regisss/math_qa huggingface dataset:
Problem: what annual payment will discharge a debt of rs . 1060 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 551.25 , c ) 570.07 , d ) 543.33 , e ) 646.33
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1060 820 x + 1060 * 441 x = 570.07 so , value of each installment = rs . 570.07 answer : option c"
Answer: c
Problem: 50 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 32256 , b ) 24000 , c ) 44936 , d ) 46080 , e ) none
Rationale: "answer ∵ 50 % of p = 23040 ∴ p = ( 23040 x 100 ) / 50 = 46080 correct option : d"
Answer: d
Problem: if the perimeter of a rectangular house is 1400 m , its length when its breadth is 300 m is ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: 2 ( l + 300 ) = 1400 = > l = 400 m answer : b
Answer: b
Problem: the price of an item is discounted 4 percent on day 1 of a sale . on day 2 , the item is discounted another 4 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 82.5 % , b ) 89.9 % , c ) 87.7 % , d ) 86.4 % , e ) 83.3 %
Rationale: "let initial price be 100 price in day 1 after 4 % discount = 96 price in day 2 after 4 % discount = 92.16 price in day 3 after 10 % discount = 82.94 so , price in day 3 as percentage of the sale price on day 1 will be = 82.94 / 96 * 100 = > 86.4 % answer will definitely be ( d )"
Answer: d
Problem: if a # b = ab – b + b ^ 2 , then 3 # 4 =
Options: a ) 2 , b ) 8 , c ) 15 , d ) 24 , e ) 35
Rationale: "solution - simply substitute 3 and 4 in equation in the place of a and b respectively . 3 # 4 = 3 * 4 - 4 + 4 ^ 2 = 12 - 4 + 16 = 24 . ans d"
Answer: d
Problem: what number has a 4 : 1 ratio to the number 100 ?
Options: a ) 40 , b ) 200 , c ) 400 , d ) 800 , e ) 4000
Rationale: "4 : 1 = x : 100 x = 4 * 100 x = 400 answer : c"
Answer: c
Problem: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5535 . what was the number of original inhabitants ?
Options: a ) 7900 , b ) 8200 , c ) 8500 , d ) 8800 , e ) 9100
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5535 ( 27 / 40 ) * x = 5535 x = 5535 * 40 / 27 = 8200 the answer is b ."
Answer: b
Problem: 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 42 , then how old is b ?
Options: a ) 16 , b ) 8 , c ) 9 , d ) 10 , e ) 11
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 = 42 5 x = 40 = > x = 8 hence , b ' s age = 2 x = 16 years . answer : a"
Answer: a
Problem: today joelle opened an interest - bearing savings account and deposited $ 7,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 7727.50 , b ) $ 7717.50 , c ) $ 7737.50 , d ) $ 7747.50 , e ) $ 7757.50
Rationale: "interest for 1 st year = 7000 * 5 / 100 = 350 interest for 2 nd year = 7350 * 5 / 100 = 367.50 total = 7000 + 350 + 367.50 = 7717.50 answer : b"
Answer: b
Problem: last year the range of the annual bonus of the 100 employees at company x was $ 20000 . if the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year , what is the range of the annual bonus of the 100 employees this year ?
Options: a ) $ 27000 , b ) $ 22000 , c ) $ 33000 , d ) $ 16000 , e ) $ 43000
Rationale: let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b
Answer: b
Problem: the list price of an article is rs . 65 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3 % , b ) 4 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 4 % answer : option b"
Answer: b
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 50 cents . how many cents does a solution of 1 liter of spirit and 3 liters of water cost ?
Options: a ) 13
b ) 33
c ) 56
d ) 50
e ) 52
Rationale: c . 50 cents yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 50 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 25 cents . fraction of spirit is 1 / 2 . 25 = k * ( 1 / 2 ) k = 50 cost per liter = 50 * ( 1 / 4 ) ( 1 part spirit , 3 parts water ) cost for 4 liters = 50 * ( 1 / 4 ) * 4 = 50 cents d . 50 cents
Answer: d
Problem: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 12 seconds , the speed of each train ( in km / hr ) is
Options: a ) 30 km / hr , b ) 36 km / hr , c ) 80 km / hr , d ) 90 km / hr , e ) none of these
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 12 s let the speed of each train = x . then relative velocity = x + x = 2 x 2 x = distance / time = 240 / 12 = 20 m / s speed of each train = x = 20 / 2 = 10 m / s = 10 * 18 / 5 km / hr = 36 km / hr option b"
Answer: b
Problem: what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 21 units ?
Options: a ) 8.5 units , b ) 2.6 units , c ) 3 units , d ) 5 units , e ) 12 units
Rationale: "sides are 8 , 15 and 21 . . . thus it is right angle triangle since 21 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 21 + 15 + 8 / 2 = 22 thus , 60 = 22 * r and hence r = in - radius = 2.6 option b"
Answer: b
Problem: if ( 4 - x ) / ( 5 + x ) = x , what is the value of x ^ 2 + 6 x - 4 ?
Options: a ) - 3 , b ) 0 , c ) 2 , d ) 4 , e ) 6
Rationale: "( 4 - x ) = x * ( 5 + x ) ( 4 - x ) = 5 x + x ^ 2 0 = x ^ 2 + 6 x - 4 the answer is b ."
Answer: b
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 $ 1004 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 53
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1004 - 640 = 364 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 364 / 28 = 13 total hrs = 40 + 13 = 53 answer e 53"
Answer: e
Problem: you have to send 3000 grapes 1000 kilometers from grapecity to appleland . your truck can carry 1000 grapes at a time . every time you travel a kilometer towards appleland you must pay a tax of 1 grape but you pay nothing when going in the other direction ( towards grapecity ) . what is highest number of grapes you can get to appleland ?
Options: a ) 833 , b ) 765 , c ) 665 , d ) 679 , e ) 874
Rationale: step one : first you want to make 3 trips of 1,000 grapes 333 kilometers . you will be left with 2,001 grapes and 667 kilometers to go . step two : next you want to take 2 trips of 1,000 grapes 500 kilometers . you will be left with 1,000 grapes and 167 kilometers to go ( you have to leave a grape behind ) . step three : finally , you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland . correct answer is a ) 833
Answer: a
Problem: the sum of all consecutive odd integers from − 19 to 29 , inclusive , is
Options: a ) 125 , b ) 135 , c ) 150 , d ) 175 , e ) 235
Rationale: "the sum of the odd numbers from - 19 to + 19 is 0 . let ' s add the remaining numbers . 21 + 23 + 25 + 27 + 29 = 5 ( 25 ) = 125 the answer is a ."
Answer: a
Problem: the contents of a certain box consist of 14 apples and 25 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 19 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 25 oranges , so to get to 6 oranges , we should remove 25 - 6 = 19 oranges . answer d"
Answer: d
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 7 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 35 : 2
Rationale: u / i = 7 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 35 : 21 : 2 i . e . u : b = 35 : 2 answer : option e
Answer: e
Problem: how many prime numbers are between 13 / 3 and 83 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "13 / 3 = 4 . xxx 83 / 6 = 13 . xxx so we need to find prime numbers between 4 ( exclusive ) - 12 ( inclusive ) there are 2 prime numbers 7 11 hence answer will be ( b ) 2 b"
Answer: b
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 80 a week . what is the % increase ?
Options: a ) 15 % , b ) 33.33 % , c ) 17.8 % , d ) 19 % , e ) 21 %
Rationale: "increase = ( 20 / 60 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b"
Answer: b
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 600 . their h . c . f is ?
Options: a ) 10 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 600 x = 10 the numbers are 3 * 10 , 4 * 10 , 5 * 10 hence required h . c . f . = 10 answer is a"
Answer: a
Problem: a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c which is at midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 180 km , b ) 127 km , c ) 178 km , d ) 188 km , e ) 111 km
Rationale: "explanation : speed in downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed in upstream = ( 14 â € “ 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 â ‡ ” x / 18 + x / 20 = 19 â ‡ ’ x = 180 km . answer : a"
Answer: a
Problem: in a division sum , the quotient is 18 , the divisor 43 and the remainder 12 , find the dividend ?
Options: a ) 586 , b ) 766 , c ) 796 , d ) 786 , e ) 686
Rationale: "explanation : 18 * 43 + 12 = 786 answer : d"
Answer: d
Problem: x and y are both integers . if x / y = 50.60 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 315 , b ) 616 , c ) 672 , d ) 900 , e ) 1024
Rationale: "remainder = 0.60 - - > 60 / 100 - - > can be written as ( 60 / 4 ) / ( 100 / 4 ) = 15 / 25 so remainders can be 15 , 30 , 45 , 60 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 15 + 30 + 45 + 60 + 75 + 90 = 315 answer : a"
Answer: a
Problem: the average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 60 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 83 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 60 + 10 x 1.5 60 + 15 = 75 kg ans : ' d '"
Answer: d
Problem: a shopkeeper sold an article at $ 1050 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 835 , b ) $ 845 , c ) $ 855 , d ) $ 865 , e ) $ 875
Rationale: "let x be the cost price . 1.2 x = 1050 x = 1050 / 1.2 = 875 the answer is e ."
Answer: e
Problem: niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ?
Options: a ) 8 / 9 , b ) 11 / 12 , c ) 8 / 13 , d ) 11 / 13 , e ) 12 / 13
Rationale: we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a
Answer: a
Problem: if 2 a = 4 b = 10 , then 40 ab =
Options: a ) 50 , b ) 100 , c ) 250 , d ) 450 , e ) 500
Rationale: 2 a * 4 b = 10 * 10 = 100 8 ab = 100 i . e . 40 ab = 500 answer : option e
Answer: e
Problem: rahim bought 52 books for rs . 1200 from one shop and 32 books for rs . 480 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 20 , e ) s . 10
Rationale: "average price per book = ( 1200 + 480 ) / ( 52 + 32 ) = 1680 / 84 = rs . 20 answer : d"
Answer: d
Problem: a rower whose speed is 4 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 2 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 6 , b ) 4 , c ) 9 , d ) 3 , e ) 2
Rationale: "time upstream = d / 2 time downstream = d / 6 total time = d / 2 + d / 6 = 2 d / 3 average speed = 2 d / ( 2 d / 3 ) = 3 km / hr the answer is d ."
Answer: d
Problem: if 2 ^ 5 , 4 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 208 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 4 * 4 = 208 smash d"
Answer: d
Problem: if 3 < x < 6 < y < 11 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 < x < 6 < y < 11 ; 3 < x y < 11 3 + y < x + 11 y - x < 8 . positive integer difference is 7 ( for example y = 10.5 and x = 3.5 ) answer : e ."
Answer: e
Problem: chris age after 20 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 5
Rationale: chris present age = x after 20 years = x + 20 5 years back = x - 5 x + 20 = 5 ( x - 5 ) x = 5 answer is e
Answer: e
Problem: if x is an integer and 2.134 × 10 ^ x is less than 2 , 200,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 2 , 200,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 2 , 200,000 to remain true , the greatest number is 2 , 134,000 , which makes x = 6 b . 6"
Answer: b
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 15 m wide at the top and 9 m wide at the bottom and the area of cross - section is 636 sq m , the depth of cannel is ?
Options: a ) 53 , b ) 28 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 15 + 9 ) = 636 d = 53 answer : a"
Answer: a
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 24 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 767 m , b ) 240 m , c ) 180 m , d ) 176 m , e ) 186 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 24 = 360 m . let the length of the platform be x m . then , ( x + 360 ) / 36 = 15 = > x = 180 m . answer : c"
Answer: c
Problem: the weight of a glass of jar is 30 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 7
Rationale: let weight of jar filled with beans = 100 g weight of jar = 30 g weight of coffee beans = 70 g weight of jar and remaining beans = 60 g weight of remaining beans = 30 g fraction remaining = 30 / 70 = 3 / 7 answer is e .
Answer: e
Problem: what will be the fraction of 12.5 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 12.5 * 1 / 100 = 1 / 8 answer : option d"
Answer: d
Problem: a number increased by 15 % gives 1150 . the number is
Options: a ) 250 , b ) 1000 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 15 % = 115 % 115 % - - - - - - - > 1150 ( 115 × 100 = 1150 ) 100 % - - - - - - - > 1000 ( 100 × 100 = 1000 ) b )"
Answer: b
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 390 m long platform ?
Options: a ) 19 , b ) 27 , c ) 51 , d ) 47 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 390 ) / 36 * 5 / 18 = 51 min . answer : c"
Answer: c
Problem: the average of 7 numbers is 23 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 115 , e ) e ) 145
Rationale: "explanation : average of new numbers = 23 * 5 = 115 answer : option d"
Answer: d
Problem: if taxi fares were $ 3.00 for the first 1 / 5 mile and $ 0.20 for each 1 / 5 mile there after , then the taxi fare for a 4 - mile ride was
Options: a ) $ 6.80 , b ) $ 6.50 , c ) $ 16.80 , d ) $ 6.85 , e ) $ 61.80
Rationale: "in 4 miles , initial 1 / 5 mile charge is $ 3 rest of the distance = 4 - ( 1 / 5 ) = 19 / 5 rest of the distance charge = 19 ( 0.2 ) = $ 3.8 ( as the charge is 0.2 for every 1 / 5 mile ) = > total charge for 4 miles = 3 + 3.8 = 6.8 answer is a"
Answer: a
Problem: if 8 men or 12 women can do a piece of work in 35 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 21 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 35 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 35 = 1 / 420 so , 20 women work = 20 / 420 = 1 / 21 ans : 21 days answer : e"
Answer: e
Problem: the total age of a and b is 18 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 18 years
Rationale: "given that a + b = 182 + b + c = > a â € “ c = 18 + b â € “ b = 18 = > c is younger than a by 18 years answer : e"
Answer: e
Problem: one pump drains one - half of a pond in 1 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.2 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 1 = 1 / 2 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 2 = 1 / 2 - - > time taken for the 2 nd pump to finish : 1 : 1 / 2 = 2 / 1 = 2 hours . c"
Answer: c
Problem: the greatest number which on dividing 1657 and 2037 leaves remainders 9 and 5 respectively , is :
Options: a ) 16 , b ) 127 , c ) 235 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1657 - 9 ) and ( 2037 - 5 ) = h . c . f . of 1648 and 2032 = 16 . answer : a"
Answer: a
Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 10 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 2387 , b ) 1298 , c ) 1128 , d ) 1237 , e ) 1200
Rationale: "l * 30 = 1200 l = 40 40 + 30 + 50 = 120 120 * 10 = 1200 e"
Answer: e
Problem: the length of a rectangle is 2 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 32 square inches
Rationale: "if the width is 4 in and the length is 2 times the width , then the length is 2 * 4 = 8 in the area is given by 4 * 8 = 32 square inches correct answer e"
Answer: e
Problem: the ratio between the sale price and the cost price of an article is 7 : 4 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 3 : 4 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25
Rationale: "c . p . = rs . 4 x and s . p . = rs . 7 x . then , gain = rs . 3 x required ratio = 3 x : 4 x = 3 : 4 a"
Answer: a
Problem: barbata invests $ 2400 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 ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.02 = 1200 ans : ` ` a ' '"
Answer: a
Problem: if a speaks the truth 30 % of the times , b speaks the truth 40 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.58 , b ) 0.9 , c ) 1.9 , d ) 2.2 , e ) 2.3
Rationale: "probability of a speaks truth p ( a ) = 3 / 10 ; false = 7 / 10 probability of b speaks truth p ( b ) = 4 / 10 ; false = 6 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 7 / 10 ) * ( 6 / 10 ) ] = 1 - 42 / 100 = 1 - 0.42 = 0.58 answer : a"
Answer: a
Problem: a certain farmer pays $ 30 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 370 feet by 605 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 360 , e ) $ 154.1
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 154.1 ( e )
Answer: e
Problem: difference between a two - digit number and the number obtained by interchanging the two digits is 36 , what is the difference between two numbers
Options: a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 14
Rationale: explanation : let the ten digit be x , unit digit is y . then ( 10 x + y ) - ( 10 y + x ) = 36 = > 9 x - 9 y = 36 = > x - y = 4 . option b
Answer: b
Problem: the average score of a cricketer in 6 matches is 27 and in other 4 matches is 32 . then find the average score in all the 10 matches ?
Options: a ) 25 , b ) 27 , c ) 30 , d ) 29 , e ) 42
Rationale: "average in 10 matches = ( 6 * 27 + 4 * 32 ) / 6 + 4 = 162 + 128 / 10 = 290 / 10 = 29 answer is d"
Answer: d
Problem: rs . 900 amounts to rs . 920 in 3 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?
Options: a ) rs . 1056 , b ) rs . 1001 , c ) rs . 2056 , d ) rs . 1026 , e ) rs . 1856
Rationale: "( 900 * 3 * 3 ) / 100 = 81 920 + 81 = 1001 answer : b"
Answer: b
Problem: the average expenditure of a labourer for 10 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 180 , b ) 100 , c ) 112 , d ) 110 , e ) none of the above
Rationale: "income of 10 months = ( 10 × 85 ) – debt = 850 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 1120 average monthly income = 1120 ÷ 10 = 112 answer c"
Answer: c
Problem: a store has 10 bottles of juice , including 5 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 4 / 9 , b ) 6 / 11 , c ) 8 / 15 , d ) 10 / 21 , e ) 12 / 25
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 5 c 3 * 5 c 3 = 10 * 10 = 100 p ( selling 3 bottles of apple juice ) = 100 / 210 = 10 / 21 the answer is d ."
Answer: d
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 136 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 24 , b ) 33 , c ) 55 , d ) 77 , e ) 88
Rationale: let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 136 = > . 1 x + 3 / 4 x = 136 = > x = 160 160 - 136 = pure gala = 24 . a
Answer: a
Problem: at a monthly meeting , 1 / 3 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 1 / 6 , b ) 2 / 15 , c ) 3 / 20 , d ) 7 / 30 , e ) 8 / 45
Rationale: "males who did not arrive on time are 1 / 5 * 1 / 3 = 1 / 15 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 3 = 1 / 9 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 15 + 1 / 9 = 8 / 45 the answer is e ."
Answer: e
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 30 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 136.8 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 130 let marked price be $ x . then , 95 / 100 x = 130 x = 13000 / 95 = $ 136.8 now , s . p . = $ 136.8 , c . p . = $ 100 profit % = 136.8 % . d"
Answer: d
Problem: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 300 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "the smallest amount that the company can spend is the lcm of 300 and 200 , which is 600 for each , which is total 1200 . the number of 1 st type of computers which costing $ 300 = 600 / 300 = 2 . the number of 2 nd type of computers which costing $ 200 = 600 / 200 = 3 . total = 2 + 3 = 5 answer is b ."
Answer: b
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 14 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 3 , d ) 8 , e ) 7
Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 14 = 36 n ^ 2 + 12 n + 1 + 14 = 36 n ^ 2 + 12 n + 12 + 3 if p = 6 n - 1 , then p ^ 2 + 14 = 36 n ^ 2 - 12 n + 1 + 14 = 36 n ^ 2 - 12 n + 12 + 3 when divided by 12 , it must leave a remainder of 3 . the answer is c ."
Answer: c
Problem: three unbiased coins are tossed . what is the probability of getting 3 heads and 1 tail ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 1 / 2 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { hhh , hth , thh , hht } p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 answer is d"
Answer: d
Problem: find 95 × × 98
Options: a ) 93 / 198 , b ) 93 / 12 , c ) 93 / 13 , d ) 93 / 10 , e ) 93 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 5 and - 2 compared with 100 . so answer : d"
Answer: d
Problem: 5 + 5
Options: a ) 9 , b ) 12 , c ) 20 , d ) 10 , e ) 0
Rationale: d
Answer: d
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , one - third of the players were absent from practice . of the players at practice that day , one - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?
Options: a ) 1 / 3 , b ) 5 / 1 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were right - handed - - > 12 * 1 / 3 = 4 were right - handed and 8 left - handed . the number of right - handed players who were not at practice that day is 9 - 4 = 5 . the number of left - handed players who were not at practice that days is 9 - 8 = 1 . the ratio = 5 / 1 . answer : b"
Answer: b
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 42 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 10 , e ) 12
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 42 = 6 k + 4 p = > k = 5 , p = 3 total red ' s in bag a will be 2 k = 10 d"
Answer: d
Problem: a man has some hens and cows . if the number of heads be 42 and the number of feet equals 124 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 42 = > h + c = 42 - - - ( equation 1 ) number of feet = 124 = > 2 h + 4 c = 124 = > h + 2 c = 62 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 62 - 42 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 42 = > h = 42 - 20 = 22 i . e . , number of hens = 22 answer : a"
Answer: a
Problem: find large number from below question the difference of two numbers is 1385 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1659
Rationale: "let the smaller number be x . then larger number = ( x + 1385 ) . x + 1385 = 6 x + 15 5 x = 1370 x = 274 large number = 274 + 1385 = 1659 e"
Answer: e
Problem: the average age of 36 students in a group is 13 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 51 years , d ) 54 years , e ) 50 years
Rationale: "explanation : age of the teacher = ( 37 * 14 - 36 * 13 ) years = 50 years . answer : e"
Answer: e
Problem: convert 0.30 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 3 / 10 , d ) 19 / 50 , e ) none
Rationale: answer 0.30 = 30 / 100 = 3 / 10 correct option : c
Answer: c
Problem: a certain galaxy is known to comprise approximately 5 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 10,000
Rationale: "total no . of stars on galaxy = 5 * 10 ^ 11 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 5 * 10 ^ 11 / 50 * 10 ^ 6 = 50 * 10 ^ 3 / 5 = 10000 therefore answer is e"
Answer: e
Problem: a room is 30 m long and 24 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :
Options: a ) 9.6 m 3
b ) 96 m 3
c ) 960 m 3
d ) 9600 m 3
e ) 96000 m 3
Rationale: let the height be h 2 ( 30 + 24 ) x h – 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d
Answer: d
Problem: if $ 120 invested at a certain rate of simple interest amounts to $ 180 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 300
Rationale: "120 amounts to 180 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 180 120 + 120 * ( r / 100 ) * ( 3 ) = 140 = > r = 50 / 3 150 in 6 years = principal + interest = 300 answer is e ."
Answer: e
Problem: find the smallest number which should be multiplied with 520 to make it a perfect square
Options: a ) 337 , b ) 297 , c ) 266 , d ) 116 , e ) 130
Rationale: "explanation : 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square . answer : e"
Answer: e
Problem: the price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980 . if its price of $ 1.20 in 1970 was 150 percent of its price in 1960 , what was its price in 1980 ?
Options: a ) $ 1.80 , b ) $ 2.00 , c ) $ 2.40 , d ) $ 2.70 , e ) $ 3.00
Rationale: the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : 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 37 , the how old is b ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 14 , e ) 10
Rationale: explanation : 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 = 37 ⇒ 5 x = 35 ⇒ x = 7 . hence , b ' s age = 2 x = 14 years . answer : d
Answer: d
Problem: if c and t are positive integers , ct + c + t can not be
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b
Answer: b
Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately
Options: a ) 2972 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 4675
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 2 ) = rs . 2972 . answer : option a"
Answer: a
Problem: a man swims downstream 30 km and upstream 12 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 2 , e ) 4
Rationale: "30 - - - 3 ds = 10 ? - - - - 1 12 - - - - 3 us = 4 ? - - - - 1 m = ? m = ( 10 + 4 ) / 2 = 7 answer : b"
Answer: b
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 7 x km .
Options: a ) 56 , b ) 18 , c ) 24 , d ) 19 , e ) 12
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 7 x / ( x / 8 ) = 56 kmph answer : a"
Answer: a
Problem: if the average of 6 digits is 16 and the average of 4 of them is 10 , calculate the average of the remaining 2 numbers ?
Options: a ) 36 , b ) 35 , c ) 28 , d ) 33 , e ) 21
Rationale: "explanation : total of the 6 digits - 6 * 16 = 96 total of the 4 digits - 4 * 10 = 40 total of the remaining 2 digits - 96 - 40 = 56 average of the remaining 2 numbers = 56 / 2 = 28 answer : c"
Answer: c
Problem: a company pays 20.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 18 , d ) 19 , e ) 41
Rationale: "explanation : dividend on 1 share = ( 20.5 * 50 ) / 100 = rs . 10.25 rs . 25 is income on an investment of rs . 100 rs . 10.25 is income on an investment of rs . ( 10.25 * 100 ) / 25 = rs . 41 answer : e"
Answer: e
Problem: how many diagonals does a 59 - sided convex polygon have ?
Options: a ) 1168 , b ) 1652 , c ) 2452 , d ) 3304 , e ) 4256
Rationale: a 59 - sided convex polygon has 59 vertices . if we examine a single vertex , we can see that we can connect it with 56 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be ( 59 ) ( 56 ) = 3304 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3304 by 2 to get 1652 . the answer is b .
Answer: b
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 33 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 133 let marked price be $ x . then , 95 / 100 x = 133 x = 13300 / 95 = $ 140 now , s . p . = $ 140 , c . p . = $ 100 profit % = 40 % . a"
Answer: a
Problem: calculate how long it will take a swimmer to swim a distance of 10 km against the current of a river which flows at 3 km / hr , given that he can swim in still water at 5 km / h
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "swim in still water at = 5 speed of river = 3 us = 5 - 3 = 2 distance = 10 t = 10 / 2 = 5 answer : c"
Answer: c
Problem: a computer store offers employees a 30 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 900 dollars and marked up the price 30 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 30 % off retail price ) as opposed to the final retail price .
Options: a ) 352 , b ) 356 , c ) 358 , d ) 362 , e ) 365
Rationale: "cost price = 900 profit = 30 % = 30 % of 900 = 270 selling price = cp + profit sp = 1170 a discount of 30 % to employees means 30 % off on 1170 so 30 % of 1170 = 351 ans a"
Answer: a
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 6360 , what is the length of the plot in metres ?
Options: a ) 70 , b ) 200 , c ) 300 , d ) 400 , e ) 140
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 6360 [ 4 l - 40 ] = 6360 / 26.50 = 240 4 l = 280 l = 280 / 4 = 70 meters . answer : a"
Answer: a
Problem: each factor of 240 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 15 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "the # of factors 240 has is 20 ; so out of 20 factors only four are multiples of 15 : 15 , 30 , 60 , 120 and 240 , itself ; so , the probability is 5 / 20 = 1 / 4 . answer : e ."
Answer: e
Problem: what is the least common multiple of 15 , 22 and 24 ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 1320 , e ) 1720
Rationale: "let us first write the numbers in the form of prime factors : 15 = 3 * 5 22 = 2 * 11 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 1320 option d"
Answer: d
Problem: a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was :
Options: a ) 665 , b ) 376 , c ) 998 , d ) 1277 , e ) 1991
Rationale: explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665
Answer: a
Problem: two integers are in the ratio of 1 to 3 . if 10 is added to the smaller number , the ratio becomes 2 to 1 . find the larger integer .
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 3 , then 3 x = y , where x is the smaller integer . if adding 10 to the smaller integer makes the ratio 2 to 1 , then x + 10 = 2 y . substituting y = 3 x into the second equation yields x + 10 = 6 x . so , x = 2 ( smaller integer ) and , y = 3 x = 6 ( larger integer ) so a is the correct answer . another option is to test the answer choices . a ) the larger number is 6 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 2 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 2 ) , we get 12 . so , the new ratio is 12 to 6 which is the same as 2 to 1 . therefore choice a is correct . b ) the larger number is 9 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 3 ) , we get 13 so , the new ratio is 13 to 9 . no good . we want a resulting ratio of 2 to 1 eliminate b c ) the larger number is 10 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3.33 ( which is not an integer ) since both numbers are integers , the larger number can not be 10 . eliminate c d ) the larger number is 12 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 4 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 4 ) , we get 14 so , the new ratio is 14 to 12 which is 7 to 6 . no good . we want a resulting ratio of 2 to 1 eliminate d e ) the larger number is 15 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 5 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 5 ) , we get 15 so , the new ratio is 15 to 15 . this is the same as the ratio of 1 to 1 eliminate e therefore a is the only correct choice ."
Answer: a
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 20 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 76 , c ) 44 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 20 / 5 = 4 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 4 = 44 secs . answer : c"
Answer: c
Problem: the price of a t . v . set worth rs . 30000 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 ) 29000 , d ) 19000 , e ) 26711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 30000 - 1000 ) = rs . 29000 answer : c"
Answer: c
Problem: 55 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 88 m , c ) 120 m , d ) 70 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 55 ⇔ = [ 55 * 20 * 20 * 7 / 22 ] = 7000 cm = 70 m . answer d"
Answer: d
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 34 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5120 , c ) 4608 , d ) 7500 , e ) 8960
Rationale: "l = ( 48 - 16 ) m = 32 m , b = ( 34 - 16 ) m = 18 m , h = 8 m . volume of the box = ( 32 x 18 x 8 ) m 3 = 4608 m 3 . answer : option c"
Answer: c
Problem: a train speeds past a pole in 15 seconds and a platform 120 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 100 m , b ) 140 m , c ) 130 m , d ) 180 m , e ) 170 m
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 120 = 25 * ( x / 15 ) 10 x = 1800 x = 180 meters the answer is d ."
Answer: d
Problem: a certain fruit stand sold apples for $ 0.70 each and guava for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 12 , b ) 13 , c ) 11 , d ) 14 , e ) 5
Rationale: some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c
Answer: c
Problem: if 25 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 500 , b ) 600 , c ) 620 , d ) 640 , e ) 660
Rationale: "we know 25 % people study biology , therefore the no of people not studying = 100 - 25 = 75 % > therefore the people not studying biology out of a total 880 people are = 75 % of 880 > ( 75 / 100 ) * 880 = 660 people e"
Answer: e
Problem: find large number from below question the difference of two numbers is 1380 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1653
Rationale: "let the smaller number be x . then larger number = ( x + 1380 ) . x + 1380 = 6 x + 15 5 x = 1365 x = 273 large number = 273 + 1380 = 1653 e"
Answer: e
Problem: 4 dice are thrown simultaneously on the board . find the probability which show the same face ?
Options: a ) 2 / 113 , b ) 3 / 117 , c ) 1 / 216 , d ) 3 / 111 , e ) 4 / 121
Rationale: "the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 × 6 × 6 × 6 = 64 = 6 × 6 × 6 × 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c"
Answer: c
Problem: tough and tricky questions : word problems . operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 8 , when a # b = 100 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17
Rationale: official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d
Answer: d