regisss/math_qa huggingface dataset:
Problem: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 6 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 225 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 6 people . so $ 150 . but , he also has to put in the average for himself ( the seventh person ) , so add $ 75 . so $ 225 is your answer . answer a"
Answer: a
Problem: what is the least value of x . so that 30 x 55 is divisible by 3 ?
Options: a ) 4 , b ) 5 , c ) 1 , d ) 2 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 3 + 0 + x + 5 + 5 = 13 + x least value of x may be 2 therefore 13 + 2 = 15 is divisible by 3 . d"
Answer: d
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 4 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 70 ) = ( r + 4 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 140 ans c"
Answer: c
Problem: 2 ^ ( 2 x / 3 ) = 2 ^ ( x / 2 ) what is the value of x ?
Options: a ) 2 , b ) 2 / 3 , c ) 1 , d ) 0 , e ) - 2
Rationale: 2 x / 3 = x / 2 4 x = 3 x 4 x - 3 x = 0 ; x = 0 ans : d
Answer: d
Problem: a box measuring 35 inches long by 20 inches wide by 10 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 54 , d ) 56 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 5 is the biggest number that could divide all three , 35 , 20 and 10 . thus side of cube must be 5 , and total number of cubes = 35 / 5 * 20 / 5 * 10 / 5 = 56 ans d it is ."
Answer: d
Problem: how many prime numbers between 1 and 100 are factors of 1771 ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "factor of 1771 = 7 * 11 * 23 - - - 3 prime numbers e"
Answer: e
Problem: what is the sum of all possible solutions to | x - 4 | ^ 2 + | x - 4 | = 20 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "denote | x - 4 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 4 | , so it ' s an absolute value and thus can not be negative . y = | x - 4 | = 4 - - > x = 8 or x = - 1 . the sum = 7 . answer : d ."
Answer: d
Problem: if p represents the product of the first 14 positive integers , then p is not a multiple of :
Options: a ) a ) 99 , b ) b ) 84 , c ) c ) 51 , d ) d ) 65 , e ) e ) 57
Rationale: a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 51 = 17 * 3 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 17 is not there in first 15 positive numbers it is the only possibility c
Answer: c
Problem: the average weight of 10 girls increases by 5 kg when a new girl comes in place of one of them weighing 50 kg . what might be the weight of the new girl ?
Options: a ) 90 kg , b ) 100 kg , c ) 95 kg , d ) 85 kg , e ) 92 kg
Rationale: "total weight increased = 10 x 5 kg = 50 kg . weight of new person = 50 + 50 kg = 100 kg answer : b"
Answer: b
Problem: on dividing 144 by a number , the quotient is 13 and the remainder is 1 . find the divisor .
Options: a ) a ) 11 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 144 - 1 ) / 13 = 143 / 13 = 11 a )"
Answer: a
Problem: a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 1100 . how many workers were part of the latter production run ?
Options: a ) 26 , b ) b ) 10 , c ) c ) 11 , d ) d ) 15 , e ) e ) 23.5
Rationale: the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1100 . . thus for the current period = 1100 - 500 = 600 ( 5 n + 45 ) k = 600 k = 600 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 600 / 5 n + 45 500 ( 5 n + 45 ) = 600 ( 5 n + 20 ) 2500 n + 22500 = 3000 n + 12000 - 500 n = - 10500 n = 21 thus n + 5 = 26 hence a
Answer: a
Problem: find the area of a parallelogram with base 24 cm and height 16 cm ?
Options: a ) 298 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 297 cm 2 , e ) 278 cm 2
Rationale: "area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : b"
Answer: b
Problem: the principal that amounts to rs . 4893 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4893 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4085 . answer : c
Answer: c
Problem: what is the remainder when 46 * 49 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 46 * 49 ) / 8 } } = remainder of ( 46 / 8 ) * remainder of ( 49 / 8 ) = 6 * 1 = 6 answer : d"
Answer: d
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 25 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 25 ( x - y ) - - > x + y = 25 . answer : d ."
Answer: d
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 15 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 67 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 15 = 67"
Answer: c
Problem: if 18 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "18 - 3 * 3 * 2 15 - 5 * 3 12 - 4 * 3 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 8 is allowed . imo e ."
Answer: e
Problem: the ratio of 2 numbers is 3 : 7 and their h . c . f . is 10 . their l . c . m . is ?
Options: a ) 220 , b ) 210 , c ) 252 , d ) 236 , e ) 260
Rationale: "let the numbers be 3 x and 7 x their h . c . f . = 10 so the numbers are 3 * 10 , 7 * 10 = 30,70 l . c . m . = 210 answer is b"
Answer: b
Problem: two trains are moving in opposite directions @ 100 kmph and 120 kmph . their length are 500 m and 700 m . the time taken by the slower train to cross faster train in second is ?
Options: a ) 15 sec , b ) 18.3 sec , c ) 19.6 sec , d ) 20.4 sec , e ) 22.5 sec
Rationale: relative speed = 100 + 120 = 220 * 5 / 18 = 550 / 9 m / s distance covered = 500 + 700 = 1200 m required time = 1200 * 9 / 550 = 19.6 sec answer is c
Answer: c
Problem: if two positive numbers are in the ratio 1 / 8 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 65 %
Rationale: "given ratio = 1 / 8 : 1 / 5 = 5 : 8 let first number be 5 x and the second number be 8 x . the second number is more than first number by 3 x . required percentage = 3 x / 5 x * 100 = 60 % . answer : c"
Answer: c
Problem: if the price of a certain bond on may 1 st was 1 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 100 % , b ) 150 % , c ) 155 % , d ) 300 % , e ) 355 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 1 / 4 * 12 = 3 ; the price on july 1 st = 3 * 1.25 = 3.75 . the average price of the bond on may 1 st and july 1 st = ( 3 + 3.75 ) / 2 = 3.375 . the price of the bond on june 1 st ( 12 ) is 32 / 9 times ( 355.55 % ) the average price of the bond on may 1 st and july 1 st . answer : e ."
Answer: e
Problem: what is the remainder when 1003 * 1005 * 1007 is divided by 15
Options: a ) 3 , b ) 17 , c ) 14 , d ) 0 , e ) 7
Rationale: "1003 / 15 = = > remainder = 13 1005 / 15 = = > remainder = 0 1007 / 15 = = > remainder = 2 13 * 0 * 2 = 0 / 15 = = > remainder = 0 answer : d"
Answer: d
Problem: how many seconds will a 250 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 12 , b ) 30 , c ) 40 , d ) 15 , e ) 60
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 250 * 3 / 50 = 15 sec . answer : option d"
Answer: d
Problem: the last two - digits in the multiplication 122 × 123 × 125 × 127 × 129 will be
Options: a ) 20 , b ) 50 , c ) 30 , d ) 40 , e ) 10
Rationale: solution the answer will be 50 since , ( 125 × 122 ) will give 50 as the last two digits . answer b
Answer: b
Problem: riya and priya set on a journey . riya moves eastward at a speed of 20 kmph and priya moves westward at a speed of 30 kmph . how far will be priya from riya after 30 minutes
Options: a ) 25 kms , b ) 10 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 20 kmph * 1 / 2 hr = 10 km total westward distance = 30 kmph * 1 / 2 hr = 15 km total distn betn them = 10 + 15 = 25 km ans 25 km answer : a"
Answer: a
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 10 sec . what is the length of the platform ?
Options: a ) 187 m , b ) 350 m , c ) 267 m , d ) 287 m , e ) 870 m
Rationale: "speed = 300 / 10 = 30 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 30 = > x = 870 m . answer : e"
Answer: e
Problem: how many digits are in the number 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 2 ?
Options: a ) 22 , b ) 20 , c ) 21 , d ) 18 , e ) 17
Rationale: "whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 2 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 x 10 ^ 2 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 x 10 ^ 2 = 2 * 11 ^ 2 * 10 ^ 16 x 10 ^ 2 = 242 * 10 ^ 18 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 18 = 21 correct option : c"
Answer: c
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 2 and 4 parts , respectively . this will give us in the final mixture ( 5 + 2 ) : ( 3 + 4 ) , which means 7 : 7 , or 1 : 1 . answer a ."
Answer: a
Problem: running at the same constant rate , 15 identical machines can produce a total of 45 bags per minute . at this rate , how many bags could 150 such machines produce in 8 minutes ?
Options: a ) 9,00 , b ) 1,800 , c ) 2,700 , d ) 3,600 , e ) 4,800
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 45 / 15 = 3 bags per minute per machine . 150 machines = 450 per minute . 8 minutes worth = 3600 bags . looking at the answers it is clear . . . we can only choose ( d ) . the correct answer is d ."
Answer: d
Problem: what is the remainder when 1031 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 24 , c ) 30 , d ) 21 , e ) 18
Rationale: "take the remainder from each of 1031 / 33 , 1047 / 33 and so on . . 1031 / 33 gives remainder = 8 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 8 * 24 * 27 * 30 break them into pairs 8 * 24 / 33 gives remainder 27 and 27 * 30 / 33 gives remainder 18 so 27 * 18 / 33 gives remainder 24 . b"
Answer: b
Problem: a train 700 m long can cross an electric pole in 40 sec and then find the speed of the train ?
Options: a ) 987 , b ) 271 , c ) 72 , d ) 27 , e ) 63
Rationale: "length = speed * time speed = l / t s = 700 / 40 s = 17.5 m / sec speed = 17.5 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 63 kmph answer : e"
Answer: e
Problem: a is twice as good a work man as b and together they finish the work in 12 days . in how many days a alone can finish the work ?
Options: a ) 12 days , b ) 14 days , c ) 28 days , d ) 18 days , e ) 16 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 12 = > x = 1 / 36 2 x = 1 / 18 a can do the work in 18 days . answer : d"
Answer: d
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 100 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 4,800 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
Rationale: solution provided by stanford 2012 is correct : 100 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 100 / 800 * 1 / 600 = 1 / 4,800 . answer : b .
Answer: b
Problem: total 85 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 85 , b ) 81 , c ) 53 , d ) 82 , e ) 84
Rationale: 84 players answer : e
Answer: e
Problem: if log 27 = 1.431 , then the value of log 9 is : 0.934 b . 0.945 c . 0.954 d . 0.958
Options: a ) 0.954 , b ) 0.93 , c ) 0.933 , d ) 0.96 , e ) 0.974
Rationale: "if log 27 = 1.431 , then the value of log 9 is : a . 0.934 b . 0.945 c . 0.954 d . 0.958 answer : option c explanation : log 27 = 1.431 log ( 33 ) = 1.431 3 log 3 = 1.431 log 3 = 0.477 log 9 = log ( 32 ) = 2 log 3 = ( 2 x 0.477 ) = 0.954 . answer a"
Answer: a
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 8 % p . a . in 5 years . what is the sum ?
Options: a ) rs . 10060.625 , b ) rs . 10040.62 , c ) rs . 12040.62 , d ) rs . 20040.625 , e ) rs . 10030.625
Rationale: "principal = ( 100 * 4016.25 ) / ( 8 * 5 ) = rs . 10040.625 . answer : b"
Answer: b
Problem: the population of a bacteria culture doubles every 5 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 45
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 5 minutes so answer is 9 * 5 = 45 minutes answer ( e )"
Answer: e
Problem: a woman complete a journey in 25 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 560 km .
Rationale: 0.5 x / 21 + 0.5 x / 24 = 25 - - > x / 21 + x / 24 = 50 - - > x = 560 km . e
Answer: e
Problem: set j consists of 10 consecutive even numbers . if the smallest term in the set is - 4 , what is the range of the positive integers in set j ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "since there are only 10 integers , another approach is the just list all 10 . we get : - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 range of positive integers = 14 - 2 = 12 answer : b"
Answer: b
Problem: a man two flats for $ 675958 each . on one he gains 12 % while on the other he loses 12 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.44 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 12 / 10 ) ^ 2 = 36 / 25 = 1.44 % answer is a"
Answer: a
Problem: in a certain company , a third of the workers do not have a retirement plan . 10 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 91
Rationale: 20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 90 * 1 + 40 * 2 ) / 3 = 170 / 3 % are men total = 120 * 300 / 170 = 211 no . of women = 211 - 120 = 91 e
Answer: e
Problem: the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 60 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 40
Rationale: the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 3 hours for the trip . dan needs to exceed a constant speed of 120 / 3 = 40 miles per hour . the answer is e .
Answer: e
Problem: jack and christina are standing 150 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 7 feet per second and christina walks in a straight line toward jack at a constant speed of 8 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "the relative speed of jack and christina is 7 + 8 = 15 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 150 / 15 = 10 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 10 = 100 feet . answer : d ."
Answer: d
Problem: how many different positive integers exist between 10 ^ 4 and 10 ^ 5 , the sum of whose digits is equal to 2 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "10001 10010 10100 11000 20000 total no . = 5 c"
Answer: c
Problem: a man by motorcycle goes from delhi to bharatpur , a distance of 192 km , at an average speed of 32 kmph . another man starts from delhi by car 2.5 h after the motorcyclist starts and reaches bharatpur half an hour late . what is the ratio of person on the motorcycle to the person going by car ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 10 : 27 , d ) 5 : 4 , e ) 4 : 5
Rationale: a man by motorcycle goes from delhi to bharatpur the time take by the motorcyclist = 192 / 32 = 6 hours another man start from delhi be car after 2.5 hour the man starts = 6 - 2.5 = 3.5 and the man on can reaches half and hour late which is = 3.5 + . 5 = 4 thus , the ratio between motorcycle to car is 4 : 6 or , 2 : 3 . answer : b
Answer: b
Problem: if p / q = 4 / 5 , then the value of 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 18 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 18 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 18 / 7 + 6 / 14 = 18 / 7 + 3 / 7 = 21 / 7 = 3 correct option : e"
Answer: e
Problem: a scuba diver descends at a rate of 30 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 2400 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 70 minutes , b ) 72 minutes , c ) 80 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 2400 / 30 = 80 minutes answer : c"
Answer: c
Problem: how many zeroes are there at the end of the number n , if n = 150 ! + 300 ! ?
Options: a ) 28 , b ) 31 , c ) 34 , d ) 37 , e ) 40
Rationale: "the number of zeroes at the end of 150 ! will be less than the number of zeroes at the end of 300 ! hence it is sufficient to calculate the number of zeroes at the end of 150 ! the number of zeroes = [ 150 / 5 ] + [ 150 / 25 ] + [ 150 / 125 ] = 30 + 6 + 1 = 37 the answer is d ."
Answer: d
Problem: how many prime numbers are between 26 / 3 and 85 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "26 / 3 = 8 . xxx 85 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"
Answer: b
Problem: average of 10 matches is 32 , how many runs one should should score to increase his average by 5 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 87
Rationale: "explanation : average after 11 innings should be 37 so , required score = ( 11 * 37 ) - ( 10 * 32 ) = 407 - 320 = 87 answer : option e"
Answer: e
Problem: if there are 4 peanuts in a box and mary puts 2 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 11 , e ) 12
Rationale: "2 + 4 = 6 correct answer is c ) 6"
Answer: c
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 6840 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 868.6 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 6840 / 18 + 6840 / 14 = 380 + 488.6 = 868.6 hours answer : option d"
Answer: d
Problem: in august , a cricket team that played 120 matches won 22 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 68 , d ) 75 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 26.4 + x by solving we get x = 75 answer : d"
Answer: d
Problem: jane started baby - sitting when she was 16 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "check two extreme cases : jane = 16 , child = 8 , years ago = 32 - 16 = 16 - - > child ' s age now = 8 + 16 = 24 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : e ."
Answer: e
Problem: a cylindrical container of radius 6 cm and height 15 cm is filled with ice - cream . the whole icecream has to be distributed to 10 children in equal cones with hemispherical tops . if the height of the conical portion is four times the radius of its base , find the radius of the ice - cream cone .
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: volume of given ice cream = ( pie ) * 6 ² * 15 = 540 ( pie ) dividing to 10 children volume given to a child = 54 ( pie ) let r be radius and h be the height of the cone , then ( pie ) r ² h / 3 + 2 ( pie ) r ³ / 3 = 54 ( pie ) also given h = 4 r 4 r ³ / 3 + 2 r ³ / 3 = 54 2 r ³ = 54 r ³ = 27 r = 3 answer : c
Answer: c
Problem: if 1 = 3 2 = 6 3 = 9 4 = 12 5 = 15 then 9 = ? hint : its a logic riddle not a mathematical riddle
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: c 3 as stated 3 = 9 = > 9 = 3 answer is c
Answer: c
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 25 cm ?
Options: a ) 827 cm 2 , b ) 216 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 475 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 25 ) = 475 cm 2 answer : e"
Answer: e
Problem: in a forest 170 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,700 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 170 tagged deers comprise 10 % of total # of deers - - > total # of deers = 170 * 10 = 1,700 . answer : d ."
Answer: d
Problem: in an examination , a student scores 5 marks for every correct answer and loses 2 marks for every wrong answer . if he attempts all 100 questions and secures 290 marks , the number of questions he attempts correctly , is :
Options: a ) 60 , b ) 80 , c ) 70 , d ) 45 , e ) 50
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 100 â € “ x ) . 5 x â € “ 2 ( 100 â € “ x ) = 290 or 7 x = 490 or x = 70 . answer : c"
Answer: c
Problem: there are 3 boats b 1 , b 2 and b 3 working together they carry 60 people in each trip . one day an early morning b 1 carried 50 people in few trips alone . when it stopped carrying the passengers b 2 and b 3 started carrying the people together . it took a total of 10 trips to carry 300 people by b 1 , b 2 and b 3 . it is known that each day on an average 300 people cross the river using only one of the 3 boats b 1 , b 2 and b 3 . how many trips it would take to b 1 , to carry 150 passengers alone ?
Options: a ) 15 , b ) 30 , c ) 25 , d ) 10 , e ) 15
Rationale: explanation : combined efficiency of all the three boats = 60 passenger / trip now , consider option ( a ) 15 trips and 150 passengers means efficiency of b 1 = 10 p / t which means in carrying 50 passengers b 1 must has taken 5 trips . so the rest trips equal to 5 ( 10 - 5 = 5 ) in which b 2 and b 3 together carried remaining 250 ( 300 - 50 = 250 ) passengers . therefore the efficiency of b 2 and b 3 = 250 / 5 = 50 p / t since , the combined efficiency of b 1 , b 2 and b 3 is 60 . which is same as given in the first statement hence option ( a ) is correct answer : a
Answer: a
Problem: the average age of 12 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 34 , d ) 38 , e ) 27
Rationale: "total age increased = ( 12 * 2 ) years = 24 years . sum of ages of two new men = ( 21 + 23 + 24 ) years = 68 years average age of two new men = ( 68 / 2 ) years = 34 years . answer : c"
Answer: c
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 112 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 112 km time taken = distance / speed = 112 / 28 = 4 hours answer : option b"
Answer: b
Problem: find the l . c . m . of 72 , 108 and 2100 .
Options: a ) 37800 , b ) 37600 , c ) 37200 , d ) 37500 , e ) none of them
Rationale: 72 = 2 ^ 3 x 3 ^ 2 , 108 = 3 ^ 3 x 2 ^ 2 , 2100 = 2 ^ 2 x 5 ^ 2 x 3 x 7 . l . c . m . = 2 ^ 3 x 3 ^ 3 x 5 ^ 2 x 7 = 37800 . answer is a .
Answer: a
Problem: the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 55 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 17 , b ) 19 , c ) 25 , d ) 31 , e ) 46
Rationale: "the total sum of the numbers should be increased by 30 . then the average will increase by 30 / 10 = 3 . the correct average is 19 . the answer is b ."
Answer: b
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 21 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 9 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 21 a – d = 3 a + d = 21 2 d = 18 d = 9 answer c"
Answer: c
Problem: how many inches are in 2000 millimeters ? ( round your answer to the nearest hundredth of of an inch ) .
Options: a ) 48.74 inches , b ) 58.74 inches , c ) 78.74 inches , d ) 28.74 inches , e ) 88.74 inches
Rationale: one inch is the same as 25.4 mm . let x inches be the same as 1000 mm x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches correct answer c
Answer: c
Problem: the average of 6 no . ' s is 6.40 . the average of 2 of them is 6.2 , while the average of the other 2 is 6.1 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.6 , c ) 6.9 , d ) 4.5 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 6.4 * 6 ) - [ ( 6.2 * 2 ) + ( 6.1 * 2 ) ] = 38.40 - ( 12.4 + 12.2 ) = 38.40 - 24.6 = 13.80 required average = ( 13.8 / 2 ) = 6.9 answer : c"
Answer: c
Problem: the current in a river is 6 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 91 miles , e ) 112 miles
Rationale: "upstream speed = 20 - 6 = 14 mph downstream speed = 20 + 6 = 26 mph d / 14 + d / 26 = 10 hours solving for d we get d = 91 answer : d"
Answer: d
Problem: a school has 6 maths 5 physics and 5 chemistry teachers each teacher can teach 4 subjects max what is he minimum number of teachers required
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "total subjects = 6 + 5 + 5 = 16 max subjects by 1 teacher = 4 so , min of teachers required = 16 / 4 = 4 answer : b"
Answer: b
Problem: if a monkey can climb 6 meter & slip down 3 meter in alternate minutes , than how much time can be taken by the monkey to climb up to a height of 60 meter .
Options: a ) 36 min , b ) 37 min , c ) 38 min , d ) 39 min , e ) 32 min
Rationale: in 1 st min it climb 6 m and in 2 nd min it slips 3 m , so it final displacement is 3 m in 2 min . now for 51 m it has taken 34 min . in 35 min it goes to 57 m . in 36 min come down to 54 m . in 37 min it goes to 60 answer : b
Answer: b
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 46 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 290 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 46 cm . : 46 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 46 / ( 3.81 ) = 290 answer will be d ."
Answer: d
Problem: the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is ?
Options: a ) 104 , b ) 106 , c ) 102 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : a"
Answer: a
Problem: how many numbers up to 200 are divisible by 2 and 3 both ?
Options: a ) 22 , b ) 33 , c ) 77 , d ) 28 , e ) 22
Rationale: explanation : 200 / 6 = 33 2 / 6 = > 33 numbers answer : b
Answer: b
Problem: a dog has 15 bones , then he finds 8 more bones . now how many bones does he have .
Options: a ) a ) 7 , b ) b ) 27 , c ) c ) 23 , d ) d ) 19 , e ) e ) 21
Rationale: 15 + 8 = 23 . answer is c .
Answer: c
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 20 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: = ( 750 * 6 + 770 * 20 ) / 26 = 765 answer is c . posted from my mobile device
Answer: c
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 200 in 4 years ?
Options: a ) 5 % , b ) 7 % , c ) 6.25 % , d ) 2 % , e ) 4 %
Rationale: "200 = ( 800 * 4 * r ) / 100 r = 6.25 % answer : c"
Answer: c
Problem: the sides of a cube are in the ratio 1 : 2 the ratio of their volume is ?
Options: a ) 1 : 6
b ) 1 : 4
c ) 1 : 0
d ) 1 : 2
e ) 1 : 1
Rationale: 1 : 4 answer : b
Answer: b
Problem: a can do a piece of work in 12 days . he worked for 15 days and then b completed the remaining work in 10 days . both of them together will finish it in .
Options: a ) 12 1 / 2 days , b ) 10 1 / 2 days , c ) 12 1 / 3 days , d ) 10 1 / 3 days , e ) 11 1 / 2 days
Rationale: explanation : 15 / 25 + 10 / x = 1 = > x = 25 1 / 25 + 1 / 25 = 2 / 25 25 / 2 = 12 1 / 2 days answer a
Answer: a
Problem: a train running at the speed of 6 km / hr crosses a pole in 2 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 3.33 , d ) 3.21 , e ) 30.1
Rationale: "speed = 6 * ( 5 / 18 ) m / sec = 5 / 3 m / sec length of train ( distance ) = speed * time 5 / 3 ) * 2 = 3.33 meter answer : c"
Answer: c
Problem: the denominator of a fraction is 5 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 7 â  „ 12 . what is the value of the original fraction ?
Options: a ) 6 / 11 , b ) 8 / 13 , c ) 11 / 16 , d ) 12 / 17 , e ) 14 / 19
Rationale: let the numerator be x . then the denominator is x + 5 . x + 1 / x + 6 = 7 / 12 . 12 x + 12 = 7 x + 42 . 5 x = 30 . x = 6 . the original fraction is 6 / 11 . the answer is a .
Answer: a
Problem: if the sum of two positive integers is 22 and the difference of their squares is 44 , what is the product of the two integers ?
Options: a ) 108 , b ) 119 , c ) 120 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 22 - - 1 x ^ 2 - y ^ 2 = 44 = > ( x + y ) ( x - y ) = 44 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 12 y = 10 product = 12 * 10 = 120 answer c"
Answer: c
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 660 ( before payroll deductions ) ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 660 x = 160 / 0.16 = 1000 the answer is c ."
Answer: c
Problem: in a stream running at 3 kmph , a motor boat goes 10 km upstream and back again to the starting point in 57 minutes . find the speed of motor boat in still water ?
Options: a ) 18 kmph , b ) 22 kmph , c ) 16 kmph , d ) 20 kmph , e ) none of these
Rationale: "explanation : let the speed of motor boat instill water be x kmph then , speed in downstream = ( x + 3 ) km and . speed in upstream = ( x - 3 ) kmph time taken to row 10 km & back = ( 10 / x + 3,10 / x - 3 ) 10 / x + 3 + 10 / x - 3 = 57 / 60 11 x 2 - 240 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 or x = - 2 / 11 then x = 22 kmph answer : option b"
Answer: b
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 4 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 22 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 4 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 4 = 4 / 9 ( t - 4 ) 10 t = 396 - 176 = > t = 22 . answer : d"
Answer: d
Problem: people were sitting in a circle . 7 th one is direct opposite to 18 th one . . then how many were there in that group ?
Options: a ) 21
b ) 22
c ) 23
d ) 24
e ) 20
Rationale: 7 th one is exactly opposite represents half of circle . with 7 and 18 total members are 12 for remaing half = 12 * 2 - 2 ( 7 th and 18 th ( already taken ) ) = 22 answer : b
Answer: b
Problem: a no . when divided by 221 gives a remainder 43 , what remainder will be obtainedby dividingthe same no . 17 ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 11 , e ) 14
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Problem: a certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water . if between 6 and 13 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 80 % = 274.4 , 90 % = 308.7 so vol above water , between 68.6 and 34.3 - - > too big if side are 4 , vol = 64 80 % = 51.2 , 90 % = 57.6 vol above water between 12.8 and 6.4 so 4 should be the answer . check option c , if sides are 5 , vol = 125 80 % = 100 , . 90 % = 112.5 vol above water between 12.5 - 25 ( sides are 4 cubic centimeters ) a"
Answer: a
Problem: there are 25 balls which are red , blue or green . if 8 balls are blue and the sum of green balls and blue balls is less than 17 , at most how many green balls are there ?
Options: a ) 8 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "r + g + b = 25 b = 8 b + g < 17 = > 8 + g < 17 = > g < 9 = > at most 8 green balls answer : a"
Answer: a
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 11 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 11 / 15
Rationale: "her tips were 11 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 11 / 4 ) ( $ 4 ) = $ 11 so , her total income = $ 4 + $ 11 = $ 15 what fraction of her income for the week came from tips $ 11 / $ 15 = 11 / 15 = e"
Answer: e
Problem: on a certain farm the ratio of horses to cows is 5 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 17 : 7 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: originally , there were 5 k horses and k cows . 7 ( 5 k - 15 ) = 17 ( k + 15 ) 35 k - 17 k = 255 + 105 18 k = 360 k = 20 the difference between horses and cows is ( 5 k - 15 ) - ( k + 15 ) = 4 k - 30 = 50 the answer is c .
Answer: c
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 50 questions and secures 130 marks , the no of questions he attempts correctly is :
Options: a ) a ) 36 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 37
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 50 – x ) = 130 = > 5 x = 180 = > x = 36 answer : a"
Answer: a
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 684 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1634 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 684 × 100 ) / ( 6 × 12 ) = rs . 950 bg = bd – td = > 684 = bd - 950 = > bd = 684 + 950 = 1634 answer : option d"
Answer: d
Problem: a sum of money at simple interest amounts to $ 780 in 3 years and to $ 930 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 698 , c ) $ 330 , d ) $ 549 , e ) $ 675
Rationale: "c $ 330 s . i . for 1 year = $ ( 930 - 780 ) = $ 150 . s . i . for 3 years = $ ( 150 x 3 ) = $ 450 . principal = $ ( 780 - 450 ) = $ 330 ."
Answer: c
Problem: what is 15 percent of 44 ?
Options: a ) 6.6 , b ) 7.8 , c ) 8.9 , d ) 9.4 , e ) 10.2
Rationale: "( 15 / 100 ) * 44 = 6.6 the answer is a ."
Answer: a
Problem: the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 90 cents more than the price of commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 90 cents more than commodity y . $ 3.00 / 25 cents = 12 years the answer is 2001 + 12 years = 2013 . the answer is d ."
Answer: d
Problem: 1 , 1 , 3 , 9 , 5 , 25 , 7 , 49 _ , 81
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "as seq is 1 , 1 , 3 , 9 , 5 , 25 , 7 , 49 9 , 81 two series are there . 1 , 3,5 , 7,9 . . . odd numbers and 1 , 9,25 , 49,81 . . square of odd numbers answer : d"
Answer: d
Problem: a shopkeeper cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 20 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 10 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 20 % , b ) 32 % , c ) 23.365 % , d ) 22.109 % , e ) 2 %
Rationale: anyways , one can infer that he ' steals ' 20 % from suppliers and then charges 10 % extra to customers so basically 1.2 * 1.1 = 1.32 given that 1 is start point , we get 32 % more hence answer is b
Answer: b
Problem: of 3 numbers , the third is 4 times the second and the second is two times the first . if their average is 165 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 19 , c ) 45 , d ) 21 , e ) 22
Rationale: explanation : let first number be x . so , 2 nd no . = 2 x & 3 rd no . = 8 x . so , x + 2 x + 8 x = 165 × 3 = 495 11 x = 495 / 11 x = 495 / 11 hence , smallest number x = 45 answer : c
Answer: c
Problem: two mixers and one t . v . cost rs . 7000 , while two t . v . s and a mixer cost rs , 9800 . the value of one t . v . is :
Options: a ) rs . 4000 , b ) rs . 4500 , c ) rs . 4300 , d ) rs . 4200 , e ) none of these
Rationale: explanation : let c . p . of a mixer be rs . x and that of a t . v . be rs . y . then , 2 x + y = 7000 and 2 y + x = 9800 . multiplying 2 nd equatien by 2 and subtracting first from it , we get 3 y = 19600 - 7000 = 12600 or y = 4200 c . p . of a t . v . = rs . 4200 answer : d
Answer: d
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 550 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 550 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 it takes a total of nine hours to cover the 550 mile distance . answer : e"
Answer: e
Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of ( a - b ) / 2 ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 5 , e ) 2
Rationale: "answer is 10 yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 ( a - b ) / 2 = 110 - 100 = 10 / 2 = 5 ans : d"
Answer: d
Problem: in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 7.8 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.16 , e ) 81.6
Rationale: degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 7.8 + 8.5 ) = 23.8 point of value of the dive = 23.8 * 3.2 = 76.16 answer d
Answer: d
Problem: the workforce of company x is 60 % female . the company hired 28 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 336 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 28 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 28 ) 0.05 x = 15.4 x = 308 - this is quantity of employees before adding 28 men so after adding it will be 336 answer is c"
Answer: c
Problem: the average of first 25 prime numbers is ?
Options: a ) 9.9 , b ) 8.8 , c ) 5.6 , d ) 11.9 , e ) 11.11
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 / 9 = 100 / 9 = 11.11 ( approx ) answer is e"
Answer: e
Problem: 14 men can complete a piece of work in 22 days . in how many days can 18 men complete that piece of work ?
Options: a ) 23 days , b ) 26 days , c ) 17 days , d ) 29 days , e ) 20 days
Rationale: "c 17 days 14 * 22 = 18 * x = > x = 17 days"
Answer: c
Problem: what amount does an investor receive if the investor invests $ 7000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 8080 , b ) $ 8130 , c ) $ 8260 , d ) $ 8320 , e ) $ 8470
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 7000 = 1.21 * 7000 = 8470 the answer is e ."
Answer: e
Problem: 15 times a number gives 150 . the number is
Options: a ) 11 , b ) 15 , c ) 13 , d ) 14 , e ) can not be determined
Rationale: explanation : let the number be ' n ' 15 × n = 150 ⇒ n = 10 correct option : b
Answer: b