regisss/math_qa huggingface dataset:
Problem: natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3.5 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 2.125 , b ) 2.375 , c ) 2.625 , d ) 2.675 , e ) 2.825
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3.5 km / hour x / 3 = 3.5 x = 10.5 km the average speed while climbing = distance / time = 10.5 / 4 = 2.625 km / h the answer is c ."
Answer: c
Problem: how many positive integers d between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Problem: the number of the members of a club is more than 50 and less than 80 . when 5 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "the number of members is 7 k + 5 = 8 j + 5 the only number in this range which satisfies this is 61 . 61 / 9 = 6 ( 9 ) + 7 the answer is d ."
Answer: d
Problem: in a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 3 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ?
Options: a ) 63 , b ) 64.28 , c ) 65 , d ) 66 , e ) 68
Rationale: given : - violets - c / 3 carnations - c tulip - c / 9 rose - c / 9 total flowers in terms of c = c / 3 + c + c / 9 + c / 9 = 14 c / 9 percentage of carnations = c / 14 c / 9 * 100 = 64.28 % answer b
Answer: b
Problem: a batsman scored 90 runs which included 4 boundaries and 6 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 500 / 11 , c ) 42.22 % , d ) 55 % , e ) 35 %
Rationale: "explanation : number of runs made by running , = > 90 − ( 4 × 4 + 6 × 6 ) . = > 90 − 52 = > 38 hence , the required percentage is : - = > 38 / 90 * 100 = > 42.22 % answer : c"
Answer: c
Problem: a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 9 : 30 am in the same direction at the rate of 84 km / h . at what time will the second train catch the first train ?
Options: a ) 11 : 00 , b ) 11 : 30 , c ) 12 : 00 , d ) 12 : 30 , e ) 1 : 00
Rationale: "in thirty minutes the first train travels 35 km . the second train catches the first train at a rate of 84 km / h - 70 km / h = 14 km / h . the second train will catch the first train in 35 / 14 = 2.5 hours , so at 12 : 00 noon . the answer is c ."
Answer: c
Problem: two brother x and y appeared for an exam . the probability of selection of x is 1 / 5 and that of b is 2 / 7 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 30 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 5 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 5 ) ã — ( 2 / 7 ) = 2 / 35 answer : a ) 2 / 35"
Answer: a
Problem: the volumes of two cones are in the ratio 1 : 30 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 6 : 5 , b ) 6 : 9 , c ) 6 : 2 , d ) 2 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 30 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 6 / 5 i . e . h 1 : h 2 = 6 : 5 answer : a"
Answer: a
Problem: the average of runs of a cricket player of 10 innings was 42 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 86 , c ) 28 , d ) 76 , e ) 80
Rationale: "average after 11 innings = 46 required number of runs = ( 46 * 11 ) - ( 42 * 10 ) = 506 - 420 = 86 . answer : b"
Answer: b
Problem: in a survey of parents , exactly 9 / 10 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 27 % , b ) 21 % , c ) 19 % , d ) 18 % , e ) 16 %
Rationale: "fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 10 * 2 / 5 = 2 / 50 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 2 / 50 = 19 / 100 = 19 % the answer is c ."
Answer: c
Problem: cereal a is 8 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 2 , d ) 1 : 4 , e ) 1 : 3
Rationale: "( 8 / 100 ) a + ( 2 / 100 ) b = ( 4 / 100 ) ( a + b ) 4 a = 2 b = > a / b = 1 / 2 answer is c ."
Answer: c
Problem: the ratio of boarders to day students at a school was originally 2 to 5 . however , after a number of new boarders join the initial 120 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90
Rationale: "let x be the number of new boarders . the ratio changed from 2 : 5 = 4 : 10 up to 1 : 2 = 5 : 10 . 120 / ( 120 + x ) = 4 / 5 x = 30 the answer is a ."
Answer: a
Problem: a 20 kg metal bar made of alloy of tin and silver lost 2 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "the bar lost certain percentage of its weight . we do n ' t know how much tin was lost and how much silver was lost but in all 2 kg was lost with is 10 % of its overall weight . tin loses 1.375 kg in 10 kg so 13.75 % of its weight when it is put in water . silver loses . 375 kg in 5 kg so . 375 / 5 * 100 = 7.5 % of its weight in water . now , we just need to use weighted averages : wt / ws = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2.5 / 3.75 = 2 / 3 answer ( e )"
Answer: e
Problem: the radius of a cylinder is 10 m , height 12 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3300 , d ) 3771.4 , e ) 4400
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 10 ã — 10 ã — 12 = 3771.4 m ( power 3 ) answer is d ."
Answer: d
Problem: what amount does an investor receive if the investor invests $ 6000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 6980 , b ) $ 7070 , c ) $ 7120 , d ) $ 7260 , e ) $ 7340
Rationale: a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 6000 = 1.21 * 6000 = 7260 the answer is d .
Answer: d
Problem: the racing magic takes 50 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 50 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 50 seconds = 450 seconds time taken for them to meet at the starting point for the second time = 450 * 2 = 900 seconds = 15 mins answer e"
Answer: e
Problem: three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 2 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 4 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 6 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 360 min = 6 hours answer : e"
Answer: e
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 340 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 56
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 340 = 700 meter time taken to cross the platform = 700 / ( 25 / 2 ) = 700 ã — 2 / 25 = 56 seconds answer : e"
Answer: e
Problem: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 6 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 15 , b ) 20 , c ) 18 , d ) 16.5 , e ) 25
Rationale: his height was = 5 feet 6 inch = 6 + 60 = 66 inch . required % correction = 66 * ( 1.25 - 1 ) = 16.5 d
Answer: d
Problem: there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability q that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: "q probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d"
Answer: d
Problem: what is the smallest positive integer k such that the product of 3675 x k is a perfect square ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 3675 = 5 ^ 2 * 7 ^ 2 * 3 , so if k = 3 then 3675 k = ( 5 * 7 * 3 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 39 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 156 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 39 = > 4 / x = 1 / 39 x = 39 ∗ 4 = 156 mins option d"
Answer: d
Problem: there are 7 non - collinear points . how many triangles can be drawn by joining these points ?
Options: a ) 22 , b ) 38 , c ) 35 , d ) 29 , e ) 18
Rationale: explanation : a triangle is formed by joining any three non - collinear points in pairs . there are 7 non - collinear points the number of triangles formed = \ inline { \ color { black } 7 c _ { 3 } } = 35 answer : c ) 35
Answer: c
Problem: a man buys 58 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 24.82 % , d ) 13.6 % , e ) 27.82 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 58 pens = rs . 46 s . p . of 58 pens = 99 % of rs . 58 = rs . 57.42 profit % = ( profit / c . p . ) x 100 profit % = ( 11.42 / 46 ) x 100 = 24.82 % answer : c"
Answer: c
Problem: the sale price sarees listed for rs . 200 after successive discount is 10 % and 5 % is ?
Options: a ) 187 , b ) 169 , c ) 172 , d ) 178 , e ) 171
Rationale: "200 * ( 90 / 100 ) * ( 95 / 100 ) = 171 answer : e"
Answer: e
Problem: if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does doug have ?
Options: a ) $ 8 , b ) $ 9 , c ) $ 27 , d ) $ 32 , e ) $ 36
Rationale: josh + doug + brad = 68 ; josh = 2 brad , josh = 3 / 4 doug josh + 1 / 2 josh + 4 / 3 josh = 68 ( substituted the given values ) josh = 24 . 24 = 3 / 4 doug = > doug = 32 answer is d .
Answer: d
Problem: the bankers discount of a certain sum of money is rs . 144 and the true discount on the same sum for the same time is rs . 120 . the sum due is :
Options: a ) 715 , b ) 716 , c ) 718 , d ) 720 , e ) 722
Rationale: sum = ( b . d * t . d ) / ( b . d - t . d ) ( 144 * 120 ) / 144 - 120 ; 720 answer : d
Answer: d
Problem: tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many t kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
Answer: c
Problem: two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 22 , b ) 12 , c ) 67 , d ) 20 , e ) 81
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 sec . answer : d"
Answer: d
Problem: pipe a fills a tank of capacity 950 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 57 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: in one cycle they fill 40 + 30 - 20 = 50 liters 950 = 50 * n = > n = 19 here n = number of cycles . total time = 19 * 3 = 57 as in one cycle there are 3 minutes . thus 57 minutes answer : a
Answer: a
Problem: during a sale , the price of a pair of shoes is marked down 12 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 14 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 88 price after sale = 100 percent increase = 12 / 88 * 100 = 14 % approx . correct option : d"
Answer: d
Problem: if p / q = 5 / 4 , then 2 p + q = ?
Options: a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 16
Rationale: "let p = 5 , q = 4 then 2 * 5 + 4 = 14 so 2 p + q = 14 . answer : b"
Answer: b
Problem: find the missing figures : 0.75 % of ? = 0.06
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let 0.75 % of x = 0.06 . then , 0.75 * x / 100 = 0.06 x = [ ( 0.06 * 100 ) / 0.75 ] = 8 . answer is c ."
Answer: c
Problem: m is 30 % of q . q is 20 % of p . n is 50 % of p . find m : n ratio
Options: a ) 1 : 25 , b ) 2 : 25 , c ) 3 : 25 , d ) 4 : 25 , e ) 5 : 25
Rationale: let p be 100 n = 50 % of 100 ( p = 100 ) = 50 q = 20 % of 100 ( p = 100 ) = 20 m = 30 % of 20 ( q = 20 ) = 6 m : n = 6 : 50 m : n = 3 : 25 answer : c
Answer: c
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 5000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 425 , c ) s . 625 , d ) s . 800 , e ) s . 850
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 5000 ) = rs . 625 answer = c"
Answer: c
Problem: a box contains 9 pairs of shoes ( 18 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 17 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 18 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 17 ( as after taking one at random there are 17 shoes left and only one is the pair of the first one ) = 1 / 17 answer : b ."
Answer: b
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 x are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) x = 8
Rationale: the combinations could be { ( 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: what is the lowest positive integer that is divisible by each of the integers 1 through 7 , inclusive ?
Options: a ) 420 , b ) 840 , c ) 1,260 , d ) 2,520 , e ) 5,040
Rationale: "the integer should be divisible by : 2 , 3 , 4 ( = 2 ^ 2 ) , 5 , 6 ( = 2 * 3 ) , and 7 . the least common multiple of these integers is lcm = 2 ^ 2 * 3 * 5 * 7 = 420 . answer : a ."
Answer: a
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 5225 . what was his original salary ?
Options: a ) 2277 , b ) 5000 , c ) 1000 , d ) 2651 , e ) 1971
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 5225 x * ( 11 / 10 ) * ( 1 / 100 ) = 55 x = 5000 answer : b"
Answer: b
Problem: the regular price per can of a certain brand of soda is $ 0.15 . if the regular price per can is discounted 10 percent when the soda is purchased in 24 - can cases , what is the price of 75 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.00 , c ) $ 10.125 , d ) $ 24.48 , e ) $ 28.80
Rationale: the discounted price of one can of soda is ( 0.9 ) ( $ 0.15 ) , or $ 0.135 therefore , the price of 75 cans of soda at the discounted price would be ( 75 ) ( $ 0.135 ) = 10.125 answer : c .
Answer: c
Problem: solve : - 666 x 666 x 666 + 555 x 555 x 555 = ? ( 666 x 666 - 666 x 555 + 555 x 555 )
Options: a ) 888 , b ) 333 , c ) 555 , d ) 1221 , e ) 889
Rationale: given exp . = ( a 3 + b 3 ) = ( a + b ) = ( 666 + 555 ) = 1221 ( a 2 - ab + b 2 ) answer d
Answer: d
Problem: when positive integer x is divided by positive integer y , the remainder is 11.52 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 11.52 - - > x = qy + 11.52 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 11.52 - - > y = 96 . answer : a ."
Answer: a
Problem: if 213 × 16 = 3408 , then 0.016 × 2.13 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) 0.03408
Rationale: "solution 0.016 × 2.13 = ( 16 / 1000 x 213 / 100 ) = ( 16 / 1000 x 213 / 100 ) = 3408 / 100000 = 0.03408 . answer e"
Answer: e
Problem: in a certain accounting class of 90 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 65 % , and the students on the make - up date had an average score of 85 % , what was the average score for the entire class ?
Options: a ) 68 % , b ) 71 % , c ) 73 % , d ) 75 % , e ) 79 %
Rationale: "70 % of the students took the final exam on the assigned day - - > 0.7 * 90 = 63 students took the final exam on the assigned day , with an average score of 65 . the rest of the students took the exam on a make - up date - - > 90 - 63 = 27 students took the exam on a make - up date , with an average score of 85 . ( average score ) = ( sum of the scores ) / ( total students ) = ( 63 * 65 + 27 * 85 ) / 90 = 71 . answer : b ."
Answer: b
Problem: 3 - 5 * 6 + 2 =
Options: a ) a ) 2 , b ) b ) - 13 , c ) c ) - 18 , d ) d ) - 17 , e ) e ) - 25
Rationale: 3 - 5 * 6 + 2 = 5 - 30 = - 25 . . . so the answer is - 25 . . . e
Answer: e
Problem: 75 boys can complete a work in 36 days . how many men need to complete twice the work in 20 days
Options: a ) 160 , b ) 170 , c ) 270 , d ) 190 , e ) 200
Rationale: one man can complete the work in 36 * 75 = 2700 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 2700 m = 270 workers answer : c
Answer: c
Problem: ratio of the earnings of a and b is 4 : 7 . if the earnings of a increases by 50 % and those of b decreased by 25 % , the new ratio of their earnings becomes 8 : 7 . what are a ' s earnings ?
Options: a ) 8 : 6 , b ) 8 : 9 , c ) 8 : 3 , d ) 8 : 7 , e ) 8 : 1
Rationale: let the original earnings of a and b be rs . 4 x and rs . 7 x . new earnings of a = 150 % 0 f rs . 4 x = ( 150 / 100 * 4 x ) = rs . 6 x new earnings of b = 75 % of rs . 7 x = ( 75 / 100 * 7 x ) = rs . 21 x / 4 6 x : 21 x / 4 = 8 : 7 this does not give x . so , the given data is inadequate . answer : d
Answer: d
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 30 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "first , let ' s translate the expression 21 # 30 , using the definition given : 21 # 30 = 21 × 24 × 27 × 30 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 30 = 3 ^ 4 ( 7 × 8 × 9 × 10 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 30 = 3 ^ 4 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) ) let ' s group the prime bases : 21 # 30 = 2 ^ 4 × 3 ^ 6 × 5 × 7 the sum of the exponents is 4 + 6 + 1 + 1 = 12 the answer is c ."
Answer: c
Problem: what is the square root of 144 , divided by 6 ?
Options: a ) 9 , b ) 36 , c ) 2 , d ) 6 , e ) 1
Rationale: "square root is a number times itself square root of 144 = 12 , 12 / 6 = 2 ( c ) 2"
Answer: c
Problem: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 20 kmph ?
Options: a ) 21.21 , b ) 20.25 , c ) 32.25 , d ) 75.75 , e ) 62.61
Rationale: distance covered in 1 min = ( 20 * 1000 ) / 60 = 333.33 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 333.33 / 4.4 = 75.75 answer : d
Answer: d
Problem: a grocer has 400 pounds of coffee in stock , 30 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 36 % , d ) 36 % , e ) 40 %
Rationale: "1 . 30 % of 400 = 120 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 180 pounds of decaffeinated out of 500 pounds , that means 180 / 500 * 100 % = 36 % . the correct answer is d ."
Answer: d
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets into it . the mass of the man is ?
Options: a ) 77 kg , b ) 60 kg , c ) 77 kg , d ) 55 kg , e ) 47 kg
Rationale: "in this type of question , first we will calculate the volume of water displaces then will multiply with the density of water . volume of water displaced = 3 * 2 * 0.01 = 0.06 m cube mass of man = volume of water displaced * density of water = 0.06 * 1000 = 60 kg answer : b"
Answer: b
Problem: a cyclist covers a distance of 500 m in 4 min 30 sec . what is the speed in km / hr of the cyclist ?
Options: a ) 2 , b ) 2.5 , c ) 3.2 , d ) 4.6 , e ) 2.8
Rationale: distance = 500 m time = 4 min 10 sec = 250 sec speed = ( 500 / 250 ) m / s = 2 m / s speed in km / hr = 2 * 18 / 5 = 3.2 km / hr correct option is c
Answer: c
Problem: the number n is 76 h 4 , where h represents the 10 ' s digit . if n is divisible by 9 , what is the value of h ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: integer is divisible by 9 - sum of digits is divisible by 9 answer : a
Answer: a
Problem: if a boat is rowed downstream for 96 km in 3 hours and upstream for 88 km in 11 hours , what is the speed of the boat and the river ?
Options: a ) 12 , 20 , b ) 20 , 20 , c ) 20 , 11 , d ) 20 , 12 , e ) 12 , 12
Rationale: explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 32 ; us = 8 x = ( 32 + 8 ) / 2 = 40 / 2 = 20 km / hr y = ( 32 - 8 ) / 2 = 24 / 2 = 12 km / hr answer : d
Answer: d
Problem: 117 x 217 + 83 x 83 = ?
Options: a ) 79698 , b ) 20578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 117 ) ^ 2 + ( 83 ) ^ 2 = ( 100 + 17 ) ^ 2 + ( 100 - 17 ) ^ 2 = 2 [ ( 100 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 10000 + 289 ] = 2 x 10289 = 20578 answer is b"
Answer: b
Problem: a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be
Options: a ) 12.5 m , b ) 10 m , c ) 17.5 m , d ) 21.25 m , e ) 9.8 m
Rationale: "let the height of the building x metres . less lengthy shadow , less in the height ( direct proportion ) 40.25 : 28.75 : : 17.5 : x 40.25 * x = 28.75 * 17.5 x = ( 28.75 x 17.5 ) / 40.25 x = 12.5 answer is a ."
Answer: a
Problem: three rugs have a combined area of 196 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 15 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 194 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 15 . answer : a ."
Answer: a
Problem: a line has a slope of 3 / 4 and intersects the point r ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point r of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Problem: 180 college students were asked in a survey if they preferred windows or mac brand computers . 50 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 60 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 70 , c ) 50 , d ) 60 , e ) 75
Rationale: "180 = 50 ( mac ) + x ( window ) + 60 ( both ) = > x = 70 answer : b"
Answer: b
Problem: a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 15 , b ) 44 , c ) 40 , d ) 27 , e ) 12
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 2 / 25 ) = 40 seconds answer : c"
Answer: c
Problem: what is the dividend . divisor 14 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 131 , c ) c ) 148 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 14 * 9 + 5 d = 126 + 5 d = 131 answer b"
Answer: b
Problem: shop offered 30 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 800 , c ) 600 , d ) 700 , e ) 750
Rationale: "sp * ( 70 / 100 ) = 560 sp = 8 * 100 = > cp = 800 answer : b"
Answer: b
Problem: if q = { 1 , 7 , 18 , 20 , 29 , 33 } , how much less is the mean of the numbers in q than the median of the numbers in q ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 1 + 7 + 18 + 20 + 29 + 33 ) / 6 = 18 median = ( 18 + 20 ) / 2 = 19 difference = 1 option a
Answer: a
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 20 % 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 ) 86 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 20 % more than company a ' s assets which is 120 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 = 60 a + b = 160 kw = 120 kw / ( a + b ) * 100 = 120 / 160 * 100 = 75 % b"
Answer: b
Problem: a bowl of fruit contains 12 apples and 23 oranges . how many oranges must be removed so that 60 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 15 , d ) 17 , e ) 20
Rationale: "number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 60 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 12 + ( 23 - x ) = 35 - x 12 / ( 35 - x ) = 6 / 10 = > 20 = 35 - x = > x = 15 answer c"
Answer: c
Problem: if a town of 25,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) 26000 , b ) 27000 , c ) 28000 , d ) 29000 , e ) 30000
Rationale: "let population in the beginning = 100 at the end of 1 st year population = 100 + 1 % of 100 = 100 + 1 = 101 at the end of 2 nd year population = 101 + 1 % of 101 = 101 + 1 approx = 102 approx ( on the lower side because 1 % of 101 is greater than 1 ) at the end of 3 rd year population = 102 + 1 % of 102 = 102 + 1 approx = 103 approx ( on the lower side because 1 % of 102 is greater than 1 ) at the end of 4 th year population = 103 + 1 % of 103 = 103 + 1 approx = 104 approx ( on the lower side because 1 % of 103 is greater than 1 ) at the end of 5 th year population = 104 + 1 % of 104 = 104 + 1 approx = 105 approx ( on the lower side because 1 % of 104 is greater than 1 ) i . e . 5 % greater than 25000 = 25000 + 5 % of 25000 = 25000 + 1250 = 26250 ( on the lower side ) i . e . population must be greater than 26250 but since the closest option is 26000 so answer : option a"
Answer: a
Problem: one ton has 2100 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 1680 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2100 pound = 13 * 2100 * 16 ounces . hence the answer is ( 13 * 2100 * 16 ) / 260 = 1680 . answer : a ."
Answer: a
Problem: the salary of a worker is first increased by 25 % and afterwards reduced by 25 % . what is the net change in the worker ' s salary ?
Options: a ) 3.25 % increase , b ) 3.25 % decrease , c ) 6.25 % increase , d ) 6.25 % decrease , e ) no change
Rationale: "let x be the original salary . the final salary is 0.75 ( 1.25 x ) = 0.9375 x the answer is d ."
Answer: d
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 13 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 13 = > m = 39 answer a"
Answer: a
Problem: perimeter of front wheel = 30 , back wheel = 20 . if front wheel revolves 240 times . how many revolutions will the back wheel take ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 360 , e ) 480
Rationale: sice the distance covered by both the wheels should be same so let x be the no . of revolutions by the back wheel so 240 * 2 * pie * 30 = x * 2 * pie * 20 so x = 360 . answer : d
Answer: d
Problem: 15 litres of mixture contains 25 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 20.83 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 %
Rationale: alcohol in the 15 litres of mix . = 25 % of 15 litres = ( 25 * 15 / 100 ) = 3.75 litres water in it = 15 - 3.75 = 11.25 litres new quantity of mix . = 15 + 3 = 18 litres quantity of alcohol in it = 3.75 litres percentage of alcohol in new mix . = 3.75 * 100 / 18 = 20.83 % answer is a
Answer: a
Problem: rs . 800 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 800 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1052 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 800 ) = rs . 156 rate = ( 100 x 156 / 800 x 3 ) = 6 1 / 2 % new rate = ( 6 1 / 2 + 4 ) % = 10 1 / 2 % new s . i . = rs . ( 800 x 21 / 2 x 3 / 100 ) rs . 252 . ∴ new amount = rs . ( 800 + 252 ) = rs . 1052 . answer c"
Answer: c
Problem: a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 17.5 % , b ) 24 % , c ) 30 % , d ) 35 % , e ) 38 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.15 = 138 increase in 1993 from 1991 = 138 - 100 = 38 answer : e"
Answer: e
Problem: sonika deposited rs . 6200 which amounted to rs . 7200 after 5 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 9680 , b ) 8130 , c ) 8134 , d ) 8556 , e ) 9808
Rationale: "( 6200 * 5 * 3 ) / 100 = 930 7200 - - - - - - - - 8130 answer : b"
Answer: b
Problem: a bag of potatoes weighs 50 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 50 ÷ 5 = 10 . answer : c"
Answer: c
Problem: if x is a positive integer , then the least value of x for which x ! is divisible by 100,000 is ? can someone please explain intuitively what the question is asking ?
Options: a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30
Rationale: in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d .
Answer: d
Problem: there is enough provisions for 600 men in an army camp for 25 days . if there were 200 men less , how long will the provision last ?
Options: a ) 50 days , b ) 60 days , c ) 70 days , d ) 75 days , e ) 90 days
Rationale: exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 200 * d 2 d 2 = 600 * 25 / 200 = 75 days . answer : d
Answer: d
Problem: a person spent rs . 8,550 from his salary on food and 8,640 on house rent . after that he was left with 40 % of his monthly salary . what is his monthly salary ?
Options: a ) 38,650 , b ) 28,650 , c ) 48,650 , d ) 68,650 , e ) 18,650
Rationale: "total money spent on food and house rent = 8,550 + 8,640 = 17,190 which is 100 - 40 = 60 % of his monthly salary ∴ his salary = 17190 x 100 / 60 = 28650 answer : b"
Answer: b
Problem: when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 62 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 26 = 62 - x or , 4 x = 88 or , x = 22 . answer : e"
Answer: e
Problem: find the principle on a certain sum of money at 6 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 979 , b ) 1288 , c ) 2778 , d ) 2682 , e ) 1021
Rationale: "1120 = p [ 1 + ( 6 * 12 / 5 ) / 100 ] p = 979 answer : a"
Answer: a
Problem: my watch gains 5 min every hour . how many degrees the second hand moves in every min ?
Options: a ) 300 , b ) 350 , c ) 390 , d ) 400 , e ) 450
Rationale: gain 5 min every 1 hr degrees moves = = > 390 answer c
Answer: c
Problem: if 5 cats can kill 5 rats in 5 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes
Rationale: "it will take 5 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 5 minutes , so 100 cats can kill 100 rats in 5 minutes answer e"
Answer: e
Problem: 4.2 x 4.2 - 1.9 x 1.9 / 2.3 x 6.1 is equal to :
Options: a ) 2 , b ) 1 , c ) 3 , d ) 4 , e ) 8
Rationale: "given expression = ( a 2 - b 2 ) / ( a + b ) ( a - b ) = ( a 2 - b 2 ) / ( a 2 - b 2 ) = 1 . answer is b ."
Answer: b
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 4 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 288 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 4 ) or $ 288 . the best answer is therefore a . answer : a ."
Answer: a
Problem: calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10 % of its volume is occupied by concrete ?
Options: a ) 6000 , b ) 5400 , c ) 3800 , d ) 4700 , e ) 2500
Rationale: "explanation : let ' b ' be the nuber of bricks . = > 10 x 4 / 100 x 5 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x b = > 10 x 20 x 90 = 15 x 2 x b = > b = 6000 answer is a"
Answer: a
Problem: in how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 28400 , b ) 28500 , c ) 28600 , d ) 28700 , e ) 28800
Rationale: "number of ways = 2 * 5 ! * 5 ! = 28800 answer is e"
Answer: e
Problem: the average monthly salary of laborers and supervisors in a factory is rs . 1250 per month ; where as the average monthly salary of 6 supervisors is rs . 2450 . if the average monthly salary of the laborers is rs . 850 find the number of laborers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "2450 850 \ / 1250 / \ 400 1200 1 : 3 1 - - > 6 3 - - > ? 18 answer : e"
Answer: e
Problem: in a digital circuit which was to implement ( a b ) + ( a ) xor ( b ) , the designer implements ( a b ) ( a ) xor ( b ) what is the probability of error in it ?
Options: a ) 25 % , b ) 35 % , c ) 75 % , d ) 45 % , e ) 55 %
Rationale: a b ab a xor b ( ab ) + ( a xor b ) ( ab ) ( a xor b ) 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 so , we are getting 3 wrong answers out of 4 probability of error is 3 / 4 = 75 % answer : c
Answer: c
Problem: if 4 men can colour 48 m long cloth in 2 days , then 5 men can colour 36 m long cloth in
Options: a ) 1.2 day , b ) 2.0 days , c ) 3 days , d ) 4.2 days , e ) 5 days
Rationale: the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 5 = 1.2 day . a
Answer: a
Problem: a man gains 10 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 120 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 110 / 100 ) x = 11 x / 10 new s . p . = 2 ( 11 x / 10 ) = 22 x / 10 profit = 22 x / 10 - x = 12 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 12 x / 10 ) * ( 1 / x ) * 100 = 120 % option b"
Answer: b
Problem: man 1 does a work in 10 days and man 2 does the same work in 15 days . in how many days they together will do the same work ?
Options: a ) 10 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: man 1 day work = 1 / 10 man 2 day work = 1 / 15 both work = 1 / 10 + 1 / 15 = = = > 3 + 2 / 30 = = > 1 / 6 answer c
Answer: c
Problem: from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is
Options: a ) 40 % pure , b ) 50 % pure , c ) 51.2 % pure , d ) 58.8 % pure , e ) none
Rationale: "solution let total quantity of original milk = 100 gm . milk after first operation = 80 % of 1000 ‹ = › 800 gm . milk after second operation = 80 % of 800 ‹ = › 640 gm . milk after third operation = 80 % of 640 ‹ = › 512 gm . strength of final mixtures = 51.2 % . answer c"
Answer: c
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ?
Options: a ) 5 , b ) 12 , c ) 10 , d ) 20 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ? 9 ^ 6 = ( 3 ^ 2 ) ^ 6 = 3 ^ 12 b . 12"
Answer: b
Problem: 1396 x 1396
Options: a ) 1948816 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1396 x 1396 = ( 1396 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 4 ) 2 - ( 4 x 1400 x 4 ) = 1948816 . answer : option a"
Answer: a
Problem: a man invested rs . 4940 in rs . 10 shares quoted at rs . 9.50 . if the rate of dividend be 14 % , his annual income is
Options: a ) 708 , b ) 718 , c ) 738 , d ) 748 , e ) 728
Rationale: "market value of a share = rs . 9.50 investment = rs . 4940 number of shares = 4940 / 9.50 = 520 face value of a share = rs . 10 dividend = 14 % dividend per share = ( 10 × 14 ) / 100 = rs . 1.4 his annual income = 520 × 1.4 = rs . 728 answer is e ."
Answer: e
Problem: if 20 gallons of grape juice are added to 40 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 40 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.10 = 4 gallons of grape juice . 40 × 0.90 = 36 gallons of other components . if we add 20 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we will have a total of 60 gallons of the mixture . so 24 / 60 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 40 / 100 = 40 % . the correct answer is choice ( e )"
Answer: e
Problem: the l . c . m . of two numbers is 30 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 25 , b ) 32 , c ) 40 , d ) 53 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 30 or x = 5 . the numbers are 10 and 15 . hence , required sum = ( 10 + 15 ) = 25 . answer : option a"
Answer: a
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and twice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 2 y solve equation # 2 for z : z = y - 12 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 12 ) = 100 4 y - 12 = 100 4 y = 112 y = 28 there are 28 blue balls . this is 15 more than the number of white balls , so z = 16 . that ' s the answer . just as a check , x = 56 , and 56 + 28 + 16 = 100 . answer = 16 , ( e )
Answer: e