regisss/math_qa huggingface dataset:
Problem: solve the quickfire maths brain teaser â ˆ š 4 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 20 %
Rationale: â ˆ š 4 % = > â ˆ š 4 / â ˆ š 100 = > 2 / 10 = > 20 / 100 = > 20 % e
Answer: e
Problem: the area of sector of a circle whose radius is 12 metre and whose angle at the center is 42 ° is ?
Options: a ) 52.7 m 2 , b ) 57.8 m 2 , c ) 52.8 metre sq , d ) 72.8 m 2 , e ) 52.8 m 2
Rationale: 42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c
Answer: c
Problem: in a race of 1000 meters , a can beat b by 100 meters , in a race of 800 meters , b can beat c by 100 meters . by how many meters will a beat c in a race of 600 meters ?
Options: a ) 125.5 meters , b ) 126.5 meters , c ) 127.5 meters , d ) 128.5 meters , e ) none of these
Rationale: explanation : when a runs 1000 meters , b runs 900 meters and when b runs 800 meters , c runs 700 meters . therefore , when b runs 900 meters , the distance that c runs = ( 900 x 700 ) / 800 = 6300 / 8 = 787.5 meters . so , in a race of 1000 meters , a beats c by ( 1000 - 787.5 ) = 212.5 meters to c . so , in a race of 600 meters , the number of meters by which a beats c = ( 600 x 212.5 ) / 1000 = 127.5 meters . answer : c
Answer: c
Problem: if a and b get profits of rs . 18,000 and rs . 15,000 respectively at the end of year then ratio of their investments are
Options: a ) 6 : 5 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: "ratio = 18000 / 15000 = 6 : 5 answer : a"
Answer: a
Problem: he ratio between the sale price and the cost price of an article is 5 : 3 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 5 : 2 , e ) 2 : 5
Rationale: let c . p . = rs . 3 x and s . p . = rs . 5 x . then , gain = rs . 2 x required ratio = 5 x : 2 x = 5 : 2 answer : d
Answer: d
Problem: the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 72 + x ) / 7 = 11 = > x = 5 . hence , the seventh observation is 5 . answer : c"
Answer: c
Problem: a certain bag contains 100 balls â € ” 50 white , 20 green , 10 yellow , 17 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 20 + 10 ) / 100 = 80 / 100 = 0.8 . answer is d"
Answer: d
Problem: simplify : 8888 + 888 + 88 + 8
Options: a ) 9872 , b ) 9782 , c ) 9827 , d ) 9287 , e ) none of them
Rationale: "8888 888 88 8 - - - - - - - 9872 answer is a ."
Answer: a
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 15 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 23 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 15 % of 300 seeds germinated , so 0.15 x 300 = 45 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 45 + 70 = 115 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 115 / 500 ) x 100 % , or 23 % . answer : c ."
Answer: c
Problem: a man sitting in a train which is travelling at 50 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed .
Options: a ) 62 kmph , b ) 58 kmph , c ) 52 kmph , d ) 50 kmph , e ) none of these
Rationale: "relative speed = ( 280 ⁄ 9 ) m / sec = ( 280 ⁄ 9 × 18 ⁄ 5 ) kmph = 112 kmph . ∴ speed of goods train = ( 112 – 50 ) kmph = 62 kmph . answer a"
Answer: a
Problem: a can do a work in 15 days and b in 20 days . if they work on it together then in how many days required to complete the work ?
Options: a ) 300 / 31 , b ) 300 / 35 , c ) 300 / 21 , d ) 300 / 15 , e ) 300 / 20
Rationale: person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( 300 / 35 ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work = 300 / 35 answer is b
Answer: b
Problem: what is the average of 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 ?
Options: a ) 1345 , b ) 1334 , c ) 1313.33 , d ) 1350 , e ) 1325
Rationale: "add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 11820 11820 / 9 = 1313.33 c"
Answer: c
Problem: the speed of a car is 90 km in the first hour and 50 km in the second hour . what is the average speed of the car ?
Options: a ) 70 , b ) 75 , c ) 88 , d ) 54 , e ) 15
Rationale: "s = ( 90 + 50 ) / 2 = 70 kmph answer : a"
Answer: a
Problem: of the 200 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 45 percent of the employees prefer city y and 55 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 135
Rationale: "110 prefer x ( group 1 ) ; 90 prefer y ( group 2 ) . city y needs 150 people : letall 90 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 40 people : 110 - 60 = 40 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 90 + 40 = 130 . answer : d ."
Answer: d
Problem: a starts business with rs . 3500 and after 9 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 21000 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 9 = 3 months . so there profit ratio = ( 3500 ã — 12 ) : ( 3 x ) = 2 : 3 â ‡ ’ x = 21000 answer : d"
Answer: d
Problem: a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 80 then it is marked down by 10 % = 80 - 8 = 72 . hence it is 72 % of the original price . hence answer is a"
Answer: a
Problem: what is the sum of all the prime factors of 220 and 330 ?
Options: a ) 15 , b ) 21 , c ) 35 , d ) 41 , e ) 64
Rationale: "prime factorization of both the numbers is as follows 220 = 2 * 2 * 5 * 11 sum of the prime factors of 220 = 20 330 = 2 * 3 * 5 * 11 sum of prime factors of 330 = 21 addition of both = 20 + 21 = 41 answer d"
Answer: d
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 5 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "share of each child ( 5 no ) and ( total share of grand children together ) 1 no = 1 / ( 5 + 1 ) = 1 / 6 as the grand children again equally share the part given to them : share of each grand child = [ ( 1 / 6 ) / 6 ] = 1 / 36 = 2.8 % answer : e"
Answer: e
Problem: how many numbers from 10 to 50 are exactly divisible by 3
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 19
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits b )"
Answer: b
Problem: at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "explanation : let rate will be r % 1200 ( 1 + r / 100 ) 2 = 134832 / 100 ( 1 + r / 100 ) 2 = 134832 / 120000 ( 1 + r / 100 ) 2 = 11236 / 10000 ( 1 + r / 100 ) = 106 / 100 = > r = 6 % option d"
Answer: d
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ?
Options: a ) 70 , b ) 105 , c ) 178 , d ) 177 , e ) 169
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 18 35 - - - ? = > 70 answer : a"
Answer: a
Problem: andrew purchased 7 kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 908 , c ) 930 , d ) 1075 , e ) 1080
Rationale: "cost of 7 kg grapes = 68 × 7 = 476 . cost of 9 kg of mangoes = 48 × 9 = 432 . total cost he has to pay = 476 + 432 = 908 b"
Answer: b
Problem: two numbers a and b are such that the sum of 5 % of a and 3 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 7 : 3 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 5 % of a + 3 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 3 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 3 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 9 b = 12 a + 16 b ⇒ 3 a = 7 b ⇒ ab = 7 / 3 ⇒ a : b = 7 : 3 answer : option c"
Answer: c
Problem: radha bought a watch for rs . 144 and got a percentage of profit equal to the cost price of the watch . what is the cost price of the watch ?
Options: a ) rs . 72 , b ) rs . 78 , c ) rs . 80 , d ) rs . 90 , e ) rs . 92
Rationale: sp = 144 cp = x profit % = x c . p . = ( 100 / ( 100 + gain % ) ) * s . p . x = ( 100 / 100 + x ) * 144 x ^ 2 + 100 x = 14400 x ^ 2 + 180 x - 80 x - 14400 = 0 ( x + 180 ) ( x - 80 ) = 0 x = - 180 x = 80 answer : d
Answer: d
Problem: a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 3 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 36 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 3 = 1 / 3 ( b + 3 ) - - - - > 3 a - 9 = b + 3 scenario 2 b - 3 = 1 / 2 ( a + 3 ) - - - - - > 2 b - 6 = a + 3 from scenario 1 , b = 3 a - 12 substitute b with this information in stmt 2 2 ( 3 a - 12 ) - 9 = a + 3 - - - - - - > 6 a - 24 - 9 = a + 3 - - - - - - > 6 a - a = 33 + 3 - - - > 5 a = 36 a = 36 / 5 , answer choice a"
Answer: a
Problem: 27 is a perfect cube . when x is perfect cube which is added to the prime factor of 27 , the result is not a prime number . what is the square root of x ?
Options: a ) 2
b ) 4
c ) 6
d ) 8
e ) 10
Rationale: 27 is 3 * 3 * 3 2 * 2 = 4 , 3 + 4 = 7 4 * 4 = 16 , 3 + 16 = 17 6 * 6 = 36 , 3 + 36 = 39 8 * 8 = 64 , 3 + 64 = 67 10 * 10 = 100 , 3 + 100 = 103 here c is the only addition that is not a prime number . so the answer is c
Answer: c
Problem: | x + 3 | – | 4 - x | = | 8 + x | how many k solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 55 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 55 has the form 4 k + 3 , so the units digit of 93 ^ 55 is 7 . the units digit of powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a
Problem: a train traveling at 36 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 120 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 36 kmph * 12 seconds convert 36 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 36 kmph = 5 / 18 ∗ 36 = 10 m / sec therefore , length of the platform = 10 m / s * 12 sec = 120 meters . choice a"
Answer: a
Problem: when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.05 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 280 , d ) 112 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.05 = 14 / j 0.05 * j = 14 j = 14 / 0.05 = 1400 / 5 = 280 so j = 280 , answer = c ."
Answer: c
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 8 ?
Options: a ) 61,600 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 8 seeing the options after dividing an finding the reminder of 2 my answer was a"
Answer: a
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose . after 100 days , he finds only 2.5 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 ) a . 43 , b ) b . 53 , c ) c . 55 , d ) d . 68 , e ) e . 60
Rationale: "35 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 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 = ( 35 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 87.5 that is approximately 88 thus , more men needed to finish the task = 88 - 35 = 53 hence answer is b"
Answer: b
Problem: what least number should be subtracted from 1,439 so that the remainder when divided by 5 , 11 , and 13 will leave in each case the same remainder 3 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the lcm of 5 , 11 , and 13 is 715 . the next multiple is 2 * 715 = 1,430 . 1,430 + { remainder } = 1,430 + 3 = 1,433 , which is 6 less than 1,439 . answer : e ."
Answer: e
Problem: a and b invests rs . 5000 and rs . 6000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 2 : 3 , b ) 82 : 31 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 5000 * 4 ) + ( 2500 * 8 ) : ( 6000 * 6 ) + ( 4000 * 6 ) 40000 : 60000 2 : 3 answer : a"
Answer: a
Problem: how long will a boy take to run round a square field of side 20 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 24 sec , e ) 39 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 20 * 4 = 80 m time taken = 80 * 3 / 10 = 24 sec answer is d"
Answer: d
Problem: ( 4300731 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1765113 , d ) 1675123 , e ) none of them
Rationale: "let 4300731 - x = 2535618 then x = 4300731 - 2535618 = 1765113 answer is c"
Answer: c
Problem: what two - digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 4 = 10 x + y = x ^ 2 y ^ 2 - 11 thus 2 xy + 4 = x ^ 2 + y ^ 2 - 11 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 26 or 98 thus the answer is c"
Answer: c
Problem: if a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius , then surface area of each ball ( in sq . cm ) is ?
Options: a ) 100 π
b ) 101 / π
c ) 99 π / 12
d ) 54 / 13 π
e ) 22 / 10 π
Rationale: explanation : 4 / 3 π x 10 x 10 x 10 = 8 x 4 / 3 π rxrxr r = 5 4 π x 5 x 5 = 100 π answer is a
Answer: a
Problem: what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1115 , 1120 , and 1 , 1252140 , 2345 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54
Rationale: add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e
Answer: e
Problem: the price of a certain painting increased by 20 % during the first year and decreased by 25 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 90 % , c ) 120 % , d ) 85 % , e ) 95 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.25 = 120 * 0.75 = 90 hence required answer = ( 90 / 100 ) * 100 % = 90 % answer is b ."
Answer: b
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 13 years and that of the other 9 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15
Rationale: explanation : age of the 15 th student = [ 15 * 15 - ( 13 * 5 + 16 * 9 ) ] = 16 years . answer : b
Answer: b
Problem: if 64 ( 2 ^ x ) = 1 then x =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) - 6 , e ) 5
Rationale: "2 ^ x = 1 / 64 2 ^ x = 1 / 2 ^ 6 2 ^ x = 2 ^ - 6 x = - 6 d"
Answer: d
Problem: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 13.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 160 , b ) $ 289 , c ) $ 334 , d ) $ 274 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 13 = 16 * 13 = 208 $ total charge = 126 + 208 = 334 $ answer c"
Answer: c
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 18 km / hr . what is the length of the platform ?
Options: a ) 80 , b ) 240 , c ) 288 , d ) 277 , e ) 221
Rationale: "speed = 18 * 5 / 18 = 5 m / sec . length of the train = 5 * 20 = 100 m . let the length of the platform be x m . then , ( x + 100 ) / 36 = 5 = > x = 80 m . answer : a"
Answer: a
Problem: if the lcm and hcf of 12 and another number is 60 and 3 respectively . find the other number ?
Options: a ) 17 , b ) 12 , c ) 15 , d ) 13 , e ) 11
Rationale: "hcf x lcm = product of numbers 3 x 60 = 12 x the other number other number = ( 3 x 60 ) / 12 other number = 15 answer : c"
Answer: c
Problem: the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 828 , c ) c ) 25 , d ) d ) 34 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : option c"
Answer: c
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 280 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.2
Rationale: price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 280 / 45 = $ 6.2 answer : e .
Answer: e
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 6 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 6 ) m = 120 m answer : option b"
Answer: b
Problem: if x / 2 = y / 4 = z / 6 , then find the value of ( x + y + z ) / z
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) none of these
Rationale: explanation : x / 2 = y / 4 = z / 6 = k , then x = 2 k , y = 4 k and z = 6 k . now , ( x + y + z ) / z = ( 2 k + 4 k + 6 k ) / 6 k = 12 k / 6 k = 2 answer : option e
Answer: e
Problem: country x taxes each of its citizens an amount equal to 15 percent of the first $ 40000 of income , plus 20 percent of all income in excess of $ 40000 . if a citizen of country x is taxed a total of $ 8000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b .
Answer: b
Problem: the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 1 / 8 is given by ?
Options: a ) 1 / 49 , b ) 1 / 42 , c ) 1 / 09 , d ) 1 / 77 , e ) 1 / 12
Rationale: "2 / 3 * 6 / 7 * 1 / 3 * 1 / 8 = 1 / 42 answer : b"
Answer: b
Problem: if w is the set of all the integers between 39 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 40
Rationale: "multiples of 2 from 39 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 38 = [ 99 / 2 ] - [ 38 / 2 ] = 49 - 19 = 30 multiples of 3 from 39 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 38 = [ 99 / 3 ] - [ 38 / 3 ] = 33 - 13 = 20 multiples of 2 and 3 bothi . e . 6 from 39 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 38 = [ 99 / 6 ] - [ 38 / 6 ] = 16 - 6 = 10 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 30 + 20 - 10 = 40 answer option e"
Answer: e
Problem: the number 500 can be written as the sum of the squares of 2 different positive integers . what is the difference of these 2 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 18 , e ) 13
Rationale: "22 ^ 2 + 4 ^ 2 = 500 - - > 22 - 4 = 18 . d"
Answer: d
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 15 percent , what was the annual interest rate last year ?
Options: a ) 14.04 % , b ) 15.04 % , c ) 13.64 % , d ) 12.04 % , e ) 10.04 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.1 i ( last year ) = 1.1 i ( last year ) 15 = 1.1 x i ( last year ) i ( last year ) = 15 / 1.1 = 150 / 11 = 13.64 % answer : c"
Answer: c
Problem: a sum of money at simple interest amounts to rs . 845 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 728
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 845 - 117 ) = rs . 728 . answer : option e"
Answer: e
Problem: find number which is 70 % less than 80 .
Options: a ) 18 , b ) 22 , c ) 24 , d ) 26 , e ) 98
Rationale: "explanation : 70 % less is 30 % of the given number therefore , 30 % of 80 is 24 . answer : c"
Answer: c
Problem: the sum of 3 consecutive odd numbers is 20 more than the first of these numbers . what is the middle number ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 10
Rationale: solution let the numbers be x , x + 2 , x + 4 then x , ( x + 2 ) + ( x + 4 ) = x + 20 ‹ = › 2 x = 14 ‹ = › x = 7 . therefore middle number = x + 2 = 9 . answer c
Answer: c
Problem: the sum of ages of 4 children born 4 years different each is 48 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 x = 6 x + 12 = 6 + 12 = 18 answer : e"
Answer: e
Problem: a tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 9.33 % , d ) 10.67 % , e ) 11.7 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 2,500 = 7,500 gallons and sodium chloride is 700 gallons ( 7 % of initial solution of 10,000 gallons ) then sodium chloride is 700 / 7,500 * 100 = ~ 9.33 % of the remaining solution of 7,500 gallons . answer : c ."
Answer: c
Problem: the speed of a boat in still water is 18 kmph . what is the speed of the stream if the boat can cover 48 km downstream or 32 km upstream in the same time ?
Options: a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "x = the speed of the stream ( 18 + x ) / ( 18 - x ) = 2 / 1 18 + x = 36 - 2 x 3 x = 18 x = 6 km / hour if the speed of the stream is 6 km / hour , then the ' downstream ' speed of the boat is 18 + 6 = 24 km / hour and the ' upstream ' speed of the boat is 18 - 6 = 12 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 24 = 48 km downstream and 2 x 12 = 24 km / hour upstream . answer : c"
Answer: c
Problem: a train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train ?
Options: a ) 322 , b ) 324 , c ) 326 , d ) 328 , e ) 330
Rationale: "length = speed * time speed = l / t s = 2000 / 25 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 324 kmph answer : b"
Answer: b
Problem: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 32 % of the original number . what percent of the red candies remain ?
Options: a ) 27.5 % , b ) 33.3 % , c ) 35.5 % , d ) 42.5 % , e ) 47.5 %
Rationale: "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.6 x red + yellow = 0.85 x red = 0.425 x , since red = yellow . the answer is d ."
Answer: d
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 61 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.65 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 61 ) = 1173 kgs actual average weight is 1177 / 20 = 58.65 kgs b"
Answer: b
Problem: n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n
Options: a ) 11
b ) 12
c ) 13
d ) 14
e ) 15
Rationale: each of 2 present in the party = > no . of pairs possible = nc 2 possible adjacent pairs = n total required combinations = nc 2 - n time taken by each combination to sing a song = 2 min total time taken = 2 ( nc 2 - n ) = 28 on solving the above equation , we get n = 14 answer : d
Answer: d
Problem: in the floor of a particular kitchen owned by an abstract artist , each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left . if there are 9 rows in all and a total of 405 tiles in the floor , how many tiles does the leftmost row contain ?
Options: a ) 53 , b ) 56 , c ) 60 , d ) 64 , e ) 68
Rationale: this question can be solved in a variety of ways : with algebra , by testing the answers and by using a great number property shortcut involving consecutive integers . we ' re given a few facts to work with : 1 ) there are 9 rows of tiles . 2 ) when going from ' left to right ' , each row contains two fewer tiles than the one next to it . 3 ) there are a total of 405 tiles we ' re asked how many tiles the left - most most row holds ( meaning the one with the most tiles ) . to start , 405 is divisible by 9 , so we can figure out the average number of tiles per row . that is 405 / 9 = 45 . since we ' re dealing with a set of 9 consecutive integers that differ by 2 each , we know that the ' 5 th row ' will have 45 tiles ( the average ) . then we just have to ' add 2 s ' until we get to the first row . . . 45 + 2 + 2 + 2 + 2 = 53 . final answer : a
Answer: a
Problem: each of 3 charities in novel grove estates has 8 persons serving on its board of directors . if exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors , then how many distinct persons serve on one or more boards of directors ? a . b . c . d . e .
Options: a ) 8 , b ) 13 , c ) 16 , d ) 24 , e ) 27
Rationale: each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b
Answer: b
Problem: a mixture of 20 kg of spirit and water contains 10 % water . how much water must be added to this mixture to raise the percentage of water to 25 %
Options: a ) 4 kg , b ) 5 kg , c ) 8 kg , d ) 30 kg , e ) 35 kg
Rationale: exp . water in the given mixture = 10 * 20 / 100 = 2 kg , and spirit = ( 20 - 2 ) = 18 kg let x kg of water added , then , x + 2 / 20 + x * 100 = = 25 4 x + 8 = 20 + x , or x = 4 kg answer : a
Answer: a
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is :
Options: a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) none
Rationale: "explanation : amount = rs . [ 7500 ( 1 + 4 / 100 ) 2 ] = rs . [ 7500 × 26 / 25 × 26 / 25 ] = rs . 8112 . correct option : d"
Answer: d
Problem: a and b invests rs . 10000 each , a investing for 4 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4000 , find their shares ?
Options: a ) 1000,3500 , b ) 1000,3000 , c ) 1000,2000 , d ) 1000,5000 , e ) 1000,2500
Rationale: the ratio of their profits a : b = 4 : 12 = 1 : 3 share of a in the total profit = 1 / 4 * 4000 = rs . 1000 share of b in the total profit = 3 / 4 * 4000 = rs . 3000 answer : b
Answer: b
Problem: for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 3 , c ) 6 , d ) 18 , e ) 60
Rationale: "mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 2 + 18 ) / 2 ] * 9 = 90 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 90 ) / ( 30 ) = 3 answer : b"
Answer: b
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 160 , b ) 320 , c ) 480 , d ) 600 , e ) 720
Rationale: there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 30 * 16 = 480 . the answer is c .
Answer: c
Problem: the difference between simple and compound interest on rs . 1600 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8 , b ) 3 , c ) 9 , d ) 4 , e ) 2
Rationale: "s . i . = ( 1600 * 10 * 1 ) / 100 = rs . 160 c . i . = [ 1600 * ( 1 + 5 / 100 ) 2 - 1600 ] = rs . 164 difference = ( 164 - 160 ) = rs . 4 . answer : d"
Answer: d
Problem: a person travels equal distances with speeds of 4 km / hr , 5 km / hr and 6 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 2 km , b ) 4 km , c ) 7 km , d ) 9 km , e ) 5 km
Rationale: "let the total distance be 3 x km . then , x / 4 + x / 5 + x / 6 = 47 / 60 37 x / 60 = 47 / 60 = > x = 1.27 total distance = 3 * 1.27 = 3.81 km . answer : b"
Answer: b
Problem: one hour after yolanda started walking from x to y , a distance of 10 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 4
Rationale: "when b started walking y already has covered 3 miles out of 10 , hence the distance at that time between them was 10 - 3 = 7 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 7 / 7 = 1 hours . in 6 hours b walked 1 * 4 = 4 miles . answer : e ."
Answer: e
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 7 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 7 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 7 × 2 / 100 = 700 his overall gain in 2 years = rs . 700 - rs . 400 = rs . 300 his overall gain in 1 year = 300 / 2 = rs . 150 answer : option b"
Answer: b
Problem: one fourth of one third of two fifth of a number is 14 . what will be 40 % of that number
Options: a ) 168 , b ) 150 , c ) 180 , d ) 200 , e ) 250
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 14 then x = 14 * 30 = 420 40 % of 420 = 168 answer : option a"
Answer: a
Problem: a vantakes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 kmph , b ) 61 kmph , c ) 62 kmph , d ) 64 kmph , e ) 66 kmph
Rationale: time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph a )
Answer: a
Problem: a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.30 until we get a multiple of $ 0.70 . $ 7.30 , $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 3 apples . the answer is b ."
Answer: b
Problem: a can do a piece of work in 4 days . b can do it in 9 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 36 / 5 days , c ) 67 days , d ) 17 / 7 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 9 = 5 / 36 = > 36 / 5 days answer : b"
Answer: b
Problem: a number when divided by a certain divisor left remainder 255 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 398 , d ) 456 , e ) 460
Rationale: easy solution : n = dq 1 + 255 2 n = 2 dq 1 + 51 0 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 398 d * some integer = 398 checking all options only ( c ) syncs with it . answer c
Answer: c
Problem: if 30 % of a number is 12.6 , find the number ?
Options: a ) 42 , b ) 40 , c ) 26 , d ) 36 , e ) 66
Rationale: "a 40"
Answer: a
Problem: 5 + 3
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: a
Answer: a
Problem: find the number , difference between number and its 3 / 5 is 60 .
Options: a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 60 , = > ( 2 / 5 ) x = 60 = > 2 x = 60 * 5 , = > x = 150 answer : option a"
Answer: a
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 16 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
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 16 days whole work will be done by y in 16 * 5 / 4 = 20 days answer is e"
Answer: e
Problem: a positive number x is multiplied by 3 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 4 / 3 because x is positive , x = 4 / 3 . the answer is c ."
Answer: c
Problem: 10 men do a work in 10 days . how many men are needed to finish the work in 4 days ?
Options: a ) 25 , b ) 20 , c ) 30 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 4 days = 10 * 10 / 4 = 25 answer is a"
Answer: a
Problem: a trader sells 80 meters of cloth for rs . 6900 at the profit of rs . 20 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 75 , c ) 90 , d ) 78 , e ) 66
Rationale: "sp of 1 m of cloth = 6900 / 80 = rs . 86 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 86 - rs . 20 = rs . 66 . answer : e"
Answer: e
Problem: during a certain two - week period , 80 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 15 a , c ) 20 a , d ) 1 / 25 a , e ) 30 a
Rationale: "movies : 80 % comedies . 20 % remaining genre . now in this 20 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 4 x . total 5 x . 5 x = 20 ; x = 4 action movies : 4 % drama movies : 16 % we can say that out of 100 z , : comedies : 80 z action : 4 z drama : 16 z now action movies werea this means : a = 4 z . z = ( a / 4 ) comedies : 80 z = 80 * ( a / 4 ) 20 a c is the answer ."
Answer: c
Problem: ( 100 x 60 ) + ( 138 x 400 ) = ? x 60
Options: a ) 880 , b ) 550 , c ) 1100 , d ) 1020 , e ) 600
Rationale: "explanation : ? = ( 100 x 60 ) + ( 138 x 400 ) / 60 = 6000 + 55200 / 60 = 1020 answer : option d"
Answer: d
Problem: the speed of the boat in still water in 12 kmph . it can travel downstream through 42 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4.2 hours , d ) 5 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 42 / 3 = 14 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 14 / 2 = 10 km / hr so time taken in upstream = 42 / 10 = 4.2 hrs answer : c"
Answer: c
Problem: tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bearsa number which is a multiple of 3 ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 ] p ( e ) = n ( e ) / n ( s ) = 6 / 20 = 3 / 10 c"
Answer: c
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 4 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 8 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 4 ) = l cx = 4 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 4 l = 1 / 8 answer will be d"
Answer: d
Problem: harry started a 6 - mile hike with a full 7 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 5 miles of the hike ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 5 , e ) 4 / 5
Rationale: "a . no of cups leaked during the trip = 2 cups . no of cups harry drank = 4 cups . no of cups harry drank during the first 5 miles = 4 . drink / mile = 4 / 5 answer : e"
Answer: e
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 60 kg . what is the correct weight ?
Options: a ) 58.6 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: actual total weight is ( 20 x 58.4 - 56 + 60 ) = 1172 kgs actual average weight is 1172 / 20 = 58.6 kgs a
Answer: a
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 4,700 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 14.0 , b ) 13.0 , c ) 12.0 , d ) 11.0 , e ) 10.0
Rationale: "solution : h stopped 700 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . c"
Answer: c
Problem: p and q are the only two applicants qualified for a short - term research project that pays 420 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 3 , b ) $ 5 , c ) $ 7 , d ) $ 9 , e ) $ 11
Rationale: let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 420 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 420 / 30 = $ 14 p ' s hourly wage is 420 / ( t - 10 ) = $ 21 which is $ 7 per hour more . the answer is c .
Answer: c
Problem: log ( a ( a ( a ) ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 here base is a .
Options: a ) 0 , b ) 21 / 64 , c ) 1 , d ) 22 / 63 , e ) 23 / 65
Rationale: log ( a ( a ( a ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 1 + 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 16 ) ^ 1 / 4 = > log ( a ^ 1 + 5 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 64 ) = > 21 / 64 log ( a ) = > 21 / 64 answer : b
Answer: b
Problem: rahul is 30 years older than his daughter mary . in 20 years rahul will be twice as old as mary . what is mary current age .
Options: a ) 12 , b ) 14 , c ) 10 , d ) 16 , e ) 18
Rationale: now : mary = x , rahul = x + 30 in 20 years mary = x + 20 , rahul = x + 30 + 20 or 2 ( x + 20 ) x + 30 + 20 = 2 ( x + 20 ) x + 50 = 2 x + 40 50 - 40 = 2 x - x x = 10 mary is 10 years old answer : c
Answer: c
Problem: a rectangular field has to be fenced on three sides leaving a side of 2020 feet uncovered . if the area of the field is 680680 sq . feet , how many feet of fencing will be required ?
Options: a ) 95 , b ) 92 , c ) 88 , d ) 82 , e ) 80
Rationale: "explanation : area of the field = 680 sq . feet . length of the adjacent sides are 20 feet and 680 / 20 = 34 feet . required length of the fencing = 20 + 34 + 34 = 88 feet answer : option c"
Answer: c
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 13 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 320 , b ) 300 , c ) 310 , d ) 315 , e ) 330
Rationale: "( 3500 * 3 * 3 ) / 100 = > 315 answer : d"
Answer: d
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11 - sided polygon ) ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 11
Rationale: "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 8 = 1 / 4 . the answer is c ."
Answer: c
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 6 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 41 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.94 * 150 x = 141 x hence total profit = 41 % option e"
Answer: e
Problem: the perimeter of a semi circle is 144 cm then the radius is ?
Options: a ) 22
b ) 28
c ) 99
d ) 77
e ) 16
Rationale: 36 / 7 r = 144 = > r = 28 answer : b
Answer: b
Problem: find the area of the square , one of whose diagonals is 3.8 m long ?
Options: a ) 7.22 m ^ 2
b ) 3.86 m ^ 2
c ) 8.96 m ^ 2
d ) 2.68 m ^ 2
e ) 7.89 m ^ 2
Rationale: area of the square = 1 / 2 ( diagonal ) ^ 2 = ( 1 / 2 * 3.8 * 3.8 ) m ^ 2 = 7.22 m ^ 2 answer ( a )
Answer: a