d
Problem: two trains 180 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.7 , b ) 10.9 , c ) 10.24 , d ) 12.24 , e ) 18.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 180 + 160 = 340 m . required time = 340 * 9 / 250 = 12.24 sec . answer : d"
Answer: d
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 267 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 178 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: explanation : let the length of train be l m . acc . to question ( 267 + l ) / 20 = l / 8 2136 + 8 l = 20 l l = 2136 / 12 = 178 m answer a
Answer: a
Problem: mixture a is 15 percent alcohol , and mixture b is 50 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 30 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 1.5 , b ) 1.7 , c ) 2.3 , d ) 2.5 , e ) 3.0
Rationale: "ratio of a to b in the final mixture = 50 - 30 : 30 - 15 = 4 : 3 gallons of a used = 4 / 7 * 4 = 2.28 answer : c"
Answer: c
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 160 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 320 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 160 ) = 2 + 2 ( extra ) = > 2 x - 320 = x = > x = 320 . answer : b"
Answer: b
Problem: a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 3.00 , what total number of pens and pencils did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: answer : algebraically , the question looks like this : 3.0 = 0.35 x + 0.25 y there are six possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 4 pens : $ 1.40 5 pens : $ 1.75 balance 1.25 5 pencils cost $ 1.25 that ' s 5 pens and 5 pencils choice ( c ) is correct .
Answer: c
Problem: what is the sum of natural numbers between 20 and 100
Options: a ) 4800 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 20 and 100 numbers = 81 = > 100 - 20 = 80 + 1 = 81 sn = 81 / 2 × 120 = 81 × 60 = 4860 b )"
Answer: b
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 6 weavers in 6 days ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: 1 weaver can weave 1 mat in 4 days . 6 weavers can weave 6 mats in 4 days . 6 weavers can weave 9 mats in 6 days . the answer is b .
Answer: b
Problem: a number whose fifth part increased by 6 is equal to its fourth part diminished by 6 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 240 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 6 = ( n / 4 ) - 6 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 12 â ‡ ’ ( 5 n - 4 n ) / 20 = 12 â ˆ ´ n = 240 option : d"
Answer: d
Problem: if 3 a – 2 b – 4 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . d"
Answer: d
Problem: find the product of the localvalue and absolutevalue of 3 in 20368 ?
Options: a ) 1000 , b ) 1100 , c ) 1200 , d ) 900 , e ) 10000
Rationale: "local value of 3 = 3 x 100 = 300 place value of 3 = 3 there fore = 3 x 300 = 900 d"
Answer: d
Problem: how many seconds will a train 120 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 32 sec , c ) 25 sec , d ) 24 sec , e ) 31 sec
Rationale: "explanation : d = 120 + 200 = 320 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 32 sec answer : option b"
Answer: b
Problem: the difference of the areas of two squares drawn on two line segments of different lengths is 32 sq . cm . find the length of the greater line segment if one is longer than the other by 2 cm .
Options: a ) 6 cm , b ) 7 cm , c ) 9 cm , d ) 11 cm , e ) none
Rationale: "solution let the lengths of the line segments be x cm and ( x + 2 ) cm . then ( x + 2 ) 2 - x 2 = 32 < = > x 2 + 4 x + 4 - x 2 = 32 < = > 4 x = 28 therefore x = 7 . length of longer line segment = ( 7 + 2 ) cm = 9 cm . answer c"
Answer: c
Problem: a cube of edge 6 cm is cut into cubes each of edge 3 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 4 , b ) 1 : 25 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 3 * 3 / 6 * 6 * 6 = 1 / 4 = 1 : 4 . answer a"
Answer: a
Problem: robert ate 7 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) 4 , b ) 7 , c ) 9 , d ) 5 , e ) 2
Rationale: 7 - 3 = 4 . answer is a
Answer: a
Problem: a car traveling at a certain constant speed takes 20 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 36 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "36 * t = 1 km = > t = 1 / 36 km / h v * ( t + 20 / 3600 ) = 1 v ( 1 / 36 + 20 / 3600 ) = 1 v ( 120 / 3600 ) = 1 v = 30 km / h the answer is d ."
Answer: d
Problem: the product of x and y is a constant . if the value of x is increased by 50 % , by what percentage must the value of y be decreased ?
Options: a ) 50 % , b ) 40 % , c ) 33 1 ⁄ 3 % , d ) 25 % , e ) 12 1 ⁄ 2 %
Rationale: "product of x and y = xy if the value of x is increased by 50 % , value of y needs to be = xy / ( 1.5 x ) = 2 / 3 y decrease in value of y = y - 2 / 3 y = 1 / 3 y % decrease in value of y = ( 1 / 3 y ) / y * 100 % = 33 1 ⁄ 3 % answer c"
Answer: c
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 sq . cm , what is the width of the rectangle ?
Options: a ) 10 cm , b ) 12 cm , c ) 14 cm , d ) 16 cm , e ) 18 cm
Rationale: "2 l + 2 w = 5 w l = 3 w / 2 w * l = 150 3 w ^ 2 / 2 = 150 w ^ 2 = 100 w = 10 the answer is a ."
Answer: a
Problem: working at a constant rate , p can finish a job in 3 hours . q , also working at a constant rate , can finish the same job in 15 hours . if they work together for 2 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 45 , e ) 48
Rationale: each hour they complete 1 / 3 + 1 / 15 = 2 / 5 of the job . in 2 hours , they complete 2 ( 2 / 5 ) = 4 / 5 of the job . the time for p to finish is ( 1 / 5 ) / ( 1 / 3 ) = ( 3 / 5 ) hour = 36 minutes the answer is b .
Answer: b
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 54 )
Options: a ) 251 , b ) 261 , c ) 262 , d ) 269 , e ) 278
Rationale: "there are 31 digits in 10 ^ 30 when we subtract 54 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 54 = 9999999 . . . . ( 30 times ) + 1 - 54 = 9999999 . . . . ( 30 times ) - 53 consider the last 2 digits , 99 - 53 = 46 the last 2 digits will be 46 . and our number would be 99999 . . . . . . 99946 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 46 the sum of the digits will be ( 28 * 9 ) + 4 + 6 = 262 answer : - c"
Answer: c
Problem: a room of 6 m 20 cm long and 5 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 88900 , b ) 87700 , c ) 88970 , d ) 88000 , e ) 89000
Rationale: "explanation : area of the room = 620 * 574 sq cm size of largest square tile = h . c . f of 620 cm and 574 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 620 * 574 ) / ( 2 * 2 ) = 88970 answer : c ) 88970"
Answer: c
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is ?
Options: a ) 287 , b ) 278 , c ) 698 , d ) 279 , e ) 275
Rationale: "s . i . for 1 year = ( 854 - 815 ) = rs . 39 s . i . for 3 years = 39 * 3 = rs . 117 principal = ( 815 - 117 ) = rs . 698 . answer : c"
Answer: c
Problem: a football team lost 5 yards and then gained 7 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: for lost , use negative . for gain , use positive . progress = - 5 + 7 = 2 yards a
Answer: a
Problem: the sum of four consecutive numbers is 102 . the greatest among these three number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 27
Rationale: "let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e"
Answer: e
Problem: what is the least common multiple of 12 , 18 , and 24 ?
Options: a ) 72 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 12 = 2 ^ 2 * 3 ^ 1 18 = 2 ^ 1 * 3 ^ 2 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 72 option a"
Answer: a
Problem: a batsman makes a score of 90 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 90 = 11 x x = 90 - 50 = 40 answer is a"
Answer: a
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 72 , then how old is b ?
Options: a ) 28 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 72 5 x = 70 = > x = 14 hence , b ' s age = 2 x = 28 years . answer : a"
Answer: a
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 14,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 4634 , c ) 4542 , d ) 2343 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 14000 . t = 3 years and r = 10 % p . a . c . i . = rs . 14000 x 1 + 10 3 - 1 100 = rs . 14000 x 331 1000 = 4634 . b"
Answer: b
Problem: dick and jane each saved $ 1,000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %
Rationale: 1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d
Answer: d
Problem: worker a takes 10 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 40 days , b ) 40 / 9 days , c ) 39 / 9 days , d ) 6 days , e ) 60 / 9 days
Rationale: "a ' s one hour work = 1 / 10 . b ' s one hour work = 1 / 15 . ( a + b ) ' s one hour work = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 . both a & b can finish the work in 6 days d"
Answer: d
Problem: a , b , c , d , e sitting in a row what is the probability that a & b sitting adjacent .
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 6 / 5
Rationale: total number of arrangement is = 5 ! = 120 favorable event i . e a and b can be arranged in 2 ! and the remaining can be arranged in 4 ! since ab can be in any of the four positions . so 4 ! * 2 ! / 5 ! = 2 / 5 answer : b
Answer: b