regisss/math_qa huggingface dataset:
Problem: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 10 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 15 days , c ) 12 days , d ) 9 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 10 x = 15 days answer : option b"
Answer: b
Problem: in a hostel there were 100 students . to accommodate 25 more students the average is decreased by rupees 10 . but total expenditure increased by rs . 500 . find the total expenditure of the hostel now ?
Options: a ) 7500 , b ) 5000 , c ) 5400 , d ) 7000 , e ) 8500
Rationale: let average is x 100 x + 500 = 125 ( x – 10 ) x = 70 100 * 70 + 500 = 7500 answer : a
Answer: a
Problem: the area of a square is 4356 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 7 : 12 , d ) 5 : 13 , e ) 7 : 22
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4356 a = 66 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 42 : 132 = 7 : 22 answer : e"
Answer: e
Problem: pat , kate , and mark charged a total of 144 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 80 , c ) 72 , d ) 90 , e ) 108
Rationale: "80 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 144 = > x = 16 32 : 16 : 96 96 - 16 = 80 answer b"
Answer: b
Problem: at the end of the first quarter , the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 50 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 15.3 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 50 = 30 + b + 30 b / 100 b = 15.3 answer ( a )"
Answer: a
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 50 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: percent of students who are 25 years old or older is 0.5 * 48 + 0.2 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 3 = 66 . answer : b .
Answer: b
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6200 ?
Options: a ) rs . 7070 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6200 * 6 ) – 30,130 ] = rs . ( 37200 – 30,130 ) = rs . 7070 answer a"
Answer: a
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 1 , 000,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 1000 ( 1 , 000,000 / 1,000 = 1000 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 1000 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . i . e . the population has to double 10 times . since it takes the population 2 minutes to double once it takes 10 * 2 minutes = 20 minutes to double nine times . thus , solution e = 20 is correct ."
Answer: e
Problem: the present worth of rs . 1183 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 1093.75 , e ) none
Rationale: "solution present worth = rs . [ 1183 / ( 1 + 4 / 100 ) ² ] = rs . ( 1183 x 25 / 26 x 25 / 26 ) = rs . 1093.75 answer d"
Answer: d
Problem: the c . p of 20 pens is equal to the s . p of 12 pens . find his gain % or loss % ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "20 cp = 12 sp 20 - - - 8 cpgain 100 - - - ? = > 40 % answer : d"
Answer: d
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 15 % solution ?
Options: a ) a ) 5.8 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 15 / 100 200 + 20 x = 300 + 3 x 17 x = 100 x = 5.8 answer is a
Answer: a
Problem: how many multiples of 4 are there between 16 and 112 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 4 up to 4 * 28 . 28 - 4 + 1 = 25 . the answer is e ."
Answer: e
Problem: jill has 35 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 60 , c ) 9 , d ) 12 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 35 1 3 / 4 w = 35 w = 20 the total number of jars = 3 w = 60 answer : b
Answer: b
Problem: a cycle is bought for rs . 850 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 27 , c ) 99 , d ) 88 , e ) 11
Rationale: 850 - - - - 180 100 - - - - ? = > 27 % answer : b
Answer: b
Problem: the number of singles that a baseball player hit increased 5 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 2 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 4 : 3 , b ) 9 : 11 , c ) 3 : 1 , d ) 2 : 1 , e ) 11 : 3
Rationale: "soln : - 1.05 s + 0.98 d = 1.02 [ s + d ] 0.03 s = 0.04 d s / d = 4 / 3 answer : a"
Answer: a
Problem: a person is traveling at 25 km / hr and reached his destiny in 5 hr find the distance ?
Options: a ) 100 km , b ) 95 km , c ) 135 km , d ) 80 km , e ) 125 km
Rationale: speed = 25 km / hr time = 5 hr distance = 25 * 5 = 125 km answer is e
Answer: e
Problem: in a theater , the first row has 14 seats and each row has 3 more seats than previous row . if the last row has 50 seats , what is the total number of seats in the theater ?
Options: a ) 404 , b ) 408 , c ) 412 , d ) 416 , e ) 420
Rationale: the number of seats in the theater is 14 + ( 14 + 3 ) + . . . + ( 14 + 36 ) = 13 ( 14 ) + 3 ( 1 + 2 + . . . + 12 ) = 13 ( 14 ) + 3 ( 12 ) ( 13 ) / 2 = 13 ( 14 + 18 ) = 13 ( 32 ) = 416 the answer is d .
Answer: d
Problem: a train 200 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 85 kmph , b ) 115 kmph , c ) 105 kmph , d ) 95 kmph , e ) 125 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 200 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 3600 x = 115 kmph answer is b"
Answer: b
Problem: 8 ^ 100 is divisible by 17 then find the remainder ?
Options: a ) 8 , b ) 10 , c ) 16 , d ) 17 , e ) 18
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Problem: a student scored an average of 80 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 21 , b ) 27 , c ) 26 , d ) 80 , e ) 28
Rationale: "given m + p + c = 80 * 3 = 240 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 240 = 80 . answer : d"
Answer: d
Problem: in an election , candidate douglas won 54 percent of the total vote in counties x and y . he won 62 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 25 % , b ) 28 % , c ) 32 % , d ) 38 % , e ) 40 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 62 % voted means 62 * 200 = 124 votes combined for xy has 300 voters and voted 54 % so total votes = 162 balance votes = 162 - 124 = 38 as y has 100 voters so 38 votes means 38 % of votes required ans d"
Answer: d
Problem: the radius of a wheel is 14.6 cm . what is the distance covered by the wheel in making 100 resolutions ?
Options: a ) 754 m , b ) 704 m , c ) 90.524 m , d ) 706 m , e ) 91.688 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 100 resolutions . = 100 * 2 * 22 / 7 * 14.6 = 9168.8 cm = 91.688 m answer : e"
Answer: e
Problem: harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 2 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 2 m = 30 books total = 40 books m ' = 40 = 5 / 6 * 60 ratio : 5 / 6 ans : e
Answer: e
Problem: on dividing a number by 8 , we get 8 as quotient and 0 as remainder . on dividing the same number by 5 , what will be the remainder ?
Options: a ) 10 , b ) 4 , c ) 8 , d ) 6 , e ) 5
Rationale: "number = 8 * 8 + 0 = 64 5 ) 64 ( 12 60 - - - - - - - - 4 required number = 4 . answer : b"
Answer: b
Problem: what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 448 * 348 ) ^ 2
Options: a ) 86 , b ) 76 , c ) 56 , d ) 36 , e ) 16
Rationale: "( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 348 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,8 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 48 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 48 ) ) ^ 2 = ( 44 * 88 ) ^ 2 = 72 ^ 2 = 84 hence answer is a"
Answer: a
Problem: the number of sailors on a ship is 82 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 47 : 25 , d ) 22 : 25 , e ) 91 : 50
Rationale: "sailor = 1.82 * officer sailor / officer = 1.82 / 1 = 182 / 100 = 91 / 50 answer will be e"
Answer: e
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 50 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: the question is finding y such that ( 50 - y ) ! is a multiple of 50 . that means we need to have 2 * 5 ^ 2 in ( 50 - y ) ! 10 ! is the smallest factorial number with 2 * 5 ^ 2 as a factor . 50 - y = 10 y = 40 the answer is c .
Answer: c
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 9 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 18 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 9 ? 9 ^ 9 = ( 3 ^ 2 ) ^ 9 = 3 ^ 18 d . 18"
Answer: d
Problem: the speed of a railway engine is 84 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
Options: a ) 19 , b ) 18 , c ) 16 , d ) 17 , e ) 14
Rationale: "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 84 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 84 - k * sqrt ( 9 ) = 84 - 3 k k = 20 now , we need to know : what value of n makes s go to zero ? 0 = 84 - 20 * sqrt ( n ) 20 * sqrt ( n ) = 84 sqrt ( n ) = 4.2 n = 4.2 ^ 2 > 17 with 18 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 17 is the maximum number of cars the engine can pull and still move . d"
Answer: d
Problem: a train covers a distance of 90 km in 20 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 675 , b ) 680 , c ) 685 , d ) 690 , e ) 695
Rationale: "speed = ( 90 / 20 * 60 ) km / hr = ( 270 * 5 / 18 ) m / sec = 75 m / sec . length of the train = 75 * 9 = 675 m . answer : option a"
Answer: a
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 3 men and 2 women will do that task .
Options: a ) 4 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 13 / 16 , e ) 4 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 3 m + 2 w = 8 w answer is 8 / 14 = 4 / 7 answer : a"
Answer: a
Problem: a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 20 . if he got 360 marks in two subjects together how many marks did he got in english ?
Options: a ) 120,60 , b ) 240,120 , c ) 280,90 , d ) 220,140 , e ) none of them
Rationale: "let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 20 2 x - 3 y = 120 â € ¦ â € ¦ > ( 1 ) x + y = 360 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 240 and y = 120 answer is b ."
Answer: b
Problem: in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is ?
Options: a ) 11 , b ) 82 , c ) 10 , d ) 28 , e ) 23
Rationale: "explanation : total employees = \ inline \ frac { ( 25 - 10 ) \ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c"
Answer: c
Problem: in the fifth grade at parkway elementary school there are 500 students . 350 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 . , d ) 91 . , e ) 115 .
Rationale: "total students = 500 boys = 350 , girls = 150 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 150 - 35 = 115 . correct option : e"
Answer: e
Problem: for what value of x between − 8 and 8 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 8 , b ) − 2 , c ) 0 , d ) 2 , e ) 8
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 8 will give the greatest value . . ans a"
Answer: a
Problem: what positive number , when squared , is equal to the cube of the positive square root of 16 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 16 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 64 = > x = 8 answer c"
Answer: c
Problem: the difference of two numbers is 1515 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310
Rationale: "let the smaller number be x . then larger number = ( x + 1515 ) . x + 1515 = 6 x + 15 5 x = 1500 x = 300 smaller number = 300 . d )"
Answer: d
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 115 mangoes .
Options: a ) 360 , b ) 383 , c ) 400 , d ) 406 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 115 mangoes = 115 * 3.33 = 383 . answer b"
Answer: b
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability r that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability r = 1 / 24 . answer c ."
Answer: c
Problem: a and b can do a work in 4 days , b and c in 5 days , c and a in 7 days . if a , b and c work together , they will complete the work in ?
Options: a ) 3 days , b ) 5 days , c ) 7 days , d ) 1 days , e ) 2 dasy
Rationale: "a + b 1 day work = 1 / 4 b + c 1 day work = 1 / 5 c + a 1 day work = 1 / 7 adding we get 2 ( a + b + c ) = 1 / 4 + 1 / 5 + 1 / 7 = 83 / 140 a + b + c 1 day work = 83 / 280 a , b , c can finish the work in 280 / 83 days = 3 days approximately answer is a"
Answer: a
Problem: there are 9 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 62 , b ) 70 , c ) 72 , d ) 71 , e ) 76
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 9 and for second = 8 so total methods = 9 * 8 = 72 answer : c"
Answer: c
Problem: how many cubes of 3 cm edge can be cut out of a cube of 18 cm edge
Options: a ) 36 , b ) 232 , c ) 216 , d ) 455 , e ) 363
Rationale: "number of cubes = ( 18 x 18 x 18 ) / ( 3 x 3 x 3 ) = 216 answer : c"
Answer: c
Problem: 600 x 223 + 600 x 77 = ?
Options: a ) 180000 , b ) 138800 , c ) 658560 , d ) 116740 , e ) none of them
Rationale: "= 600 x ( 223 + 77 ) ( by distributive law ) = 600 x 300 = 180000 answer is a"
Answer: a
Problem: a volume of 10976 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 2744 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10976 l can be kept in ( 10976 / 4 ) hemispheres ans . 2744 answer : d"
Answer: d
Problem: at the end of the day , february 14 th , a florist had 150 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 15 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 50 % , b ) 25 % , c ) 250 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 150 s + l = 150 1 / 3 * 150 = 50 short - stemmed white = 20 short - stemmed pink = 15 = > short - stemmed red = 15 15 / p = 15 / r = > r = p so total long stemmed = 100 and long stemmed red + long stemmed pink = 100 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 150 = > r = 130 and r = 65 long stemmed r = 65 - 15 = 50 so long stemmed red / r = 50 / 100 = 50 % answer - a"
Answer: a
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 260 before any discount ?
Options: a ) $ 130.00 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 210.00
Rationale: "original price : 260 $ max first discount = - 30 % thus : 260 ∗ ( 1 − 30 / 100 ) = 182 second discount on the discounted price = - 20 % thus : 182 ∗ ( 1 − 20 / 100 ) = 145,6 answer b ."
Answer: b
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 11 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 27,720
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , 2 * 5 , and 11 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 * 11 = 27,720 the answer is e ."
Answer: e
Problem: carl bought 16 gumballs , lewis bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?
Options: a ) 20 , b ) 16 , c ) 22 , d ) 18 , e ) 24
Rationale: smallest gumballs = ( 19 - 16 ) + ( 19 - 12 ) + 19 = 29 largest gumballs = ( 25 - 16 ) + ( 25 - 12 ) + 25 = 47 difference = 47 - 29 = 18 d
Answer: d
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 28 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 35
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 28 days whole work will be done by y in 28 * 5 / 4 = 35 days answer is e"
Answer: e
Problem: find the principle on a certain sum of money at 7 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 939.6 , b ) 958.9 , c ) 927.78 , d ) 926.82 , e ) 902.1
Rationale: "1120 = p [ 1 + ( 7 * 12 / 5 ) / 100 ] p = 958.90 answer : b"
Answer: b
Problem: find the simple interest on rs . 69,600 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8700 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500
Rationale: "p = rs . 69600 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 69,600 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8700 answer is b ."
Answer: b
Problem: the lcm and hcf of two numbers are 60 and 2 respectively . find the larger of the two numbers if their sum is 22 .
Options: a ) 12 , b ) 2 , c ) 4 , d ) 54 , e ) 56
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 60 * 2 = 120 so the answer which we are looking for has to be a factor of 120 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 120 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Problem: excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 20 , e ) 22
Rationale: "due to stoppages , it covers 9 km less . time taken to cover 9 km = ( 9 / 54 x 60 ) min = 10 min . answer : b"
Answer: b
Problem: the number of stamps that p and q had were in the ratio of 7 : 2 respectively . after p gave q 15 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 2 : 1 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "p started with 7 k stamps and q started with 2 k stamps . ( 7 k - 15 ) / ( 2 k + 15 ) = 2 / 1 3 k = 45 k = 15 p has 7 ( 15 ) - 15 = 90 stamps and q has 2 ( 15 ) + 15 = 45 stamps . the answer is c ."
Answer: c
Problem: if a , b and c together can finish a piece of work in 6 days . a alone in 12 days and b in 18 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 36
Rationale: "c = 1 / 6 - 1 / 12 – 1 / 18 = 1 / 36 = > 36 days ' answer : e"
Answer: e
Problem: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 33 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 105 , e ) 122
Rationale: solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 33 / 100 40 x + 700 = 33 x + 1155 7 x = 855 x = 122 lts correct option : e
Answer: e
Problem: the average of 10 numbers is 23 . if each number is increased by 6 , what will the new average be ?
Options: a ) 36 , b ) 29 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 6 , the total increase = 6 * 10 = 60 the new sum = 230 + 60 = 290 the new average = 290 / 10 = 29 . answer : b"
Answer: b
Problem: each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 16 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 40 minutes , d ) 55 minutes , e ) 52 minutes
Rationale: "as they arrived 16 minutes earlier than usual , they saved 16 minutes on round trip from home to station ( home - station - home ) - - > 8 minutes in each direction ( home - station ) - - > wife meets husband 8 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 8 minutes = 52 minutes . answer : e"
Answer: e
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 49 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 296 , e ) 308
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 49 cm . : 49 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 49 / ( 3.81 ) = 308 answer will be e ."
Answer: e
Problem: if three painters can complete three rooms in three hours , how many painters would it take to do 27 rooms in 9 hours ?
Options: a ) 10 , b ) 8 , c ) 7 , d ) 9 , e ) 11
Rationale: explanation : three painters can complete three rooms in three hours . so 27 rooms can be painted in 9 hrs by 9 painters answer : d ) 9 painters
Answer: d
Problem: how much is 80 % of 40 is greater than 2 / 5 of 25 ?
Options: a ) 22 , b ) 27 , c ) 18 , d ) 12 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 2 / 5 ) * 25 32 - 10 = 22 answer : a"
Answer: a
Problem: 5000 - 4500 ÷ 10.00 = ?
Options: a ) 4550 , b ) 5000 , c ) 0.5 , d ) 4000 , e ) none
Rationale: "answer given expression = 5000 - 4500 ÷ 10.00 = 5000 - 450 = 4550 correct option : a"
Answer: a
Problem: the average age of applicants for a new job is 30 , with a standard deviation of 7 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 14 , c ) 15 , d ) 18 , e ) 30
Rationale: "within one standard deviation of the average age means 31 + / - 7 23 - - 30 - - 37 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 total = 15 c"
Answer: c
Problem: a worker can load one truck in 5 hours . a second worker can load the same truck in 4 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 1.8 , b ) 2.0 , c ) 2.2 , d ) 2.4 , e ) 2.6
Rationale: "the workers fill the truck at a rate of 1 / 5 + 1 / 4 = 9 / 20 of the truck per hour . then the time to fill one truck is 20 / 9 which is about 2.2 hours . the answer is c ."
Answer: c
Problem: find the largest 4 digit number which isexactly divisible by 88 ?
Options: a ) 8765 , b ) 8907 , c ) 9944 , d ) 9954 , e ) 9990
Rationale: "largest 4 digit number is 9999 after doing 9999 ÷ 88 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 c"
Answer: c
Problem: how many of the positive divisors of 600 are also multiples of 4 not including 600 ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 12
Rationale: "600 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 * 3 * 5 ^ 2 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 1 , 1 , and 2 . there are ( 1 + 1 ) ( 1 + 1 ) ( 2 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 600 . the answer is d ."
Answer: d
Problem: little john had $ 8.50 . he spent $ 1.25 on sweets and gave to his two friends $ 1.20 each . how much money was left ?
Options: a ) $ 3.85 , b ) $ 4.85 , c ) $ 5.85 , d ) $ 2.85 , e ) $ 1.85
Rationale: "john spent and gave to his two friends a total of 1.25 + 1.20 + 1.20 = $ 3.65 money left 8.50 - 3.65 = $ 4.85 correct answer is b ) $ 4.85"
Answer: b
Problem: the ratio of buses to cars on river road is 1 to 17 . if there are 80 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 40 , b ) 85 , c ) 60 , d ) 30 , e ) 20
Rationale: b / c = 1 / 17 c - b = 80 . . . . . . . . . > b = c - 80 ( c - 80 ) / c = 1 / 17 testing answers . clearly eliminate acde put c = 85 . . . . . . . . . > ( 85 - 80 ) / 85 = 5 / 85 = 1 / 17 answer : b
Answer: b
Problem: a car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour . the average speed for the entire trip was 60 mph . how many hours long is the trip ?
Options: a ) 6 , b ) 8 , c ) 11 , d ) 12 , e ) 14
Rationale: "in 4 hr journey = 55 * 4 = 220 mph let in the next additional hour journey = 70 * x = 70 x mph so , ( 220 + 70 x ) / ( 4 + x ) = 60 = > 220 + 70 x = 240 + 60 x = > 10 x = 20 = > x = 2 h so the trip is ( 4 + x ) = > 6 hours long answer : a"
Answer: a
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 11 0 = a + d - 10 a + d = 10 a = d ( as they are twin brothers ) a = d = 5 c is the answer"
Answer: c
Problem: one men and three women working 7 hours a day finish a work in 5 days . four men and four women working 3 hours a day complete the work in 7 days . the number of days in which only 7 men working 4 hours a day will finish the work is ?
Options: a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "1 m + 3 w - - - - - 35 h 4 m + 4 w - - - - - - - 21 h 7 m - - - - - - - ? d 35 m + 105 w = 84 m + 84 m 21 w = 49 m 4 * 35 = 7 * x = > x = 20 hours 20 / 4 = 5 days answer : b"
Answer: b
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 40 kg of fresh grapes ?
Options: a ) 5 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) none of these
Rationale: "the weight of non - water in 20 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 40 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 5 answer : a"
Answer: a
Problem: a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 250 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 500 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 500 = 375 250 - - - - - - - - - - - - - 125 1 / 4 - - - - - - - - 125 1 - - - - - - - - - ? = > rs . 500 answer : d"
Answer: d
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 40 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 46
Rationale: we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 40 hence answer is d
Answer: d
Problem: a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of c .
Options: a ) 150 , b ) 450 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 » ) = rs . 150 . answer is a"
Answer: a
Problem: a big container is 30 % full with water . if 27 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters
Rationale: "a big container is 30 % full with water and after 27 liters of water is added , the container becomes 75 % full . hence these 27 liters account for 45 % of the container , which means that the capacity of it is 27 / 0.45 = 60 liters . or : if the capacity of the container is x liters then : 0.3 x + 27 = 0.75 x - - > x = 60 liters . answer : e ."
Answer: e
Problem: in a group of cows and hens , the number of legs are 14 more than twice the number of heads . the number of cows is
Options: a ) 22 , b ) 7 , c ) 8 , d ) 6 , e ) 51
Rationale: "let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 14 4 x + 2 y = 2 x + 2 y + 14 2 x = 14 x = 7 . answer : b"
Answer: b
Problem: a computer store offers employees a 15 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 500 dollars and marked up the price 15 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 15 % off retail price ) as opposed to the final retail price .
Options: a ) 52.5 , b ) 54.5 , c ) 55.5 , d ) 57.5 , e ) 59.5
Rationale: cost price = 500 profit = 15 % = 15 % of 500 = 75 selling price = cp + profit sp = 575 a discount of 10 % to employees means 10 % off on 575 so 10 % of 575 = 57.5 ans d
Answer: d
Problem: find the area of trapezium whose parallel sides are 30 cm and 12 cm long , and the distance between them is 16 cm ?
Options: a ) 288 cm 2 , b ) 277 cm 2 , c ) 285 cm 2 , d ) 336 cm 2 , e ) 340 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 30 + 12 ) * ( 16 ) = 336 cm 2 answer : d"
Answer: d
Problem: working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 360 , e ) 1500
Rationale: answer : d .
Answer: d
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 964 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 22200 , b ) 31897 , c ) 38799 , d ) 40000 , e ) 42782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 964 p = 40000 answer : d"
Answer: d
Problem: a box contains 9 slips that are each labeled with one number : 1 , 3 , 5 , 8 , 13 , 21 , 34 and 55 . two of the slips are drawn at random from the box without replacement . what is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box ?
Options: a ) 7 / 72 , b ) 1 / 6 , c ) 5 / 28 , d ) 15 / 36 , e ) 21 / 36
Rationale: probability = no : of desired outcomes / total no : of outcomes . you are picking two slips out of 8 slips . so total no : of outcomes = 8 c 2 = 28 desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box . how many such outcomes are there ? if you look at the numbers closely , you will see that the following pair of numbers will give you the desired outcome . ( 3,5 ) ( 5,8 ) ( 8,13 ) ( 13,21 ) ( 21,34 ) . there are 7 such pairs . if the two numbers which i pick is from any of these 5 pairs , then i get my desired outcome . so no : of desired outcomes = 5 probability = 5 / 28 answer : c
Answer: c
Problem: the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 9 = 160 , what is the value of x ?
Options: a ) 18 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "ab = ( a - 1 ) ( b - 1 ) x 9 = ( x - 1 ) ( 9 - 1 ) = 160 - - > x - 1 = 20 - - > x = 21 answer : e"
Answer: e
Problem: what percent is 3 gm of 1 kg ?
Options: a ) 1.5 % , b ) 0.3 % , c ) 2.5 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 3 / 1000 × 100 = 300 / 1000 = 3 / 10 = 0.3 % b )"
Answer: b
Problem: john began driving from home on a trip averaging 30 miles per hour . how many miles per hour must carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after john ?
Options: a ) 35 , b ) 55 , c ) 39 , d ) 40 , e ) 60
Rationale: carla starts 30 minutes later and it takes 3 hr for carla to meet john so john total time travelled = 3 hr + 30 minutes john distance = 30 * ( 3 1 / 2 ) = 105 so carla need to travle 105 to meet john in 3 hrs speed of carla = 105 / 3 = 35 miles per hour answer is a
Answer: a
Problem: two brother x and y appeared for an exam . let a be the event that x is selected and b is the event that y is selected . the probability of a is 17 and that of b is 29 . find the probability that both of them are selected .
Options: a ) 2 / 63 , b ) 2 / 67 , c ) 2 , d ) 3 / 31 , e ) 4
Rationale: given , a be the event that x is selected and b is the event that y is selected . p ( a ) = 17 , p ( b ) = 29 . let c be the event that both are selected . p ( c ) = p ( a ) × p ( b ) as a and b are independent events : = ( 17 ) × ( 29 ) = 2 / 63 answer is a
Answer: a
Problem: sandy is younger than molly by 12 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 12 x = 6 sandy is 42 years old . the answer is a .
Answer: a
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 302 to 400 inclusive ?
Options: a ) 11,550 , b ) 14,550 , c ) 17,550 , d ) 20,550 , e ) 23,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 302 + 304 + . . . + 400 = 50 ( 300 ) + ( 2 + 4 + . . . + 100 ) = 15,000 + 2550 = 17,550 the answer is c ."
Answer: c
Problem: walking at the rate of 8 kmph a man cover certain distance in 3 hrs . . running at a speed of 16 kmph the man will cover the same distance in .
Options: a ) 1.2 hr , b ) 2.5 hr , c ) 1.5 hr , d ) 48 min , e ) 58 min
Rationale: distance = speed * time 8 * 3 = 24 km new speed = 16 kmph therefore time = d / s = 24 / 16 = 1.5 hr . answer : c .
Answer: c
Problem: a man can row 3.3 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1
Rationale: speed of boat in still water ( b ) = 3.3 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.1 km / hr . answer : e
Answer: e
Problem: two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer q between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) q = 12 , b ) q = 15 , c ) q = 17 , d ) q . 18 , e ) q = 20
Rationale: "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Problem: if three numbers in the ratio 3 : 2 : 5 be such that the sum of their squares is 1862 , the middle number will be
Options: a ) 10
b ) 14
c ) 18
d ) 22
e ) 24
Rationale: explanation : let the numbers be 3 x , 2 x and 5 x . then , 9 x + 4 x + 25 x = 1862 ⇒ 38 x = 1862 ⇒ x = 49 ⇒ x = 7 . middle number = 2 x = 14 option b
Answer: b
Problem: factory x ' s bulbs work for over 5000 hours in 79 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 85 % of cases . it is known that factory x supplies 80 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 80.2 % , b ) 88 % , c ) 87.4 % , d ) 85 % , e ) 83.9 %
Rationale: for x , 80 % of 79 % will work . for y , 20 % of 85 % will work . * 20 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.80 ( 0.79 ) = . 632 0.20 ( 0.85 ) = 0.17 the combined probability then is 63.2 + 17 = 80.2 % ans a
Answer: a
Problem: a train 150 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 13 km / hr , b ) 59 km / hr , c ) 17 km / hr , d ) 18 km / hr , e ) 12 km / hr
Rationale: "speed of the train relative to man = ( 150 / 10 ) m / sec = ( 15 ) m / sec . [ 15 ) * ( 18 / 5 ) ] km / hr = 54 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 54 = = > x = 59 km / hr . answer : b"
Answer: b
Problem: each factor of 210 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 40 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 16 . answer : a"
Answer: a
Problem: if the population of a certain country increases at the rate of 10 person every 60 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 200 , c ) 600 , d ) 800 , e ) 1000
Rationale: "answer = 10 * 60 ( 1 hour = 60 minutes ) = 600 answer = c"
Answer: c
Problem: the units digit of ( 10 ) ^ ( 87 ) + ( 5 ) ^ ( 46 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . done . the second term anything power to 10 unit digit will be zero then 5 + 0 = 5 , e"
Answer: e
Problem: double of quarter of 4 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.0005 , c ) 0.25 , d ) 0.02 , e ) none of these
Rationale: explanation : solution : ( 2 ) * ( 1 / 4 ) * 4 % = 2 * ( 1 / 4 * 1 / 100 ) = 0.02 . answer : d
Answer: d
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 1100 m long ?
Options: a ) 200 sec , b ) 230 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2300 m t = d / s t = 2300 / 10 t = 230 sec answer : b"
Answer: b
Problem: a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?
Options: a ) 270 , b ) 279 , c ) 348 , d ) 371 , e ) 372
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 841 = 348 answer : c"
Answer: c
Problem: a one - foot stick is marked in 1 / 4 and 1 / 6 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "lcm of 24 = 12 1 / 4 marking are ( table of 3 ) 0 . . . . . . 3 . . . . . . . . . . . 6 . . . . . . . . . . 9 . . . . . . . . . . 12 ( total = 5 ) 1 / 6 marking are ( table of 2 ) 0 . . . . . . . 2 . . . . . . 4 . . . . . . 6 . . . . . . . . 8 . . . . . . . . . 12 ( ( total = 6 ) overlapping markings are 0 . . . . . . . . 6 . . . . . . . . . 12 ( total = 3 ) total markings = 5 + 6 - 3 = 8 answer = a"
Answer: a