regisss/math_qa huggingface dataset:
Problem: a regular hexagon is there . the mid points of the sides were joined and formed another hexagon . then what is the percentage reduction in area .
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: let abcdef be the regular hexagon with sides ab and ed parallel . p and q are mid points of af and ef resp . ae = root ( 3 ) * s ( s is side of hexagon ) then pq = ( root ( 3 ) * s ) / 2 mid point theorem now u know side of inner hexagon use formula area of hexagon = ( 3 * root ( 3 ) ) 2 * s ^ 2 and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon ans 25 % answer : a
Answer: a
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 85 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 606 . , d ) 644 . , e ) 666 .
Rationale: "answer is c : 606 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 85 % of total is 515 , so 100 % is approx . 606 ."
Answer: c
Problem: if the length of the longest chord of a certain circle is 20 , what is the radius of that certain circle ?
Options: a ) 2.5 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 20 = 2 * 10 so radius of the circle = 10 correct answer - c"
Answer: c
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 6 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 6 % of 10,000 which is $ 600 . so for the four quarters in the year , he will approximately play 600 * 4 = 2400 over the entire year . the compound interest will be more than 2400 . all other options are not right except d . answer : d"
Answer: d
Problem: in a certain game of dice , the player ’ s score is determined as a sum of four throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 26 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 1296 , d ) 1 / 84 , e ) 1 / 42
Rationale: "toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 + 6 + 6 = 24 , because if he gets even one less than that so 23 , someone can get 24 and jim will get nothing . p ( 24 ) = 1 / 6 ^ 4 = 1 / 1296 . answer : c ."
Answer: c
Problem: 3 candidates in an election and received 4136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 45 % , b ) 49 % , c ) 50 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 4136 + 7636 + 11628 ) = 23400 so , required percentage = 11628 / 23400 * 100 = 50 % c"
Answer: c
Problem: by selling a book for 200 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 166 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: sp = 120 % of cp ; : . cp = 200 × 100 / 120 = 166 option ' b '
Answer: b
Problem: a piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse , leaving a smaller triangle . there was a 35 % reduction in the length of the hypotenuse of the triangle . if the area of the original triangle was 34 square inches before the cut , what is the area ( in square inches ) of the smaller triangle ?
Options: a ) 16.665
b ) 16.565
c ) 15.465
d ) 14.365
e ) 14.378
Rationale: explanation : smaller triangle and original triangle will be similar to each other . ratio of area = ( ratio of side ) 2 area of smaller triangle = area of original triangle * ( 65 / 100 ) 2 = 14.365 . answer : d
Answer: d
Problem: in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 80 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 80 = ( 80 * 30 ) / 40 = 60 . in x game of 100 points , y gives ( 80 - 60 ) = 20 points to c . b"
Answer: b
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 110 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 ) 35 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 + 110 = 350 m . time taken = 350 / 10 = 35 sec . answer : c"
Answer: c
Problem: a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations f are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) f = 8
Rationale: "the combinations could be f { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e"
Answer: e
Problem: by travelling at 50 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 23 kmph , b ) 24 kmph , c ) 25 kmph , d ) 26 kmph , e ) 27 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 50 * 3 x = 150 x km he covered 2 / 3 * 150 x = 100 x km in 1 / 3 * 3 x = x hours so , the remaining 50 x km , he has to cover in 2 x hours . required speed = 50 x / 2 x = 25 kmph . answer : c"
Answer: c
Problem: what is the 29 th digit to the right of the decimal point in the decimal form of 4 / 11 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "4 / 11 = 0.363636 . . . the odd numbered positions in the decimal expansion are all 3 . the answer is c ."
Answer: c
Problem: the average of 100 , 200300 and x is 250 and the average of 300 , 150100 , x and y is 200 . what is the value of y ?
Options: a ) 100 , b ) 150 , c ) 50 , d ) 200 , e ) 250
Rationale: we have : ( 100 + 200 + 300 + x ) / 4 = 250 600 + x = 1000 x = 400 ( 300 + 150 + 100 + x + y ) / 5 = 200 550 + 400 + y = 1000 y = 50 answer is c
Answer: c
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 500 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 1250 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 500 = 1250 answer : b"
Answer: b
Problem: a passenger train takes two hours less for a journey of 300 km if its speed is increased by 5 kmph from its normal speed . the normal speed is
Options: a ) 35 kmph , b ) 50 kmph , c ) 25 kmph , d ) 30 kmph , e ) 38 kmph
Rationale: let normal speed = x increased speed = x + 5 initial = > x = 300 / t 1 = > t 1 = 300 / x after = > ( x + 5 ) = 300 / ( t 1 - 2 ) = > ( x + 5 ) = 300 / [ ( 300 / x ) - 2 ] = > x = 25 kmph answer : c
Answer: c
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 54 seconds . what is the length of each train ( in meters ) ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 54 seconds , the relative difference in distance traveled is 54 * 25 / 9 = 150 meters this distance is twice the length of each train . the length of each train is 150 / 2 = 75 meters the answer is d ."
Answer: d
Problem: the jogging track in a sports complex is 660 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 5.28 min , c ) 5.08 min , d ) 4.8 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 660 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 660 m apart , they take ( 100 / 825 * 660 / 1000 ) hrs = ( 660 / 8250 * 60 ) min = 4.8 min . answer : d"
Answer: d
Problem: in a room with 9 people , 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 1
Rationale: "( 6 / 9 ) ( 7 / 8 ) + ( 5 / 9 ) ( 6 / 8 ) if you choose one of the 6 with one other friend , then you have a 7 / 8 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 8 chance of not picking one of their friends second . add them up . 42 / 72 + 30 / 72 72 / 72 = 1 e . 1"
Answer: e
Problem: find the area of trapezium whose parallel sides are 24 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 315 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 24 + 18 ) * ( 15 ) = 315 cm 2 answer : c"
Answer: c
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 20 , 60 , and what number ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 a"
Answer: a
Problem: a and b started a business investing rs . 92,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 2 , c ) 23 : 5 , d ) 18 : 4 , e ) 17 : 4
Rationale: a : b = 92000 : 20000 = 92 : 20 = 46 : 10 = 23 : 5 answer : c
Answer: c
Problem: the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 15 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 13 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 85 y thus 75 x = 85 y or x = 1.13 y ans r = 113 y so increase = 13 % answer : d"
Answer: d
Problem: if a large pizza has a radius that is 20 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 20 % , b ) 36 % , c ) 44 % , d ) 50 % , e ) 64 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.2 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.2 * r ) ^ 2 = 1.44 * pi * r ^ 2 , an increase of 44 % . the answer is c ."
Answer: c
Problem: how many cubes of 5 cm edge can be cut out of a cube of 15 cm edge
Options: a ) 36 , b ) 232 , c ) 27 , d ) 48 , e ) none of these
Rationale: "explanation : number of cubes = ( 15 x 15 x 15 ) / ( 5 x 5 x 5 ) = 27 answer : c"
Answer: c
Problem: 160 is what percent of 50 ?
Options: a ) 5 % , b ) 20 % , c ) 320 % , d ) 200 % , e ) 500 %
Rationale: "50 * x = 160 - - > x = 3.2 - - > 3.2 expressed as percent is 320 % . answer : c ."
Answer: c
Problem: a precious stone weighing 35 grams worth rs . 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5 . if the price varies as the square of the weight then find the loss incurred .
Options: a ) rs . 5750 , b ) rs . 6000 , c ) rs . 5500 , d ) rs . 5000 , e ) rs . 7000
Rationale: the price varies as the square of the weight , p = k x w 2 12250 = k x 352 k = 10 thus , p = 10 w 2 when the two pieces are in the ratio 2 : 5 ( weight wise ) then we know that their weights must be 10 g and 25 g respectively . their values should be : 10 g piece : 10 x 102 = rs . 1000 ; 25 g piece : 10 x 252 = rs . 6250 . total value of stone now , = 1000 + 6250 = rs . 7250 loss incurred = 12250 - 7250 = rs . 5000 answer : d
Answer: d
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 1 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) = 0.25 answer : d"
Answer: d
Problem: find the least number must be subtracted from 5474827 so that remaining no . is divisible by 12 ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 2
Rationale: "on dividing 5474827 by 12 we get the remainder 7 , so 7 should be subtracted d"
Answer: d
Problem: how many even integers from 1 to 200 ( both inclusive ) have even number of factors ?
Options: a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7
Rationale: "integers having even number of factors will be perfect squares . even numbers will have even perfect squares . thus , the possible values for the perfect squares are : 4 , 16,36 , 64,100 , 144,196 and the corresponding integers are 2 , 4,6 , 8,10 , 12,14 ( more than 6 ) . thus e is the correct answer ."
Answer: e
Problem: working alone , pump a can empty a pool in 6 hours . working alone , pump b can empty the same pool in 9 hours . working together , how many minutes will it take pump a and pump b to empty the pool ?
Options: a ) 192 , b ) 200 , c ) 208 , d ) 216 , e ) 224
Rationale: "pump a can empty ( 1 / 6 ) of the pool per hour . pump b can empty ( 1 / 9 ) of the pool per hour . together the pumps can empty 1 / 6 + 1 / 9 = 5 / 18 of the pool per hour . 1 pool / ( 5 / 18 ) pool per hour = 18 / 5 hours = 216 minutes . the answer is d ."
Answer: d
Problem: a bakery has 6 employees . it pays annual salaries of $ 18,000 to each of 2 employees , $ 20,000 to 1 employee , and $ 21,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 19,200 , b ) $ 19,500 , c ) $ 19,800 , d ) $ 20,000 , e ) $ 20,400
Rationale: "average = 2 ( 18000 ) + ( 20000 ) + 3 ( 21000 ) / 6 = $ 19,833 the answer is c ."
Answer: c
Problem: a box contains 4 black , 3 red and 6 green marbles . 3 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 24 / 286 , b ) 25 / 709 , c ) 25 / 286 , d ) 24 / 268 , e ) 24 / 226
Rationale: "explanation : total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 3 marbles are drawn from 13 marbles at random . therefore , n ( s ) = 13 c 3 = 286 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 4 c 3 + 3 c 3 + 6 c 3 = 4 + 1 + 20 = 25 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 25 / 286 answer : c"
Answer: c
Problem: how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 19 inches than that of a rectangular sheet of paper measuring 9.5 inches by 11 inches ?
Options: a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
Rationale: "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 19 is twice 9.5 then the area will be double which means 100 % greater . the answer is c ."
Answer: c
Problem: annika hikes at a constant rate of 10 minutes per kilometer . she has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 45 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "set up two r x t = d cases . 1 . 1 / 10 km / min x t = 2.5 from which t = 25 mins . we know total journey time now is 45 + 25 = 70 the rate is the same ie 1 / 10 km / min . set up second r x t = d case . 1 / 10 km / min x 70 = 7 km now the total journey would be halved as distance would be same in each direction . 7 / 2 = 3.5 b ."
Answer: b
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 18 of money ?
Options: a ) 1800 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 18 ( 100 / 10 ) 2 = > p = 1800 answer : a"
Answer: a
Problem: 544 , 509 , 474 , 439 , . . . ?
Options: a ) 404 , b ) 302 , c ) 108 , d ) 115 , e ) 210
Rationale: "each number is 35 less than the previous number . 544 544 - 35 = 509 509 - 35 = 474 474 - 35 = 439 439 - 35 = 404 answer : a"
Answer: a
Problem: if the sum of a number and its square is 182 , what is the number ?
Options: a ) 15 , b ) 26 , c ) 28 , d ) 91 , e ) none of these
Rationale: "let the number be x . then , x + x 2 = 182 ( x + 14 ) ( x - 13 ) = 0 x = 13 answer : e"
Answer: e
Problem: the difference between compound and simple interest on a certain sum of money for 3 years at 6 2 / 3 % p . a is rs . 184 . find the sum ?
Options: a ) 33772 , b ) 26782 , c ) 26788 , d ) 13500 , e ) 27761
Rationale: p = ( 184 * 106 ) / [ 6 2 / 3 * 6 2 / 3 * ( 300 * 6 2 / 3 ) ] p = 13500 answer : d
Answer: d
Problem: a block of wood has dimensions 10 cm x 10 cm x 80 cm . the block is painted red and then cut evenly at the 40 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5.6 %
b ) 8.4 %
c ) 11.2 %
d ) 14.8 %
e ) 17.5 %
Rationale: the area of each half is 100 + 4 ( 400 ) + 100 = 1800 the area that is not painted is 100 . the fraction that is not painted is 100 / 1800 = 1 / 18 = 5.6 % the answer is a .
Answer: a
Problem: the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 3200 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 3200 x = ( 2 ^ 7 * 25 ) / 2 ^ 9 = 25 / 4 the answer is b ."
Answer: b
Problem: a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 45 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 33 % . , e ) 51 % .
Rationale: "30 % of 2 litres = 0.6 litres 45 % of 6 litres = 2.7 litres therefore , total quantity of alcohol is 3.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 33 % d"
Answer: d
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 60 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 89 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 60 % more than company a ' s assets which is 160 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 80 a + b = 180 kw = 160 kw / ( a + b ) * 100 = 160 / 180 * 100 = 88.88 % or 89 % c"
Answer: c
Problem: a certain rectangular window is ( 2 / 5 ) times as long as it is wide . if its perimeter is 28 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2 , b ) 11 by 3 , c ) 10.5 by 3.5 , d ) 10 by 4 , e ) 9 by 3
Rationale: "2 x + 2 y = 28 x + y = 14 x + ( 2 / 5 ) x = 14 1.4 x = 14 x = 10 answer d"
Answer: d
Problem: a person travels equal distances with speeds of 5 km / hr , 6 km / hr and 7 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 5 km , b ) 3 km , c ) 7 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 5 + x / 6 + x / 7 = 27 / 53 27 x / 53 = 47 / 60 = > x = 1.54 total distance = 3 * 1.54 = 4.61 km . answer : a"
Answer: a
Problem: if the a radio is sold for rs 490 and sold for rs 465.50 . find loss value .
Options: a ) 24.5 , b ) 12.5 , c ) 17.25 , d ) 6.5 , e ) 13.62
Rationale: "cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . ans : a"
Answer: a
Problem: set s consists of integers { 4 , 7 , 10 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 50 % . what is the value of integer n ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 50 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d ."
Answer: d
Problem: a ’ s speed is 51 / 44 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 51 , b ) 4 / 51 , c ) 7 / 51 , d ) 3 / 44 , e ) 7 / 44
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 51 meters , b covers 44 meters in that time . so if the race is 51 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 51 meters ) would be the same as the time required by b ( to cover 44 meters ) to reach the finish line . so b should get a head start of 7 / 51 th of the race . answer ( c )"
Answer: c
Problem: john and mike enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if john received $ 800 more than mike did , what was the profit made by their business in that year ?
Options: a ) 46457 , b ) 465745 , c ) 3000 , d ) 3456 , e ) 35346
Rationale: say the profit was $ x . john share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 mike ' s share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is c
Answer: c
Problem: two men are walking towards each other alongside a railway track . a freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction . the train passes this man is 18 seconds . assume the velocities are constant throughout . how long after the train has passed the second man will the two men meet ?
Options: a ) 89.7 minutes , b ) 90 minutes , c ) 90.3 seconds , d ) 91 seconds , e ) none of these
Rationale: explanation : let ‘ l ’ be the length of train , ‘ x ’ be the speed of the first man , ‘ y ’ be the speed of the second man and ‘ z ’ be the speed of the train . = > 20 = 1 / ( z − x ) and = > 18 = 1 / ( z + x ) = > z = 10 x + 9 y . distance between the two men = 600 ( z + y ) . time = ( 600 ( z + y ) - 600 ( x + y ) ) / ( x + y ) . = > 600 ( 9 x + 9 y ) / ( x + y ) . = > 90 minutes . answer : b
Answer: b
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 16 % , then the cost price of the article is :
Options: a ) 500 , b ) 334 , c ) 531 , d ) 664 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 116 = rs . 531 answer : option c"
Answer: c
Problem: a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is :
Options: a ) 2 , b ) 5 , c ) 9 , d ) 7 , e ) 6
Rationale: let the number be x x - 4 = 21 / x x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 correct answer d
Answer: d
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3520 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 420 , d ) s . 440 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3520 × ( 1 / 8 ) = 440 answer : option d"
Answer: d
Problem: a is half good a work man as b and together they finish a job in 15 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 45 / 2 , d ) 36 , e ) 48
Rationale: "c 45 / 2 wc = 1 : 2 2 x + x = 1 / 15 = > x = 1 / 45 2 x = 2 / 45 = > 45 / 2 days"
Answer: c
Problem: bookman purchased 30 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 240 , how many paperback copies were sold ?
Options: a ) 8 , b ) 12 , c ) 6 , d ) 4 , e ) 5
Rationale: "the bookman had 10 hardback ad 30 - 10 = 20 paperback copies ; 14 copies were sold , hence 30 - 14 = 16 copies were left . let # of paperback copies left be p then 10 p + 20 ( 16 - p ) = 240 - - > 10 p = 80 - - > p = 8 # of paperback copies sold is 20 - 8 = 12 answer : b"
Answer: b
Problem: what is the perimeter , in meters , of a rectangular garden 4 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48
b ) 56
c ) 60
d ) 76
e ) 104
Rationale: say length of garden is l meters . then ( l * 4 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 48 meters . perimeter of garden = 2 * ( 48 + 4 ) = 104 meter . answer is e
Answer: e
Problem: a train running at the speed of 80 km / hr crosses a pole in 10 seconds . what is the length of the train ?
Options: a ) 450 m , b ) 350 m , c ) 150 m , d ) 250 m , e ) 240 m
Rationale: speed = ( 90 * 5 / 18 ) m / sec = 25 m / sec length of the train = ( speed x time ) = ( 25 * 10 ) m = 250 m . answer : d
Answer: d
Problem: a sum of rs . 1360 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ' s share is :
Options: a ) 240 , b ) 120 , c ) 280 , d ) 160 , e ) 200
Rationale: "let c ' s share = rs . x then , b ' s share = rs . x / 4 , a ' s share = rs . ( 2 / 3 x ( x / 4 ) ) = rs . x / 6 therefore , x / 6 + x / 4 + x = 1360 = 17 x / 12 = 1360 x = 1360 x 12 / 17 = rs . 960 hence , b ' s share = rs . ( 960 / 4 ) = rs . 240 . answer is a ."
Answer: a
Problem: the present worth of rs . 242 due in 2 years at 10 % per annum compound interest is :
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 240 , d ) rs . 220 , e ) rs . 230
Rationale: "explanation : present worth of rs . x due t years hence is given by present worth ( pw ) = x / ( 1 + r / 100 ) t present worth ( pw ) = 242 / ( 1 + 10 / 100 ) 2 = 242 / ( 11 / 10 ) 2 = rs . 200 answer : option a"
Answer: a
Problem: beginning in town a , biker bob rides his bike 20 miles west , 6 miles north , 10 miles east , and then 18 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 28 miles , b ) 30 miles , c ) 26 miles , d ) 18 miles , e ) 22 miles
Rationale: using pythagoras we have one side i , e total distance traveled in north direction = 18 + 6 = 24 m other being the base ie distance traveled west - distance traveled eat = 20 - 10 = 10 m now this third side or the distance between town a and town b = 24 ^ 2 + 10 ^ 2 = sq root 676 = 26 m answer : c
Answer: c
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 23 m * 2 m * 0.75 m ?
Options: a ) 22377 , b ) 27782 , c ) 27891 , d ) 25000 , e ) 23000
Rationale: "23 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 23 = 1 / 100 * x = > x = 23000 answer : e"
Answer: e
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1340 in total compensation , how many total hours did he work that week ?
Options: a ) 76 , b ) 60 , c ) 65 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1340 - 640 = 700 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 700 / 28 = 25 total hrs = 40 + 25 = 65 answer c 65"
Answer: c
Problem: find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm .
Options: a ) 34 cm ²
b ) 38 cm ²
c ) 54 cm ²
d ) 56 cm ²
e ) 64 cm ²
Rationale: ab ² = ac ² - bc ² = 15 ² - 12 ² = 225 - 144 = 81 therefore , ab = 9 therefore , area of the triangle = ¹ / ₂ × base × height = ¹ / ₂ × 12 × 9 = 54 cm ² answer : c
Answer: c
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 24 / 60 oxen = 12 days the answer is b ."
Answer: b
Problem: the time it took car p to travel 300 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 34 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 300 / x ) - ( 300 / ( x + 10 ) ) = 2 solving for x = 34 miles \ hr . a"
Answer: a
Problem: a boat having a length 7 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 140 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 7 x 2 x 0.01 ) m 3 = 0.14 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.14 x 1000 ) kg = 140 kg . answer : a"
Answer: a
Problem: a certain car can travel 64 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 64 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 64 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : e ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 64 x 3.9 x 3.8 / 5.7 x 1.6 = 104 e"
Answer: e
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 9 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1800 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 9 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2700 . hence , ( r - p ) = ( 2700 - 900 ) = 1800 answer : a"
Answer: a
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6000 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6000 * 6 ) – 30,130 ] = rs . ( 36000 – 30,130 ) = rs . 5870 answer a"
Answer: a
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 10 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 4.8 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.4 tax on others = 2.4 percentage = 4.8 / 100 = 4.8 % answer : e"
Answer: e
Problem: x ^ 2 + sx + 72 = 0 has two distinct integer roots ; how many values are possible for s ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 24
Rationale: for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know that total factors are ( 3 + 1 ) * ( 2 + 1 ) = 12 ( reason : with 2 ^ n , we have n + 1 possibilities . n ^ 0 to n ^ n . so n + 1 ) = d
Answer: d
Problem: the sides of a square region , measured to the nearest centimeter , are 5 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 25.25 sq cm , b ) 20.25 sq cm , c ) 30.25 sq cm , d ) 36.25 sq cm , e ) 40.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 4.5 is equidistant from both 4 and 5 ) the answer still should be : 4.5 ^ 2 = 20.25 . answer : b"
Answer: b
Problem: an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets water in at the rate of 4 litres / min then outlet pipe would take 6 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 6400 litres , c ) 12800 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 4 litres / min , or 4 * 60 = 240 liters / hour ; net outflow rate when both pipes operate would be x - 240 liters / hour . capacity of the tank = x * 10 hours = ( x - 240 ) * ( 10 + 6 ) hours 10 x = ( x - 240 ) * 16 - - > x = 640 - - > capacity = 10 x = 6400 liters . answer : b ."
Answer: b
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 350 more than a :
Options: a ) 10150 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 350 total earning = \ inline \ frac { 58 xy } { 100 } = 10150 answer : a ) rs . 10150"
Answer: a
Problem: a train 50 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 3 sec . , b ) 7 sec . , c ) 9 sec . , d ) 11 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 50 m at ( 50 / 3 ) m / sec = ( 112 - 50 ) kmph = ( 50 x 3 / 50 ) sec = 3 sec . answer a"
Answer: a
Problem: indu gave bindu rs . 4375 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) s . 10 , b ) s . 7 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "4375 = d ( 100 / 4 ) 2 d = 7 answer : b"
Answer: b
Problem: how many books each of volume 100 meter cube can be packed into a crate of volume 3000 meter cube ?
Options: a ) 50 , b ) can not be determined , c ) 150 , d ) 300 , e ) 350
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 3000 m 3 can be 300 * 10 or 30 * 100 or just 3000 * 1 we do n ' t know , so we cant calculate answer : b"
Answer: b
Problem: an article is bought for rs . 675 and sold for rs . 700 , find the gain percent ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "675 - - - - 25 100 - - - - ? = > = 4 % answer : c"
Answer: c
Problem: having scored 98 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 98 = 19 ( n + 4 ) = > n = 22 so , average score after 19 th innings = x + 4 = 26 . answer : c"
Answer: c
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 50 days to complete the same work . then q alone can do it in
Options: a ) 30 days , b ) 25 days , c ) 20 days , d ) 15 days , e ) 24 days
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 50 work done by p , q and r in 1 day = 1 / 10 + 1 / 50 = 6 / 50 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day × 2 = 6 / 50 = > work done by p in 1 day = 3 / 50 = > work done by q and r in 1 day = 3 / 50 hence work done by q in 1 day = 3 / 50 – 1 / 50 = 2 / 50 = 1 / 25 so q alone can do the work in 25 days option b"
Answer: b
Problem: dhoni spent 40 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 30 % , b ) 28 % , c ) 32 % , d ) 33 % , e ) 34 %
Rationale: "say dhoni ' s earning last month was $ 100 . dhoni spent 40 percent of his earning last month on rent - - > $ 40 on rent ; 20 percent less than what he spent on rent to purchase a new dishwasher - - > $ 40 * 0.8 = $ 32 on the dishwasher . left over amount 100 - ( 40 + 32 ) = $ 28 answer : b"
Answer: b
Problem: a man whose bowling average is 12.4 , takes 7 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147
Rationale: 12.4 * x + 26 = ( 7 + x ) 12 solve equation x = 145 answer : c
Answer: c
Problem: 137 + 276 = 435 how much is 731 + 672 ?
Options: a ) 534 , b ) 1403 , c ) 1623 , d ) 1513 , e ) 1613
Rationale: 137 - 731 and 276 - 672 similarly 435 - 534 answer : a
Answer: a
Problem: a batsman scored 120 runs which included 6 boundaries and 4 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 60 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: number of runs made by running = 110 - ( 6 x 4 + 4 x 6 ) = 120 - ( 48 ) = 72 now , we need to calculate 60 is what percent of 120 . = > 72 / 120 * 100 = 60 % b
Answer: b
Problem: a bag contains 3 red , 2 blue and 4 green balls . if 2 balls are picked at random , what is the probability that both are red ?
Options: a ) 1 / 12 , b ) 1 / 13 , c ) 1 / 14 , d ) 1 / 15 , e ) 1 / 18
Rationale: "p ( both are red ) , = 3 c 2 / 9 c 2 = 1 / 12 a"
Answer: a
Problem: two pipes can separately fill a tank in 20 and 30 hours respectively . both the pipes are opened to fill the tank but when the tank is full , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 17 hrs , b ) 16 hrs , c ) 15 hrs , d ) 13 hrs , e ) 12 hrs
Rationale: 1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs answer : b
Answer: b
Problem: the area of playground is 5900 sq . meters . what will be the cost of covering it with grass sheet 1 cm deep , if cost of grass sheet is $ 2.80 per cubic meter .
Options: a ) a ) $ 144
b ) b ) $ 150.50
c ) c ) $ 165
d ) d ) $ 158.60
e ) e ) $ 160.70
Rationale: total volume * unit cost = total cost or , 5900 * 0.01 * 2.8 = total cost = 165 = c
Answer: c
Problem: hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 48 , then the other number is ?
Options: a ) 99 , b ) 66 , c ) 132 , d ) 264 , e ) 364
Rationale: "12 * 396 = 48 * x x = 99 answer : a"
Answer: a
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 4 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 36 , b ) 41 , c ) 38 , d ) 40 , e ) 42
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 4 th year = 50 , 5 th year = 50 - 4 = 46 6 th year = 46 - 5 = 41 the correct answer is b ."
Answer: b
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 20 % ?
Options: a ) 600 , b ) 2877 , c ) 208 , d ) 1882 , e ) 191
Rationale: explanation : cost price = rs . 500 profit = 20 % of 500 = rs . 100 selling price = cost price + profit = 500 + 100 = 600 answer : a
Answer: a
Problem: if x ^ 2 is divisible by 240 what is the least possible value of integer x ?
Options: a ) 120 , b ) 30 , c ) 90 , d ) 60 , e ) 12
Rationale: 240 can be written as ( 2 ^ 4 ) * 3 * 5 . for x ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option e because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option d is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : d
Answer: d
Problem: machine t can produce x units in 3 / 4 of the time it takes machine n to produce x units . machine n can produce x units in 2 / 3 the time it takes machine o to produce x units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33
Rationale: let the following be true : t makes x in time t then the following follows : n makes x in 4 t / 3 o makes x in 3 / 2 ( 4 t / 3 ) = 2 t m : n : o = 1 : 4 / 3 : 2 = 3 : 4 : 6 so n = 4 / ( 3 + 4 + 6 ) = 4 / 13 = c
Answer: c
Problem: ( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) what is m ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 31 , e ) 36
Rationale: ( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / ( 2 * ( 2 * 5 ) ^ 31 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ m = ( 1 / 5 ) ^ 31 ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / [ ( 2 ^ 32 ) * ( 5 ^ 31 ) ] so , m = 31 answer d
Answer: d
Problem: in a recent head - to - head run - off election , 12000 absentee ballets were cast . 1 / 6 of the absentee ballets were thrown out and 3 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 4,000 , d ) 8,000 , e ) 9,000
Rationale: 5 / 6 * 2 / 5 ( total absentee votes ) = 1 / 3 ( total votes ) = 1 / 3 * 12000 = 4000 answer is c
Answer: c
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 00,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 40000 , c ) 50000 , d ) 75000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 100000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 100000 - x ) = x / 3 + x / 2 = 50000 = 5 x / 6 = 50000 = x = 50000 x 6 / 5 = 60000 savings in public provident fund = rs . ( 100000 - 60000 ) = rs . 40000 answer is b ."
Answer: b
Problem: what is the probability that company g ' s advertisement will be one of the first two be shown during the first commercial break ?
Options: a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15
Rationale: g 1 / 15 + ( 14 / 15 ) * 1 / 14 = 2 / 15 d
Answer: d
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 10 years ?
Options: a ) 6 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 10 * r ) / 100 r = 2 % answer : b"
Answer: b
Problem: one drier dries certain quantity of material in 24 minutes . another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ?
Options: a ) 1.00 minutes , b ) 1.20 minutes , c ) 1.50 min , d ) 1.85 min , e ) 2.00 minutes
Rationale: by guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes therefore , answer 1.85 minutes will be correct . answer - d
Answer: d
Problem: if the lcm and hcf of 8 and another number is 24 and 4 respectively . find the other number ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 16
Rationale: "hcf x lcm = product of numbers 4 x 24 = 8 x the other number other number = ( 4 x 24 ) / 8 other number = 12 answer : b"
Answer: b