regisss/math_qa huggingface dataset:
Problem: total dinning bill for 10 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 24.26
Rationale: 211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 10 = 24.26 answer : e
Answer: e
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 40 % profit on the first article and 40 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 400 , e ) 270
Rationale: "profit on first article = 40 % of 1000 = 400 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d"
Answer: d
Problem: sawyer is mixing up a salad dressing . regardless of the number of servings , the recipe requires that 5 / 8 of the finished dressing mix be peanut oil , 1 / 4 vinegar , and the remainder an even mixture of salt , pepper and sugar . if sawyer accidentally doubles the vinegar and forgets the sugar altogether , what proportion of the botched dressing will be peanut oil ?
Options: a ) 15 / 29 , b ) 5 / 8 , c ) 5 / 16 , d ) 1 / 2 , e ) 13 / 27
Rationale: peanut oil = 5 / 8 = 15 / 24 - - > 15 parts out of 24 ; vinegar = 1 / 4 = 6 / 24 - - > 6 parts out of 24 ; salt + pepper + sugar = 1 - ( 15 / 24 + 6 / 24 ) = 3 / 24 , so each = 1 / 24 - - > 1 part out of 24 each ; if vinegar = 12 ( instead of 6 ) and sugar = 0 ( instead of 1 ) then total = 15 + 12 + 1 + 1 + 0 = 29 parts out of which 15 parts are peanut oil - - > proportion = 15 / 29 . answer : a .
Answer: a
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 30 % profit on the first article and 30 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 202 , e ) 300
Rationale: "profit on first article = 30 % of 1000 = 300 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : e"
Answer: e
Problem: a number is doubled and 11 is added . if resultant is doubled , it becomes 74 . what is that number
Options: a ) 18 , b ) 10 , c ) 13 , d ) 14 , e ) 16
Rationale: "explanation : = > 2 ( 2 x + 11 ) = 74 = > 4 x + 22 = 74 = > 4 x = 52 = > x = 13 option c"
Answer: c
Problem: raja and ram can together complete a piece of work in 4 days . if raja alone can complete the same work in 12 days , in how many days can ram alone complete that work ?
Options: a ) 6 days , b ) 5 days , c ) 7 days , d ) 8 days , e ) 10 days
Rationale: ( raja + ram ) ' s 1 days work = 1 / 4 raja 1 day work = 1 / 2 ram 1 day work = ( 1 / 4 - 1 / 12 ) = 1 / 6 = = > 6 days answer a
Answer: a
Problem: fresh grapes contain 60 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 37.5 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 60 = 40 % of whole weight ) , so 20 * 0.75 = x * 0.4 - - > x = 37.5 . 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 330 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 660 , e ) 720
Rationale: "explanation : 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 - 330 ) = 2 + 2 ( extra ) = > 2 x - 660 = x = > x = 660 . answer : d"
Answer: d
Problem: what is the remainder when 617 + 1176 is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "617 + 1176 mod 7 = > 617 % 7 + 1176 % 7 = > 1 + 0 = > 1 % 7 = > 1 answer : a"
Answer: a
Problem: a and b together can complete a piece of work in 4 days . if a alone can complete the same work in 12 days , in how many days can b alone complete that work ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 8
Rationale: "a and b ' s one day work = 1 / 4 a ' s 1 day ' s work = 1 / 12 b ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 12 ) = 2 / 12 = 1 / 6 hence b alone can complete the work in 6 days . answer is option c"
Answer: c
Problem: a train 300 m long , running with a speed of 90 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec time taken = 300 * 1 / 25 = 12 sec answer : e"
Answer: e
Problem: tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 75 ?
Options: a ) 4 , b ) 18 , c ) 15 , d ) 20 , e ) 24
Rationale: you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 18 * 50 600 1800 - 900 0900 12 75.00 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is b
Answer: b
Problem: if x is an integer and 2.134 × 10 ^ x is less than 21000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "if x = 4 2.134 × 10 ^ 4 = 21340 > 21000 so , x = 3 answer : e"
Answer: e
Problem: the sum of two consecutive number is 97 . which is the larger number ?
Options: a ) 42 , b ) 49 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 97 2 x + 1 = 97 2 x = 96 x = 48 therefore larger number is x + 1 = 49 answer : b"
Answer: b
Problem: 3,10 , 29,66 , __
Options: a ) 125 , b ) 165 , c ) 145 , d ) 127 , e ) 112
Rationale: "3 = 1 * 1 * 1 + 2 10 = 2 * 2 * 2 + 2 29 = 3 * 3 * 3 + 2 66 = 4 * 4 * 4 + 2 similarly 5 * 5 * 5 + 2 = 127 answer : d"
Answer: d
Problem: the sale price sarees listed for rs . 450 after successive discount is 20 % and 15 % is ?
Options: a ) 321 , b ) 276 , c ) 306 , d ) 265 , e ) 162
Rationale: "explanation : 450 * ( 80 / 100 ) * ( 85 / 100 ) = 306 answer : c"
Answer: c
Problem: if there are 200 questions in a 3 hr examination . among these questions are 15 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 72 min , b ) 25.11628 min , c ) 70 min , d ) 74.11682 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 185 x + 15 * 2 x = 180 x = 180 / 215 x = 0.837209 time taken for type a problem = 15 * 2 * 0.837209 = 25.11628 min answer : b"
Answer: b
Problem: express 45 mps in kmph ?
Options: a ) 170 , b ) 160 , c ) 162 , d ) 130 , e ) 122
Rationale: "45 * 18 / 5 = 162 kmph answer : c"
Answer: c
Problem: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a
Options: a ) rs . 300 , b ) rs . 56 , c ) rs . 100 , d ) rs . 240 , e ) rs . 90
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = rs . 240 answer : d"
Answer: d
Problem: express a speed of 126 kmph in meters per second ?
Options: a ) 10 mps , b ) 35 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "126 * 5 / 18 = 35 mps answer : b"
Answer: b
Problem: the product of two numbers is 2028 and their h . c . f is 13 . the number of such pairs is ?
Options: a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 9
Rationale: "let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer : b"
Answer: b
Problem: a cricket bat is sold for $ 850 , making a profit of $ 245 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "245 / ( 850 - 245 ) = 245 / 605 = 49 / 121 = 40 % . answer : e ."
Answer: e
Problem: the speed of a car is 90 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 54 , e ) 15
Rationale: "s = ( 90 + 60 ) / 2 = 75 kmph answer : b"
Answer: b
Problem: if shares of two persons in profits are rs . 300 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "total profit = 1000 ratio = 300 / 600 = 1 : 2 answer : e"
Answer: e
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 8 managers , if 2 managers will not attend the meeting together ?
Options: a ) 40 , b ) 36 , c ) 42 , d ) 45 , e ) 47
Rationale: "we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together so 6 c 5 + ( 6 c 4 * 2 c 1 ) this is 6 + 30 = 36 answer : b"
Answer: b
Problem: a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % sunflower , and brand b , which is 65 % millet and 35 % sunflower . if a customer purchases a mix of the two types of birdseed that is 50 % sunflower , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "yes there is a simple method : consider the following method brand a : 40 % millet and 60 % sunflower brand b : 65 % millet and 35 % sunflower mix : 50 % sunflower here the weighted average is 50 % , now brand a has 60 % sunflower , which is 10 % more than the weighted average of mix = + 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 35 % sunflower , which is 15 % less than the weighted average of mix = - 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 3 : 5 = ( 3 / 5 ) * 100 = 60 % here is a pictorial representation : brand a = 60 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 above average , a times - - - - - - - - - - - - - - - - - total below = + 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 35 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 below average , b times - - - - - - - - - - - - - - - - - total above = - 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore a / total = 3 : 5 = 60 % answer : e"
Answer: e
Problem: sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is :
Options: a ) 15 , b ) 16 , c ) 22 , d ) 18 , e ) 25
Rationale: "work done by sakshi in 1 day = 1 / 20 since tanya is 25 % efficient than sakshi , she completes 25 % more work in a day than sakshi . = > tanya ' s 1 day work = 1 / 20 + 1 / 20 * 25 / 100 = 1 / 16 so time taken by tanya to finish the work = 16 days answer : b"
Answer: b
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1504 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1504 20 x / 100 = 1504 x = 1504 * 100 / 20 = 7520 answer is d
Answer: d
Problem: two boats are heading towards each other at constant speeds of 5 miles / hr and 21 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 13 / 30 , e ) 1 / 5
Rationale: the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 21 = 26 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 26 * 1 / 60 = 13 / 30 miles apart . answer : d .
Answer: d
Problem: 36 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 12 , b ) 18 , c ) 22 , d ) 24 , e ) 26
Rationale: "solution let the required number of days be x . then , less men , more days ∴ 27 : 36 : : 18 : x ⇔ 27 × x = 36 × 18 ⇔ x = 36 x 18 / 27 x = 24 . answer d"
Answer: d
Problem: of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 2 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 2 is 1200 * 1 / 2 so it reduced 600 people , so there is 600 clerical people left but since 600 people left , it also reduced from the total of 3600 so there are 3000 people total since 600 clerical left / 3000 people total you get ( c ) 20 %"
Answer: c
Problem: toby is 4 years younger than debby . thrice the sum of the ages of toby and debby equals their mother ’ s age . if the age of the mother is 60 , find the ages of toby and debby ?
Options: a ) 8 and 12 , b ) 5 and 9 , c ) 6 and 10 , d ) 5 and 10 , e ) 12 and 16
Rationale: let the age of debby be x and toby be x - 4 3 ( x + x - 4 ) = 60 x = 12 the ages of toby and debby are 8 and 12 . answer : a
Answer: a
Problem: if a lends rs . 2800 to b at 15 % per annum and b lends the same sum to c at 18.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 294 , b ) 289 , c ) 240 , d ) 233 , e ) 200
Rationale: "( 2800 * 3.5 * 3 ) / 100 = > 294 answer : a"
Answer: a
Problem: find the average of all prime numbers between 20 and 30
Options: a ) 15 , b ) 20 , c ) 18 , d ) 32 , e ) 26
Rationale: "prime numbers between 20 and 30 are 23,29 required average = ( 23 + 29 ) / 2 = 52 / 2 = 26 answer is e"
Answer: e
Problem: a and b together can complete work in 4 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 4 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 4 - 1 / 6 = 1 / 12 b alone can complete the work in 12 days so half of the work in 6 days answer : option d"
Answer: d
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1 % more . she would get how much ?
Options: a ) 9440 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 1 ) / 100 = 240 9200 - - - - - - - - 9440 answer : a"
Answer: a
Problem: john is 3 times as old as sam . if john will be twice as old as sam in 9 years , how old was sam two years ago ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7
Rationale: j = 3 s after 9 years j + 9 = 2 ( s + 9 ) j = 2 s + 9 2 s + 9 = 3 s s = 9 two years ago s = 9 - 2 = 7 e is the answer
Answer: e
Problem: a bowl of fruit contains 14 apples and 23 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 23 - x ) = 37 - x 14 / ( 37 - x ) = 7 / 10 = > 20 = 37 - x = > x = 17 answer d
Answer: d
Problem: √ ( 49 ) 2
Options: a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 49 ) 2 = ? or , ? = 49 answer c"
Answer: c
Problem: one woman and one man can build a wall together in three hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them five hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 2 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 22 / 7
Rationale: "solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 3 - - > ( 1 ) , w + 2 g = 1 / 3 - - > ( 2 ) and m + g = 1 / 5 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 15 , m = 2 / 15 and w = 1 / 5 . so , n = 1 / ( 2 / 5 ) = 5 / 2 option , a"
Answer: a
Problem: two trains each 170 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 55 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely .
Options: a ) 15 sec , b ) 11.6 sec , c ) 31.6 sec , d ) 12.6 sec , e ) 23 sec
Rationale: explanation : d = 170 m + 170 m = 340 m rs = 55 + 50 = 105 * 5 / 18 = 146 / 5 t = 340 * 5 / 146 = 11.6 sec answer : option b
Answer: b
Problem: 8 cups of water are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of water should be poured into the 8 - cup bottle ?
Options: a ) 2 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 8 / 3 , e ) 16 / 3
Rationale: let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : e
Answer: e
Problem: a candidate got 30 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 2028 , c ) 2775 , d ) 10000 , e ) 6851
Rationale: "30 % - - - - - - - - - - - l 70 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 40 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 10000 answer : d"
Answer: d
Problem: the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 15 years old . what is the value of n ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "14 n + 32 = 15 ( n + 1 ) n = 17 the answer is e ."
Answer: e
Problem: the average of 7 numbers is 26 . 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 ) 125 , e ) e ) 130
Rationale: "explanation : average of new numbers = 26 * 5 = 130 answer : option e"
Answer: e
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 345 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 100 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 345 = 5 x / 20 = 5 = > x = 100 answer : c"
Answer: c
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 88 , what is the difference between the ages of patrick and monica ?
Options: a ) 22 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 88 x = 2 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 2 = 22 answer a"
Answer: a
Problem: 14 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 189 , e ) 45
Rationale: "there are 14 business exec and in each handshake 2 business execs are involved . hence 14 c 2 = 91 also , each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake . total = 91 + 98 = 189 ans : d"
Answer: d
Problem: 5 n - 3 > 12 and 7 n - 5 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9
Rationale: 5 n - 3 > 12 5 n > 15 n > 3 7 n - 5 < 44 7 n < 49 n < 7 so n must be between 3 and 7 3 < n < 7 correct answer d
Answer: d
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 12 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 12 . then 4 n < 12 and n < 3 . the largest possible integer is n = 2 . the answer is b ."
Answer: b
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 11 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 6.24 , b ) 7.4 , c ) 7.92 , d ) 6.28 , e ) 7.24
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 11 ) = 7 / 44 the cistern will be filled in 44 / 7 hrs i . e . , 6.28 hrs . answer : d"
Answer: d
Problem: what is 3 / 7 of 7 / 8 of 1 / 3 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 9 / 16 , d ) 1 / 8 , e ) 16 / 9
Rationale: 3 / 7 * 7 / 8 * 1 / 3 = 1 / 8 answer : d
Answer: d
Problem: the least number which should be added to 2400 so that the sum is exactly divisible by 5 , 6,4 and 3 is :
Options: a ) 3 , b ) 13 , c ) 20 , d ) 33 , e ) 43
Rationale: solution l . c . m . of 5 , 6,4 and 3 = 60 . on dividing 2400 by 60 , the remainder is 40 . ∴ number to be added = ( 60 - 40 ) = 20 . answer c
Answer: c
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 82 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 8400 , b ) 8200 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 82 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 82 = > total appeared candidates in state b = 82 x 100 = 8200 = > total appeared candidates in state a = total appeared candidates in state b = 8200"
Answer: b
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 100 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 34 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 100 = 340 m . time taken = 340 / 10 = 34 sec . answer : c"
Answer: c
Problem: in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 8720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 8720 32.5 k = 32.5 k / 100 k * 8720 = 2834 the number of valid votes polled in favour of b is 2834 . answer : c"
Answer: c
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ?
Options: a ) $ 1200 , b ) $ 1005.8 , c ) $ 555.6 , d ) $ 1009.2 , e ) $ 1490.7
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2500 = $ 555.6"
Answer: c
Problem: 23 , 29 , 31 , 37 , 41 , 43 , ( . . . )
Options: a ) 53 , b ) 48 , c ) 59 , d ) 47 , e ) 50
Rationale: "all are prime numbers in their order , starting from 23 hence , next number is 47 answer is d"
Answer: d
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 81 . how much was lent at 5 % ?
Options: a ) 299 , b ) 666 , c ) 778 , d ) 900 , e ) 977
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 81 5 x / 100 + 90 – 6 x / 100 = 81 x / 100 = 9 = > x = 900 answer : d"
Answer: d
Problem: what will be the difference between simple and compound interest at 16 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 164.19 , b ) 164.12 , c ) 170.6 , d ) 167.1 , e ) 165.11
Rationale: "s . i . = ( 1000 * 16 * 4 ) / 100 = rs . 640 c . i . = [ 1000 * ( 1 + 16 / 100 ) 4 - 1000 ] = rs . 810.6 difference = ( 810.6 - 640 ) = rs . 170.6 answer : c"
Answer: c
Problem: in what time will a train 350 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.95 sec , c ) 1.3 sec , d ) 8.75 sec , e ) 1.85 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 100 / 40 = 8.75 sec . answer : d"
Answer: d
Problem: an aeroplane covers a certain distance of 530 kmph in 5 hours . to cover the same distance in 3 2 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 540 , c ) 640 , d ) 722 , e ) 250
Rationale: "speed of aeroplane = 530 kmph distance travelled in 5 hours = 530 * 5 = 2650 km speed of aeroplane to acver 2650 km in 11 / 3 = 2650 * 3 / 11 = 722 km answer d"
Answer: d
Problem: there are 4 red books and 4 blue books on a shelf . if 2 books are selected at random from the shelf , what is the probability that both books selected are red books ?
Options: a ) 2 / 7 , b ) 3 / 7 , c ) 3 / 14 , d ) 5 / 28 , e ) 9 / 28
Rationale: the number of ways of choosing 2 books from the shelf is 8 c 2 = 28 . the number of ways of choosing 2 red books is 4 c 2 = 6 . p ( 2 red books ) = 6 / 28 = 3 / 14 . the answer is c .
Answer: c
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 4 attempts ?
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 11 / 16 , e ) 15 / 16
Rationale: p ( missing all 4 ) = ( 1 / 2 ) ^ 4 = 1 / 16 p ( success on at least one attempt ) = 1 - 1 / 16 = 15 / 16 the answer is e .
Answer: e
Problem: a no . when divided by 222 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 10 , e ) 15
Rationale: "222 + 43 = 265 / 17 = 10 ( remainder ) d"
Answer: d
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 4 : 7 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 8 , b ) 1 : 7 , c ) 1 : 6 , d ) 1 : 5 , e ) 1 : 4
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 4 : 7 , thus the smaller number must have a ratio of 1 . the ratio of the smaller number to the larger number is 1 : 7 . the answer is b ."
Answer: b
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 5 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 5 then x = 5 / 1000 = 0.005 . the answer is a"
Answer: a
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 265 m long ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 77 , e ) 21
Rationale: ": speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 265 = 625 m required time = 625 * 2 / 25 = 50 sec answer : a"
Answer: a
Problem: if the sales tax be reduced from 4 ( 1 / 2 ) % to 3 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 10500 ?
Options: a ) rs . 105 , b ) rs . 150 , c ) rs . 146 , d ) rs . 135 , e ) none of these
Rationale: "explanation : required difference = ( 4 ( 1 / 2 ) of rs . 10500 ) - ( 3 ( 1 / 2 ) of rs . 10500 ) = ( 9 / 2 – 7 / 2 ) % of rs . 10500 = ( 1 ) x ( 1 / 100 ) x 10500 = rs . 105 answer a"
Answer: a
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 151 ?
Options: a ) 2050 , b ) 2350 , c ) 2650 , d ) 2950 , e ) 3250
Rationale: "100 + 102 + . . . + 150 = 100 * 26 + ( 2 + 4 + . . . + 50 ) = 100 * 26 + 2 * ( 1 + 2 + . . . + 25 ) = 100 * 26 + 2 ( 25 ) ( 26 ) / 2 = 100 * 26 + 25 * 26 = 125 ( 26 ) = 3250 the answer is e ."
Answer: e
Problem: in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 3 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 50 , b ) 70 , c ) 100 , d ) 130 , e ) 140
Rationale: "rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 3 of all one - bedroom : 1 / 3 * { all one bedroom } = 40 - - > { all one - bedroom } = 120 { all two - bedroom } = 490 - 120 = 370 . two - bedroom not rented = 370 - 240 = 130 answer : d ."
Answer: d
Problem: if six machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 72 , d ) 80 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 6 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 4 = 10 / 3 * x x = 6 / 5 hour so 72 minutes answer : c"
Answer: c
Problem: a fill pipe can fill 1 / 2 of cistern in 30 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 15 min , b ) 20 min , c ) 25 min , d ) 30 min , e ) 35 min
Rationale: "required time = 30 * 2 * 1 / 2 = 30 minutes answer is d"
Answer: d
Problem: the value of ( 4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31 ) is
Options: a ) 0.47 , b ) 47 , c ) 470 , d ) 4700 , e ) none
Rationale: "solution given expression = 4.7 × ( 13.26 + 9.43 + 77.31 ) = 4.7 × 100 = 470 . answer c"
Answer: c
Problem: a is 30 % more efficient than b . how much time will they working together take to complete a job which a alone could have done in 23 days ?
Options: a ) 11 , b ) 13 , c ) 20 3 / 17 , d ) 14 , e ) none of these
Rationale: explanation : ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b takes x days to work the 10 : 13 : : 23 : x = > x = 23 x 13 / 10 = 299 / 10 a ’ s one day work = 1 / 23 and b ’ s is 10 / 299 then a + b ‘ s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 = > 13 days answer : option b
Answer: b
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2445 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 815 , d ) s . 900 , e ) s . 920
Rationale: "2445 * 1 / 3 = 815 option c"
Answer: c
Problem: if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 18 km , d ) 60 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 20 ) / 15 5 x - 300 = > x = 60 km . answer : d"
Answer: d
Problem: gwen drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 30 miles / hr for the remaining 40 miles of the trip if she made no stops during the trip what was gwen ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 80 miles total time = 40 / 15 + 40 / 30 = 4 avg . speed = 20 . answer - b
Answer: b
Problem: a boat m leaves shore a and at the same time boat b leaves shore b . they move across the river . they met at 500 yards away from a and after that they met 300 yards away from shore b without halting at shores . find the distance between the shore a & b .
Options: a ) 1100 yards , b ) 1200 yards , c ) 1300 yards , d ) 1400 yards , e ) 1000 yards
Rationale: "if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b"
Answer: b
Problem: 78 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 8 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: "78 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 78 = 80 , 48 = 50 , 25,075 = 25,000 are derived , which makes ( 78 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is b ."
Answer: b
Problem: the average salary / head of all the workers in a workshop is rs . 1000 , if the average salary / head of 10 technician is rs . 1200 and the average salary / head of the rest is rs . 820 , the total no . of workers in the work - shop is ?
Options: a ) 120 / 9 , b ) 140 / 9 , c ) 150 / 9 , d ) 190 / 9 , e ) 170 / 9
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y - 10 workers . 10 x 1200 + 820 ( y - 10 ) = 1000 y ⇒ 12000 + 820 y - 8200 = 1000 y ⇒ 180 y = 3800 ∴ y = 190 / 9 so total number of workers = 190 / 9 d
Answer: d
Problem: the maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 40 , c ) 80 , d ) 90 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1080 and 920 = 40 . answer b"
Answer: b
Problem: 76 ^ 77 / 7 remainder is ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: as , 4 ^ 3 / 3 = 64 / 3 remainder = 1 and also 4 / 3 = 1 and 5 ^ 3 / 3 remainder = 2 and also 5 / 3 = 2 so it does not matter on the power value so the answer will be 76 / 7 remainder = 6 answer : b
Answer: b
Problem: 30 ^ 10 / 240 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) ( 15 / 4 ) ^ 5 , c ) 3 ^ 6 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 240 ^ 5 = ? a . 6 ^ 5 b . ( 15 / 4 ) ^ 5 c . 3 ^ 6 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 240 ^ 5 = ( 30 ^ 10 ) / ( 8 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 8 ^ 5 ) = ( 2 ^ 5 ) ( 15 ^ 5 ) / ( 2 ^ 5 ) ( 4 ^ 5 ) = ( 15 / 4 ) ^ 5 . thus , b is the answer ."
Answer: b
Problem: 20 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 ) 380 , b ) 470 , c ) 560 , d ) 650 , e ) 740
Rationale: "2 * 20 c 2 = 2 * 190 = 380 the answer is a ."
Answer: a
Problem: working alone , a can complete a certain kind of job in 15 hours . a and d , working together at their respective rates , can complete one of these jobs in 10 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "let total time taken by d to complete the job = d total time taken by a to complete the job = 15 work done by a in an hour 1 / a = 1 / 15 working together a and d can complete the job in 10 hours 1 / a + 1 / d = 1 / 10 = > 1 / d = 1 / 10 - 1 / 15 = 1 / 10 - 1 / 15 = 1 / 30 = > d = 30 hours answer e"
Answer: e
Problem: a can do a job in 12 days and b can do it in 20 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 15 days , b ) 13 days , c ) 22 days , d ) 11 days , e ) 19 days
Rationale: "a 1 / 12 + 1 / 20 = 2 / 15 15 / 2 * 2 = 15 days"
Answer: a
Problem: fresh grapes contain 80 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 40 kg of fresh grapes ?
Options: a ) 10 kg , b ) 12 kg , c ) 15 kg , d ) 16 kg , e ) 20 kg
Rationale: "from the question we know : 40 kg * 80 % = 32 kg of water in the fresh grapes 40 kg - 32 kg of water = 8 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 20 % of the weight of the dry graps is water and we know that 8 kg is non - water mass we can set up the following equation : x = 1 / 5 ( x ) + 8 kg 4 / 5 ( x ) = 8 kg x = 10 kg answer - a"
Answer: a
Problem: java house charges $ 4.25 for a cup of coffee that costs a total of $ 3.85 to make . cup ' o ' joe charges $ 4.80 for a cup that costs $ 4.65 to make . if java house sells 55000 cups of coffee , how many must cup ' o ' joe sell to make at least as much in total gross profit as its competitor does ?
Options: a ) 7,858 , b ) 8,301 , c ) 14,667 , d ) 63,840 , e ) 146,667
Rationale: java : profit / cup = 4.25 - 3.85 = 0.4 : no of cups = 55,000 : gross profit = 55,000 * 0.4 = 22,000 joe : profit / cup = 0.15 : gross profit = 22,000 : no of cups = 22,000 / 0.15 = 220,000 / 1.5 ( only closes is 146,667 ) answer e
Answer: e
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 14 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 14 + 11 - - > { bike } = 49 - - > # those who have bike only is { bike } - { both } = 49 - 14 = 35 . answer : b ."
Answer: b
Problem: if the product of two numbers is 62216 and their h . c . f . is 22 , find their l . c . m .
Options: a ) 2828 , b ) 2850 , c ) 1365 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 62216 , because we know product of two numbers = product of hcf and lcm lcm = 62216 / 22 = 2828 option a"
Answer: a
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) 287 , b ) 1287 , c ) 140 , d ) 988 , e ) 271
Rationale: "3 x * 2 x = 4704 = > x = 28 2 ( 84 + 56 ) = 280 m 280 * 1 / 2 = rs . 140 answer : c"
Answer: c
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 12 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 96 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,12 = 12 / 100 x = 80 * 12 / 100 x = 9.6 9.6 / 10 = 0.96 = 96 % , answer d"
Answer: d
Problem: a train crosses a tunnel of 1200 m in 45 sec , same train crosses another platform of length 180 m in 15 sec . then find the length of the train ?
Options: a ) 350 m , b ) 400 m , c ) 272 m , d ) 330 m , e ) 267 m
Rationale: length of the train be ‘ x ’ ( x + 1200 ) / 45 = ( x + 180 ) / 15 x + 1200 = 3 x + 540 2 x = 660 x = 330 m answer : d
Answer: d
Problem: if 8 men or 12 women can do a piece of work in 40 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 ) 24 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 40 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 40 = 1 / 480 so , 20 women work = 20 / 480 = 1 / 24 ans : 24 days answer : e"
Answer: e
Problem: if the sides of a triangle are 21 cm , 19 cm and 5 cm , what is its area ?
Options: a ) 42.25 cm 2 , b ) 57.5 cm 2 , c ) 42.5 cm 2 , d ) 47.5 cm 2 , e ) 52.5 cm 2
Rationale: "the triangle with sides 21 cm , 19 cm and 5 cm is right angled , where the hypotenuse is 21 cm . area of the triangle = 1 / 2 * 19 * 5 = 47.5 cm 2 answer : d"
Answer: d
Problem: excluding stoppages , the speed of a bus is 90 km / hr and including stoppages , it is 84 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 18 min , b ) 4 min , c ) 8 min , d ) 6 min , e ) 5 min
Rationale: "due to stoppages , it covers 6 km less . time taken to cover 6 km = 6 / 90 * 60 = 4 min . answer : b"
Answer: b
Problem: two persons a and b can complete a piece of work in 18 days and 24 days respectively . if they work together , what part of the work will be completed in 2 days ?
Options: a ) 7 / 36 , b ) 9 / 35 , c ) 4 / 37 , d ) 8 / 35 , e ) 5 / 3
Rationale: "a ' s one day ' s work = 1 / 18 b ' s one day ' s work = 1 / 24 ( a + b ) ' s one day ' s work = 1 / 18 + 1 / 24 = 7 / 72 the part of the work completed in 3 days = 2 ( 7 / 72 ) = 7 / 36 . answer : a"
Answer: a
Problem: present birth rate is 32 per 1000 while death rate is 11 per 1000 . what will be the percentage increase in the rate of population ?
Options: a ) 0.21 % , b ) 21 % , c ) 0.021 % , d ) 2.1 % , e ) none of these
Rationale: birth rate = 32 / 1000 = 0.032 death rate = 11 / 1000 = 0.011 increase in population = 0.032 - 0.011 = 0.021 = 2.1 % answer : d
Answer: d
Problem: on selling 11 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 45 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 120
Rationale: "( c . p . of 11 balls ) - ( s . p . of 11 balls ) = ( c . p . of 5 balls ) c . p . of 6 balls = s . p . of 11 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 6 = rs . 120 . answer : option e"
Answer: e
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 2 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) ( a ) 7 / 16 , b ) ( b ) 7 / 11 , c ) ( c ) 10 / 21 , d ) ( d ) 17 / 35 , e ) ( e ) 1 / 2
Rationale: "a simpler way i guess would be to think that in total 5 cups were sold . out of which 2 are small and 3 are large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 2 * 6 = 12 and 3 * 7 = 21 . total revenue was 12 + 21 = 33 and large cup sales as found above is 21 therefore answer is 21 / 33 i . e 7 / 11 b"
Answer: b
Problem: a boy is travelling from his home to school at 3 km / hr and reached 7 min late . next day he traveled at 6 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 1.2 km , b ) 1.3 km , c ) 1.4 km , d ) 1.5 km , e ) 1.6 km
Rationale: "let the distance be x t 1 = x / 3 hr t 2 = x / 6 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 3 - x / 6 = 1 / 4 x / 6 = 1 / 4 x = 1.5 km answer is d"
Answer: d
Problem: a parking garage rents parking spaces for $ 15 per week or $ 30 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 420 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 15 = 780 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 30 = 360 $ 780 - 360 = 420 ans d"
Answer: d
Problem: the price of commodity x increases by 40 cents every year , while the price of commodity y increases by 15 cents every year . in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 6.30 . in which year will the price of commodity x be 15 cents more than the price of commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 15 cents more than commodity y . $ 2.25 / 25 cents = 9 years the answer is 2001 + 9 years = 2010 . the answer is a ."
Answer: a
Problem: steve traveled the first 2 hours of his journey at 60 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
Options: a ) 60 mph , b ) 72 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "distance traveled in 2 hours = 2 * 60 = 120 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 120 = 360 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 360 / 5 = 72 mph answer : b"
Answer: b
Problem: a 12 % stock yielding 10 % is quoted at :
Options: a ) rs . 83.33 , b ) rs . 110 , c ) rs . 112 , d ) rs . 120 , e ) rs . 140
Rationale: income of rs 10 on investment of rs 100 income of rs 12 on investment of ? = ( 12 * 100 ) / 10 = 120 answer : d
Answer: d
Problem: machine a takes 100 hours to complete a certain job and starts that job at 7 am . after two hour of working alone , machine a is joined by machine b and together they complete the job at 12 pm . how long would it have taken machine b to complete the jobif it had worked alone for the entire job ?
Options: a ) 100.11 , b ) 10.98 , c ) 18.07 , d ) 45.01 , e ) 35.09
Rationale: let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 2 hr ( so 2 units done ) then a and b finish total work in 15 hours . hence a and b finish 98 units in 15 hours . of these 1 x 15 = 15 units were done by a . hence b did 83 units in 15 hours . hence b ( working rate ) = 83 / 15 units / hr hence b takes 100 x 15 / 83 = 18.07 hours to complete the job . answer c .
Answer: c
Problem: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,070 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 8 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: "79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,070 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,070 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is b ."
Answer: b
Problem: to fill a tank , 20 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to one - fifth of its present ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 20 x . new capacity of bucket = 1 / 5 x therefore , required number of buckets = ( 20 x ) / ( 1 x / 5 ) = ( 20 x ) x 5 / 1 x = 100 / 1 = 100 answer is a ."
Answer: a