regisss/math_qa huggingface dataset:
Problem: the average age of an adult class is 40 years . 18 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 18 x 32 = ( y + 18 ) x 36 â ‡ ’ 40 y + 576 = 36 y + 648 â ‡ ’ 4 y = 72 â ˆ ´ y = 18 e"
Answer: e
Problem: a number whose fifth part increased by 7 is equal to its fourth part diminished by 7 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 280 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 7 = ( n / 4 ) - 7 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 14 â ‡ ’ ( 5 n - 4 n ) / 20 = 14 â ˆ ´ n = 280 option : d"
Answer: d
Problem: a tradesman sold an article at a loss of 25 % . if the selling price had been increased by $ 500 , there would have been a gain of 15 % . what was the cost price of the article ?
Options: a ) $ 1000 , b ) $ 1200 , c ) $ 1120 , d ) $ 1350 , e ) $ 1250
Rationale: let c . p . be $ x then 125 % of x - 85 % of x = 500 40 % of x = 500 2 x / 5 = 500 x = $ 1250 answer is e
Answer: e
Problem: find the area , diameter = 9 m .
Options: a ) 63.00 square meter , b ) 63.64 square meter , c ) 63.08 square meter , d ) 63.24 square meter , e ) 63.43 square meter
Rationale: "diameter = 9 meter . radius = diameter / 2 . = 9 / 2 . = 4.5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 4.5 . area of a circle = 3.14 ã — 4.5 ã — 4.5 . = 3.14 ã — 20.25 . = 63.64 m 2 . answer : b"
Answer: b
Problem: if 1.5 x = 0.04 y then the value of ( y - x ) / ( y + x ) is
Options: a ) 730 / 77 , b ) 73 / 77 , c ) 7.3 / 77 , d ) 7.3 / 770 , e ) 7.3 / 77
Rationale: x / y = 0.04 / 1.5 y / x = 1.5 / 0.04 by componendo dividendo rule ( y + x ) / ( y - x ) = 1.54 / 1.46 ( y - x ) / ( y + x ) = 1.46 / 1.54 = 73 / 77 answer : b
Answer: b
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 8 ) , how many units is p from the y - axis ?
Options: a ) 20 , b ) 16 , c ) 8 , d ) 4 , e ) 2
Rationale: the x - axis is 8 units from the point p . thus the y - axis is 16 units from the point p . the answer is b .
Answer: b
Problem: 150 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 90 liters , b ) 20 liters , c ) 50 liters , d ) 20 liters , e ) 70 liters
Rationale: "milk = 3 / 5 * 150 = 90 liters water = 50 liters 90 : ( 50 + p ) = 3 : 4 150 + 3 p = 360 = > p = 70 50 liters of water are to be added for the ratio become 3 : 4 . answer : c"
Answer: c
Problem: two years ago , john put $ 5000 into a savings account . at the end of the first year , his account had accrued $ 500 in interest bringing his total balance to $ 5500 . the next year , his account balance increased by 10 % . at the end of the two years , by what percent has john ' s account balance increased from his initial deposit of $ 5000 ?
Options: a ) 19 % , b ) 21 % , c ) 20 % , d ) 22 % , e ) 25 %
Rationale: investment 5000 dollars 1 st year total gained = 500 total amount end of first year = 5500 second year account increased by 10 % = 5500 * 0.1 = 550 therefore total amount by second year end = 6050 so total percentage increase in money = ( 6050 - 5000 ) * 100 / 5000 = 21 % correct answer b = 21 %
Answer: b
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 6 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 6.5 , b ) 7.0 , c ) 7.5 , d ) 8.0 , e ) 8.5
Rationale: "in one hour , the crow eats 1 / 30 of the nuts . ( 1 / 4 ) / ( 1 / 30 ) = 7.5 hours the answer is c ."
Answer: c
Problem: how much is 65 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 66 , d ) 12 , e ) 6
Rationale: "( 65 / 100 ) * 40 – ( 4 / 5 ) * 25 26 - 20 = 6 answer : e"
Answer: e
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number r and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number r of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Answer: d
Problem: if the numerator of a fraction be increased by 12 % and its denominator decreased by 2 % the value of the fraction becomes 6 / 7 . thus , the original fraction is :
Options: a ) 1 / 4 , b ) 2 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 3
Rationale: if original fraction is x / y , then 1.12 x / 0.98 y = 6 / 7 ( 8 / 7 ) * ( x / y ) = 6 / 7 x / y = 6 / 8 = 3 / 4 answer : c
Answer: c
Problem: 3 - fourth of two - third of 3 - seventh of a number is 27 . what is 10 % of that number ?
Options: a ) 12.6 % , b ) 6.3 % , c ) 27 % , d ) 25.2 % , e ) none of these
Rationale: explanation : solution : assume the number be x . then , 3 / 4 of 2 / 3 of 3 / 7 of x = 27 . x = 27 * 7 / 3 * 3 / 2 * 4 / 3 . x = 126 . ' . 10 % of 126 = 10 / 100 * 126 = 12.6 answer : a
Answer: a
Problem: a shipment of 250 smartphones contains 67 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 14 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: probability of chosing one defective phone from a lot of 250 which ontains 67 defective phones is = ( 67 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 66 ( we already picked one ) defective phones is = ( 66 / 249 ) combined probability of series of events = product of the probabilities = ( 67 / 250 ) * ( 66 / 249 ) 67 / 250 is close to ( 26 / 97 ) and ( 66 / 249 ) = ( 22 / 83 ) so answer is ( 26 / 97 ) * ( 22 / 83 ) = ( 1 / 14 ) so , answer will be b
Answer: b
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 11 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 6 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
Rationale: "( 1 mph + 11 mph ) / 2 = 6 mph correct option is : a"
Answer: a
Problem: ( 17 ) 4.25 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 3.75 , e ) none of these
Rationale: "solution let ( 17 ) 4.25 * ( 17 ) x = 178 . then , ( 17 ) 4.25 + x = ( 17 ) 8 . ∴ 4.25 + x = 8 ⇔ x = ( 8 - 4.25 ) ⇔ x = 3.75 answer d"
Answer: d
Problem: cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 75 time from work to home = x / 105 total time = 2 hrs ( x / 75 ) + ( x / 105 ) = 2 solving for x , we get x = 175 / 2 time from home to work in minutes = ( 175 / 2 ) * 60 / 75 = 70 minutes ans = b"
Answer: b
Problem: 65 % of x = 20 % of 487.50 . find the value of x ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 180 , e ) 199
Rationale: 65 % of x = 20 % of 487.50 then , 65 / 100 * x = 20 / 100 * 4875 / 10 x = 150 answer is b
Answer: b
Problem: m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , 5 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 3 / 7 , c ) 2 / 5 , d ) 1 / 2 , e ) 5 / 9
Rationale: we will have a negative product only if 1 , 2 , 3 , 4 , or 5 are selected from set t . p ( negative product ) = 5 / 9 the answer is e .
Answer: e
Problem: how many pieces of 85 cm length can be cut from a rod of 42.5 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 4250 / 85 = 850 / 17 = 50 answer is a ."
Answer: a
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 45000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 2100
Rationale: "30 sec approach - solve it using approximation 45000 sheet at full price , 5 cent = 2250 45000 sheet at max discount price , 4 cent = 2000 your ans got to be between these two . ans e it is ."
Answer: e
Problem: a man buys an article for $ 10 . and sells it for $ 15 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 15 % , e ) 30 %
Rationale: c . p . = $ 10 s . p . = $ 15 gain = $ 5 gain % = 5 / 10 * 100 = 50 % answer is b
Answer: b
Problem: there are 10 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 675 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 10 c 2 number of ways of selecting 2 non fiction books = 6 c 2 10 c 2 * 6 c 2 = 45 * 15 = 675 answer : c"
Answer: c
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 5 .
Options: a ) 2 , b ) 5 , c ) 11 , d ) 3 , e ) 4
Rationale: 6 * 15 * 5 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 5 + 1 ) = ( √ 8 * 18 ) / 6 = ( √ 144 ) / 6 = 12 / 6 = 2 answer is a
Answer: a
Problem: the speed of a car is 120 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 92 kmph , c ) 90 kmph , d ) 65 kmph , e ) 77 kmph
Rationale: "s = ( 120 + 60 ) / 2 = 90 kmph c"
Answer: c
Problem: if a ( a + 6 ) = 7 and b ( b + 6 ) = 7 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 6 , c ) 2 , d ) 46 , e ) 48
Rationale: "a ( a + 6 ) = 7 = > we have a = 1 or - 7 also b ( b + 6 ) = 7 = > b = 1 or - 7 given a ≠ b 1 ) when a = 1 , b = - 7 and a + b = - 6 1 ) when a = - 7 , b = 1 and a + b = - 6 answer choice b"
Answer: b
Problem: fred and sam are standing 50 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 5 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45
Rationale: "relative distance = 50 miles relative speed = 5 + 5 = 10 miles per hour time taken = 50 / 10 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c"
Answer: c
Problem: when a number is divided by 6 & then multiply by 12 the answer is 9 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 9 = > 2 x = 9 = > x = 4.5 a"
Answer: a
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 12 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 23 , c ) c ) 24 , d ) d ) 29 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 12 . . so total who won n = 11 + 12 = 23 . . b"
Answer: b
Problem: of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 3 / 5 of the students are female , what fraction of all the students are on the honor roll ?
Options: a ) 5 / 9 , b ) 3 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "for total students take lcm of factions = 6 * 5 = 30 let female students = x , so male students = 30 - x now , female stu . on honor roll = 5 / 6 ( x ) and male stu . on honor roll = 2 / 3 ( 30 - x ) as given total female stu . = 3 / 5 ( 30 ) = 18 female stu . = ( 5 / 6 ) * 18 = 15 and male stu . = ( 2 / 3 ) * 12 = 8 fraction of honor student = ( 15 + 8 ) / 30 = 23 / 30 . correct answer is c ."
Answer: c
Problem: the average of 10 numbers is 23 . if each number is increased by 3 , what will the new average be ?
Options: a ) 36 , b ) 26 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 3 , the total increase = 3 * 10 = 40 the new sum = 230 + 30 = 260 the new average = 260 / 10 = 26 . answer : b"
Answer: b
Problem: in an election , candidate a got 60 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 285600 , b ) 340000 , c ) 347000 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 60 % therefore , the number of valid votes polled in favour of candidate a = 60 % of 476000 = 60 / 100 × 476000 = 28560000 / 100 = 285600 a )"
Answer: a
Problem: the duplicate ratio of 2 : 6 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 9 , d ) 1 : 18 , e ) 1 : 13
Rationale: "2 ^ 2 : 6 ^ 2 = 4 : 36 = 1 : 9 answer : c"
Answer: c
Problem: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 5 is :
Options: a ) 545 , b ) 488 , c ) 542 , d ) 548 , e ) 560
Rationale: required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 5 = 540 + 5 = 545 . answer : a
Answer: a
Problem: excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 43 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 16 min , c ) 20 min , d ) 8.4 min , e ) 40 min
Rationale: "d 8.4 min due to stoppages , it covers 7 km less . time taken to cover 9 km = ( 7 / 50 x 60 ) min = 8.4 min"
Answer: d
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 7000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) 49000
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 7000 = > total profit = 7000 * 7 = 49000 . answer : option e"
Answer: e
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 36 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 17 , d ) 19 , e ) 21
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 36 - x now , 50 * x + 500 * ( 36 - x ) = 10350 50 x + 18000 - 500 x = 10350 - 450 x = - 7650 x = 17 . no . of 50 rupees note = 17 . answer : option c"
Answer: c
Problem: a part of certain sum of money is invested at 8 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 3 : 2 , b ) 4 : 8 , c ) 4 : 3 , d ) 4 : 0 , e ) 4 : 9
Rationale: "12 : 8 = 3 : 2 answer : a"
Answer: a
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 3 : 5 . what is the ratio of the smaller number to the larger ?
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 2 , e ) 2 : 3
Rationale: "let the numbers be a , b acc . to problem , ( a + b ) / 2 ∗ a ( a + b ) / 2 ∗ a = 3 / 53 / 5 1 / 21 / 2 + b / 2 ∗ ab / 2 ∗ a = 3 / 53 / 5 b / ab / a = 1 / 51 / 5 ans . a"
Answer: a
Problem: what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 20 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 5 : 4 , d ) 13 : 11 , e ) 14 : 8
Rationale: correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 5 : 4
Answer: c
Problem: a sum of money deposited at c . i . amounts to rs . 3000 in 3 years and to rs . 3600 in 4 years . find the rate percent ?
Options: a ) 25 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 20 %
Rationale: "3000 - - - 600 100 - - - ? = > 20 % answer : e"
Answer: e
Problem: the product z of two prime numbers is between 15 and 36 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24 , then what is z ?
Options: a ) 35 , b ) 33 , c ) 28 , d ) 21 , e ) 15
Rationale: the smallest possible product is 33 which is 3 * 11 . all other products are too big . the answer is b .
Answer: b
Problem: a sum amounts to rs . 3087 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 4000 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 2800
Rationale: "ci = 3087 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 3087 = p [ 21 / 20 ] ^ 2 3087 [ 20 / 21 ] ^ 2 2800 answer : e"
Answer: e
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 37 . in the company , what is the maximum number of non - managers in a department that has 11 managers ?
Options: a ) 56 , b ) 57 , c ) 58 , d ) 59 , e ) 60
Rationale: "11 / 7 * 37 = 58.1 the answer is c ."
Answer: c
Problem: rebecca ' s yearly income is $ 15000 and jimmy ' s annual income is $ 18000 . by how much must rebecca ' s yearly income increase so that it constitutes 55 % of rebecca and jimmy ' s combined income ?
Options: a ) 7000 , b ) 8000 , c ) 9000 , d ) 10000 , e ) 11000
Rationale: total rebecca = x + 15000 ; total = x + 15000 + 18000 ; x + 15000 / x + 33000 = 55 / 100 therefore x = 7000 a
Answer: a
Problem: a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 75 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 78
Rationale: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 75 hours = 3,600 / 75 seconds = 48 seconds ; time to cover 1 kilometer at regular speed is 48 + 5 = 53 seconds = 53 / 3,600 hours = 1 / 70 hours ; so , we get that to cover 1 kilometer 1 / 70 hours is needed - - > regular speed 70 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : a"
Answer: a
Problem: by investing in 1623 % stock at 64 , one earns rs . 1900 . the investment made is
Options: a ) s . 9600 , b ) s . 7500 , c ) s . 5640 , d ) s . 5760 , e ) - 7296
Rationale: explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1500 , investment needed = 64 × 3 × 1500 / 50 = 5760 answer : option d
Answer: d
Problem: the average of 10 numbers is 23 . if each number is increased by 5 , what will the new average be ?
Options: a ) 36 , b ) 28 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 5 , the total increase = 5 * 10 = 50 the new sum = 230 + 50 = 280 the new average = 280 / 10 = 28 . answer : b"
Answer: b
Problem: how many days per calendar year is the month a factor of the day
Options: a ) 0 , b ) 1 , c ) 59 , d ) 90 , e ) 124
Rationale: solution : 124 all 31 days in january , because 1 is a factor of all integers 14 of the 28 days in february ( because every other day is divisible by 2 ) 10 of the 31 days in march ( the multiples of 3 between 3 and 30 ) 7 days in april ( the multiples of 4 between 4 and 28 ) 6 days in may ( the multiples of 5 between 5 and 30 ) 5 days in june ( the multiples of 6 between 6 and 30 ) 4 days in july ( the multiples of 7 between 7 and 28 ) 3 days in august ( the multiples of 8 between 8 and 24 … so , so close if only the month were 32 days long ! ) 3 days in september ( 9 th , 18 th , 27 th ) 3 days in october ( 10 th , 20 th , 30 th ) 2 days in november ( 11 th , 22 nd ) 2 days in december ( 12 th , 24 th ) and there you have it ! as you can see , as you move through the months , your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights … this is a very valuable skill to remember on test day ! e
Answer: e
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days m will the work get over ?
Options: a ) 60 , b ) 70 , c ) m = 75 , d ) 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Problem: a train 100 m long crosses a platform 100 m long in 12 sec ; find the speed of the train ?
Options: a ) 60 kmph , b ) 65 kmph , c ) 54 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 100 + 100 = 200 t = 12 s = 200 / 12 * 18 / 5 = 60 kmph answer : a"
Answer: a
Problem: if circles x and y have the same area and circle x has a circumference of 14 π , half of the radius of circle y is :
Options: a ) 16
b ) 8
c ) 4
d ) 3.5
e ) 1
Rationale: x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 14 * pi x = 7 thus y = 7 y / 2 = 3.5 ans : d
Answer: d
Problem: the sum of three consecutive integers is 93 . what are the integers ?
Options: a ) 20 , 21,22 , b ) 10 , 11,12 , c ) 30 , 31,32 , d ) 40 , 41,42 , e ) 30 , 31,32
Rationale: "first x make the first number x second x + 1 to get the next numberwe go up one or + 1 third x + 2 add another 1 ( 2 total ) to get the third f + s + t = 93 first ( f ) plus second ( s ) plusthird ( t ) equals 93 ( x ) + ( x + 1 ) + ( x + 2 ) = 93 replace f with x , s with x + 1 , and t with x + 2 x + x + 1 + x + 2 = 93 here the parenthesis aren ′ t needed . 3 x + 3 = 93 combine like terms x + x + x and 2 + 1 − 3 − 3 add 3 to both sides 3 x = 90 the variable ismultiplied by 3 3 3 divide both sides by 3 x = 30 our solution for x first 30 replace x in our origional listwith 30 second ( 30 ) + 1 = 31 the numbers are 30 , 31 , and 32 third ( 30 ) + 2 = 32 correct answer e"
Answer: e
Problem: a store owner estimates that the average price of type a products will increase by 25 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,585 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.25 * 4500 = 5625 cost of type b products next year = 1.2 * 8300 = 9960 total 5625 + 9960 = 15585 option b"
Answer: b
Problem: when n is divided by 20 , the remainder is 6 . what is the remainder when n + 16 is divided by 5 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 14 remainder ( n / 20 ) = 6 n + 16 = 36 remainder ( 36 / 5 ) = 1 option a"
Answer: a
Problem: on a sum of money , the s . i . for 2 years is $ 660 , while the c . i . is $ 693 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 10 % , b ) 32 % , c ) 72 % , d ) 14 % , e ) 82 %
Rationale: "difference in c . i . and s . i for 2 years = $ 693 - $ 660 = $ 33 s . i for one year = $ 330 s . i . on $ 330 for 1 year = $ 33 rate = ( 100 * 33 ) / ( 330 ) = 10 % the answer is a ."
Answer: a
Problem: in a group of ducks and cows , the total number of legs are 32 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 32 more than twice the number of heads = > 2 ( d + 2 c ) = 32 + 2 ( c + d ) = > d + 2 c = 16 + c + d = > 2 c = 16 + c = > c = 16 i . e . , total number of cows = 16 answer is c ."
Answer: c
Problem: a is half good a work man as b and together they finish a job in 12 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 18 , d ) 36 , e ) 48
Rationale: "c 18 wc = 1 : 2 2 x + x = 1 / 12 = > x = 1 / 36 2 x = 1 / 18 = > 18 days"
Answer: c
Problem: a cyclist traveled for two days . on the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 280 miles and spent a total of 10 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: "solution : d = 280 mi t = 12 hrs day 1 time = t 1 day 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs day 1 rate = r 1 day 2 rate = r 2 r 1 - r 2 = 10 mph i . e . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 i . e . 280 = 8 r 2 + 4 ( 10 + r 2 ) i . e . r 2 = 20 mph answer : e"
Answer: e
Problem: a pair of articles was bought for $ 50 at a discount of 40 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 15 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 60 % of x = 25 x = 25 * . 6 = $ 15 answer is b
Answer: b
Problem: find the area of trapezium whose parallel sides are 28 cm and 20 cm long , and the distance between them is 21 cm ?
Options: a ) 288 cm 2 , b ) 277 cm 2 , c ) 504 cm 2 , d ) 510 cm 2 , e ) 287 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 28 + 20 ) * ( 21 ) = 504 cm 2 answer : c"
Answer: c
Problem: by selling 16 pencils for a rupee a man loses 5 % . how many for a rupee should he sell in order to gain 15 % ?
Options: a ) 12.95 , b ) 19 , c ) 17.56 , d ) 16.56 , e ) 15
Rationale: "85 % - - - 16 105 % - - - ? 85 / 105 * 16 = 8 answer : a"
Answer: a
Problem: if 7 : 13 : : 301 : x then the value of ‘ x ’ is :
Options: a ) 493 , b ) 537 , c ) 559 , d ) 587 , e ) 567
Rationale: "given the question ; 7 : 13 : : 301 : x 7 / 13 = 301 / x 7 x = 301 * 13 x = 301 * 13 / 7 x = 559 answer : c"
Answer: c
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 45 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 93 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 45 + 45 = 90 km / hr . 90 * 5 / 18 = 25 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 25 = 40 sec . answer : a"
Answer: a
Problem: the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 49 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: $ 49 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 49 x = 0.07 the answer is c .
Answer: c
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 66 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: d ) 6
Answer: d
Problem: 9823 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 3377 , e ) none of these
Rationale: "answer x = 13200 - 9823 = 3377 option : d"
Answer: d
Problem: a store ’ s selling price of $ 2500 for a certain printer would yield a profit of 40 percent of the store ’ s cost for the printer . what selling price would yield a profit of 50 percent of the printer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2650 , d ) $ 2478 , e ) $ 2800
Rationale: 1.4 x = 2500 x = 2500 / 1.4 so , 1.5 x = 2500 * 1.5 / 1.4 = 2478 answer : - d
Answer: d
Problem: in a soccer bet , we play 4 teams . first team odd 1.28 , second 5.23 , third 3.25 , fourth 2.05 . we place the bet with 5.00 euros . how much money we expect to win ?
Options: a ) 219.5 , b ) 223.0 , c ) 235.01 , d ) 266.74 , e ) 669.0
Rationale: in the case we won the bet , we have : 1.28 * 5.23 * 3.25 * 2.0 * 5.00 = 219.50 we will win 223 so correct answer is b
Answer: b
Problem: sum of two numbers prime to each other is 16 and their l . c . m . is 63 . what are the numbers ?
Options: a ) 9 and 10 , b ) 8 and 9 , c ) 11 and 5 , d ) 7 and 8 , e ) 7 and 9
Rationale: as two numbers are prime , only options satisfy all but option c will not make the product of numbers i . e 63 answer : e
Answer: e
Problem: find the area of trapezium whose parallel sides are 22 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 300 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 22 + 18 ) * ( 15 ) = 300 cm 2 answer : c"
Answer: c
Problem: 18 men can complete a piece of work in 20 days . in how many days can 12 men complete that piece of work ?
Options: a ) 23 days , b ) 30 days , c ) 22 days , d ) 29 days , e ) 20 days
Rationale: "b 30 days 18 * 20 = 12 * x = > x = 30 days"
Answer: b
Problem: two trains each 150 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 7.8 sec , b ) 7.2 sec , c ) 8.2 sec , d ) 6.2 sec , e ) 9.2 sec
Rationale: "d = 150 m + 150 m = 300 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 300 * 3 / 125 = 7.2 sec answer : b"
Answer: b
Problem: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 60 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 120 , d ) 90 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 60 kmph , speed of b must be 80 * ( 3 / 2 ) = 90 kmph d"
Answer: d
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 123 hours , it must travel at a speed of :
Options: a ) 234 , b ) 377 , c ) 720 , d ) 378 , e ) 268
Rationale: speed and time are inversely proportional ⇒ speed ∝ 1 time ( when distance is constant ) here distance is constant and speed and time are inversely proportionalspeed ∝ 1 time ⇒ speed 1 speed 2 = time 2 time 1 ⇒ 240 speed 2 = ( 123 ) 5 ⇒ 240 speed 2 = ( 53 ) 5 ⇒ 240 speed 2 = 13 ⇒ speed 2 = 240 × 3 = 720 km / hr answer : d
Answer: d
Problem: a certain car increased its average speed by 3 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 20 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: "in the third time interval the average speed of the car was 20 + 3 + 5 = 28 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 28 * 1 / 12 = 2 miles . answer : c ."
Answer: c
Problem: 500 is increased by 30 % . find the final number .
Options: a ) 550 , b ) 500 , c ) 650 , d ) 600 , e ) 700
Rationale: explanation final number = initial number + 30 % ( original number ) = 500 + 30 % ( 500 ) = 500 + 150 = 650 . answer c
Answer: c
Problem: linda spent 4 / 5 of her savings on furniture and the rest on a tv . if the tv cost her $ 100 , what were her original savings ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 500 , d ) $ 700 , e ) $ 800
Rationale: "if linda spent 4 / 5 of her savings on furniture , the rest 5 / 5 - 4 / 5 = 1 / 5 on a tv but the tv cost her $ 100 . so 1 / 5 of her savings is $ 100 . so her original savings are 5 times $ 100 = $ 500 correct answer c"
Answer: c
Problem: marla starts running around a circular track at the same time nick starts walking around the same circular track . marla completes 30 laps around the track per hour and nick completes 15 laps around the track per hour . how many minutes after marla and nick begin moving will marla have completed 4 more laps around the track than nick ?
Options: a ) 5 , b ) 16 , c ) 12 , d ) 15 , e ) 20
Rationale: "maria ' s rate - 30 laps per hour - - > 30 / 60 laps / min nick ' s rate - 15 laps per hour - - > 15 / 60 laps / min lets set equations : 30 / 60 * t = 4 ( since maria had to run 4 laps before nick would start ) 15 / 60 * t = 0 ( hick has just started and has n ' t run any lap yet ) ( 30 / 60 - 15 / 60 ) * t = 4 - 0 ( since nick was chasing maria ) t = 16 min needed maria to run 4 laps answer : b"
Answer: b
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 500 / 3 , c ) 900 , d ) 480 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 300 then y = 900 answer : c"
Answer: c
Problem: a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 35.00 ?
Options: a ) $ 10.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 16.00 , e ) $ 19.60
Rationale: for retail price = $ 35 first maximum discounted price = 35 - 30 % of 35 = 35 - 10.5 = 24.5 price after additional discount of 20 % = 24.5 - 20 % of 24.5 = 24.5 - 4.9 = 19.6 answer : option e
Answer: e
Problem: when 242 is divided by a certain divisor the remainder obtained is 8 . when 698 is divided by the same divisor the remainder obtained is 9 . when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 4 . what is the value of the divisor ?
Options: a ) 11 , b ) 17 , c ) 13 , d ) 23 , e ) none of these
Rationale: "explanatory answer when 242 is divided by a certain divisor the remainder obtained is 8 . let the divisor be d . when 242 is divided by d , let the quotient be ' x ' . the remainder is 8 . therefore , 242 = xd + 8 when 698 is divided by the same divisor the remainder obtained is 9 . let y be the quotient when 698 is divided by d . then , 698 = yd + 9 . when the sum of the two numbers , 242 and 698 , is divided by the divisor , the remainder obtained is 4 . 242 + 698 = 940 = xd + yd + 8 + 9 940 = xd + yd + 17 as xd and yd are divisible by d , the remainder when 940 is divided by d should have been 17 . however , because we know that the remainder is 4 , it would be possible only when 17 / d leaves a remainder of 4 . if the remainder obtained is 4 when 17 is divided by ' d ' , then ' d ' has to be 13 . choice c"
Answer: c
Problem: the lateral surface area of cube is 100 sq . units . find the volume of cube ?
Options: a ) 135
b ) 155
c ) 125
d ) 145
e ) 115
Rationale: lateral surface = 4 a ( power ) 2 = 100 sq . units a ( power ) 2 = 25 a = 5 . cube volume = a ( power ) 3 = > 125 m ( power ) 3 answer is c .
Answer: c
Problem: 10 men can complete a piece of work in 35 days . in how many days can 7 men complete that piece of work ?
Options: a ) 23 days , b ) 46 days , c ) 22 days , d ) 29 days , e ) 50 days
Rationale: e 50 days 10 * 35 = 7 * x = > x = 50 days
Answer: e
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 12 candidates . she plans to have one working interview with 3 of the 12 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "300 . answer c"
Answer: c
Problem: the number of positive integer solutions for the equation x + y + z + t = 10 is
Options: a ) 60 , b ) 74 , c ) 84 , d ) 54 , e ) 104
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 10 - 1 c 4 - 1 = 9 c 3 = 84 answer : c"
Answer: c
Problem: two boys starts from the same place walking at the rate of 5.3 kmph and 5.6 kmph respectively in the same direction . what time will they take to be 10.5 km apart ?
Options: a ) 32 , b ) 36 , c ) 39 , d ) 38 , e ) 35
Rationale: "explanation : relative speed = 5.6 - 5.3 = 0.3 kmph ( because they walk in the same direction ) distance = 10.5 km time = distance / speed = 10.5 / 0.3 = 35 hr answer : e"
Answer: e
Problem: a train 320 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 77 kmph , c ) 54 kmph , d ) 72 kmph , e ) 88 kmph
Rationale: "s = 320 / 16 * 18 / 5 = 72 kmph answer : d"
Answer: d
Problem: if x is a positive number and 1 / 2 the square root of x is the cube root of x , then x =
Options: a ) 64 , b ) 32 , c ) 16 , d ) 4 , e ) 1
Rationale: 1 / 2 the square root of x is cube root of x . if x = 64 . . then 1 / 2 the square root of x = 4 and cube of x is 64 . option a .
Answer: a
Problem: if k is the greatest positive integer such that 4 ^ k is a divisor of 32 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: "32 / 4 = 8 32 / 16 = 2 8 + 2 = 10 = k answer : e"
Answer: e
Problem: an engineer undertakes a project to build a road 10 km long in 300 days and employs 30 men for the purpose . after 100 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: 30 workers working already let x be the total men required to finish the task in next 200 days 2 km done hence remaining is 8 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 100 ) / ( 2 * 200 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : c
Answer: c
Problem: the average of first four prime numbers greater than 50 is ?
Options: a ) 50 , b ) 57 , c ) 89 , d ) 56 , e ) 60
Rationale: "53 + 59 + 61 + 67 = 240 / 4 = 60 answer : e"
Answer: e
Problem: thirty percent of the women in a college class are science majors , and the non - science majors make up 80 % of the class . what percentage of the women are science majors if 40 % of the class are men ?
Options: a ) 2 % , b ) 5 % , c ) 28 % , d ) 30 % , e ) 45 %
Rationale: "3 / k + 2 / m = 6 / t assuming total # is 100 : [ science - women ] will have - 0.3 * 60 = 18 [ non - science - women ] will have - 42 [ science - men ] will have = 20 - 18 = 2 s 0 18 / 60 * 100 = 30 % answer - d"
Answer: d
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.51 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34 , c ) 37.8 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.51 - - > 15 p - 13.5 p = 51 - - > p = 34 . answer : b ."
Answer: b
Problem: on dividing 122 by a number , the quotient is 6 and the remainder is 2 . find the divisor ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "d = ( d - r ) / q = ( 122 - 2 ) / 6 = 122 / 6 = 20 d )"
Answer: d
Problem: evaluate : 434 - 12 * 3 * 2 = ?
Options: a ) 426 , b ) 526 , c ) 626 , d ) 726 , e ) 826
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 434 - 12 * 3 * 2 = 434 - 8 = 426 correct answer a"
Answer: a
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,628 , d ) 2,124 , e ) 2,256
Rationale: "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.55 = 0.65 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer c"
Answer: c
Problem: some of 60 % - intensity red paint is replaced with 30 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let total paint = 1 let amount replaced = x 60 ( 1 - x ) + 30 x = 40 x = 2 / 3 answer : a"
Answer: a
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 4 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "in one hour , the crow eats 1 / 20 of the nuts . ( 1 / 4 ) / ( 1 / 20 ) = 5 hours the answer is b ."
Answer: b
Problem: 2 , 3 , 4.5 , 6.75 , 10.12 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 58.11 , d ) 15.18 , e ) 16.21
Rationale: "2 ( 2 ã — 3 ) ã · 2 = 3 ( 3 ã — 3 ) ã · 2 = 4.5 ( 4.5 ã — 3 ) ã · 2 = 6.75 ( 6.75 ã — 3 ) ã · 2 = 10.12 ( 10.12 ã — 3 ) ã · 2 = 15.78 answer is d"
Answer: d
Problem: there are 20 brown dogs , 10 white dogs , 15 black dogs . totally how many dogs are there in all ?
Options: a ) 45 , b ) 15 , c ) 25 , d ) 5 , e ) 30
Rationale: 20 + 10 + 15 = 45 . answer is a
Answer: a
Problem: in an examination , there were 2000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 70.20 % , e ) none of these
Rationale: girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d
Answer: d
Problem: if 3 ^ x * 4 ^ y = 1 , 594,323 and x – y = 13 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 1 , 594,323 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 13 and y = 0 , then x = 13 . the answer is d ."
Answer: d
Problem: if a speaks the truth 80 % of the times , b speaks the truth 60 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.8 , b ) 0.92 , c ) 1.02 , d ) 1.2 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 8 / 10 ; false = 2 / 10 probability of b speaks truth p ( b ) = 6 / 10 ; false = 4 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 2 / 10 ) * ( 4 / 10 ) ] = 1 - 8 / 10 = 1 - 0.08 = 0.92 answer : b"
Answer: b
Problem: joe invested a certain sum of money in a simple interest bond whose value grew to $ 460 at the end of 3 years and to $ 560 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 460 - $ 60 = 400 . the interest rate is $ 20 / $ 400 = 5 % the answer is c ."
Answer: c
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent t ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . t = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c"
Answer: c
Problem: 36 people { a 1 , a 2 , . . . , a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , . . . , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Options: a ) 11
b ) 12
c ) 13
d ) 15
e ) 18
Rationale: if we take person a 1 in the set then it will cover a 36 and a 2 for shaking hand . similarly if we take person a 4 in the set then it will cover a 5 and a 3 for shaking hand and so on , so minimum 12 persons are required . answer : b
Answer: b
Problem: a palindrome is a number that reads the same forward and backward , such as 787 . how many even , 8 - digit numbers are palindromes ?
Options: a ) 4055 , b ) 4500 , c ) 5000 , d ) 9000 , e ) 4000
Rationale: "first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 2,4 , 6,8 will be odd , which is 4 / 9 ths of the combinations . 4 / 9 * 9000 = 4000 answer : e"
Answer: e