regisss/math_qa huggingface dataset:
Problem: a man rows his boat 85 km downstream and 25 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 12 , c ) 5 , d ) 8 , e ) 9
Rationale: "speed downstream = d / t = 85 / ( 2 1 / 2 ) = 34 kmph speed upstream = d / t = 25 / ( 2 1 / 2 ) = 10 kmph the speed of the stream = ( 34 - 10 ) / 2 = 12 kmph answer : b"
Answer: b
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 4 of the mixture is sand , 2 / 5 of the mixture is water , and the remaining 14 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 9 , b ) 14 , c ) 28 , d ) 40 , e ) 60
Rationale: let the total weight be x . sand content = ( 1 / 4 ) x water content = ( 2 / 5 ) x gravel = x - ( 1 / 4 ) x - ( 2 / 5 ) x = ( 7 / 20 ) x = 14 x = 40 then answer will be d = 40
Answer: d
Problem: the length of a rectangle is 2 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 50 square inches
b ) 75 square inches
c ) 68 square inches
d ) 89 square inches
e ) 92 square inches
Rationale: if the width is 5 in and the length is 2 times the width , then the length is 2 * 5 = 10 in the area is given by 5 * 10 = 50 square inches correct answer a
Answer: a
Problem: if a is the smallest positive integer such that 5880 multiplied by a is the square of an integer , then ya must be
Options: a ) 30 , b ) 15 , c ) 12 , d ) 23 , e ) 17
Rationale: 5880 = 2 * 2 * 7 * 7 * 5 * 6 , so we need one 5 and one 6 to make it a square of a number . so 5 * 6 = 30 ans : a
Answer: a
Problem: working simultaneously and independently at an identical constant rate , 6 machines of a certain type can produce a total of x units of product p in 10 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 5 x units of product p in 6 days ?
Options: a ) 50 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "6 machines do x units in 10 days we have x / 10 = > rate of the 6 machines we know that we need to have 5 x units in 6 days therefore , we need to get to 5 x / 6 rate of the machines . rate of one machine is x / 10 * 1 / 6 = x / 60 . now , we need to know how many machines need to work simultaneously , to get 5 x done in 6 days . 5 x / 6 work needs to be done by machines that work at x / 60 rate . let ' s assign a constant y for the number of machines : ( x / 60 ) * y = 5 x / 6 y = 5 x / 6 * 60 / x cancel 6 with 60 , and x with x and get - > 50 . answer choice a"
Answer: a
Problem: if the difference between the compound interest & simple interest of a certain sum of money is rs . 72 at 12 % p . a . per two year . find the sum ( in rs . ) ?
Options: a ) 200 / 15 , b ) 200 / 17 , c ) 220 / 17 , d ) 240 / 17 , e ) 260 / 17
Rationale: 200 / 17 c . i = a - p a = p ( 1 + 12 / 100 ) ^ 2 s . i = p * 2 * 12 / 100 c . i - s . i = 72 given substitute and solve p = 200 / 17 answer : b
Answer: b
Problem: each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 3125 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
Options: a ) 1287 , b ) 1285 , c ) 1283 , d ) 1280 , e ) 1281
Rationale: "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , c , e the answer to be d again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 1280 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 1280 = 3125 hence , correct answer = d"
Answer: d
Problem: if n is a natural number , then 6 n ^ 2 + 6 n is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) 18 only , e ) 20 only
Rationale: "6 n ^ 2 + 6 n = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer is b"
Answer: b
Problem: how many seconds will a train 100 meters long take to cross a bridge 120 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 27 sec , c ) 25 sec , d ) 24 sec , e ) 11 sec
Rationale: "explanation : d = 100 + 120 = 220 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 22 sec answer : option a"
Answer: a
Problem: a certain fruit stand sold apples for $ 0.70 each and bananas for $ 0.60 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let ' s start with 1 apple for $ 0.70 . let ' s subtract $ 0.70 from $ 6.30 until we get a multiple of $ 0.60 . $ 6.30 , $ 5.60 , $ 4.90 , $ 4.20 = 7 * $ 0.60 the customer purchased 7 bananas and 3 apples . the answer is c ."
Answer: c
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is :
Options: a ) 8.5 km / hr , b ) 10 km / hr , c ) 12.5 km / hr , d ) 9 km / hr , e ) none of these
Rationale: "explanation : man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 15 - 2.5 = 12.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km / hr answer is b"
Answer: b
Problem: a shopkeeper sold an article at $ 1200 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 1000 , b ) $ 1020 , c ) $ 1040 , d ) $ 1060 , e ) $ 1080
Rationale: "let x be the cost price . 1.2 x = 1200 x = 1200 / 1.2 = 1000 the answer is a ."
Answer: a
Problem: at company x , senior sales representatives visit the home office once every 20 days , and junior sales representatives visit the home office once every 15 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 60 - day period , senior representatives visit the home office 3 times while junior representatives visit 4 times , thus 33 % more . the answer is c ."
Answer: c
Problem: daniel went to a shop and bought things worth rs . 25 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 5 % , then what was the cost of the tax free items ?
Options: a ) a ) 18.7 , b ) b ) 20 , c ) c ) 21.3 , d ) d ) 21.5 , e ) e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 5 % ∴ ( 25 − 30 / 100 − x ) 5 / 100 = 30 / 100 ⇒ 5 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 6 ⇒ x = 25 − 0.3 − 6 = 18.7 a"
Answer: a
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 190 kilometers ?
Options: a ) 3.5 gallons , b ) 2.7 gallons , c ) 5.7 gallons , d ) 4.75 gallons , e ) 7.5 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 190 kilometers ? 190 ã · 40 = 4.75 ã — 1 gallon = 4.75 gallons correct answer is d ) 4.75 gallons"
Answer: d
Problem: in the faculty of reverse - engineering , 300 second year students study numeric methods , 600 second year students study automatic control of airborne vehicles and 200 second year students study them both . how many students are there in the faculty if the second year students are approximately 70 % of the total ?
Options: a ) 750 , b ) 800 , c ) 900 , d ) 950 , e ) 1000
Rationale: "total number of students studying both are 300 + 600 - 200 = 700 ( subtracting the 200 since they were included in the both the other numbers already ) . so 70 % of total is 700 , so 100 % is 1000 answer is e"
Answer: e
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.8 hr , b ) 2.4 hr , c ) 3.6 hr , d ) 1.8 hr , e ) 2.0 hr
Rationale: explanation : part filled by one tap in 1 hour = 1 / 4 part emptied by second tap 1 hour = 1 / 8 net part filled by both these taps in 1 hour = 1 / 3 - 1 / 8 = 5 / 24 i . e , the cistern gets filled in 24 / 5 hours = 4.8 hrs answer : option a
Answer: a
Problem: in a graduating class of 233 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 114 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 233 = 30 greatest - smallest is 144 - 30 = 114 so answer must be a . 114"
Answer: a
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 48 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 296 , e ) 302
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 48 cm . : 48 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 47 / ( 3.81 ) = 302 answer will be e ."
Answer: e
Problem: if | 4 x + 6 | = 42 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 3 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 42 or 4 x + 6 = - 42 = > x = 9 or x = - 12 sum of both the values will be - 12 + 9 = - 3 answer is b"
Answer: b
Problem: a pipe can empty 1 / 4 th of a cistern in 12 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 3 / 7 , c ) 4 / 9 , d ) 1 / 6 , e ) 4 / 7
Rationale: "1 / 4 - - - - 12 ? - - - - - 8 = = > 1 / 6 d"
Answer: d
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 16 mat - weavers in 16 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 64
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 16 : : 4 : x days 4 : 16 4 * 4 * x = 16 * 16 * 4 x = ( 16 * 16 * 4 ) / ( 4 x 4 ) x = 64 . answer is e ."
Answer: e
Problem: suppose 8 monkeys take 8 minutes to eat 8 banana ' s . how many minutes would it take 3 monkeys to eat 3 banana ' s ?
Options: a ) 5 min , b ) 6 min , c ) 7 min , d ) 8 min , e ) 9 min
Rationale: there are equal no . of monkeys and equal no . of bananas and they take equal time and the time is 8 mint to eat a banana so each monkey take 8 mints to eat a banana ' s so 3 monkeys will take 8 mints to eat 3 banana ' s . answer : d
Answer: d
Problem: if x + | x | + y = 4 and x + | y | - y = 3 what is x + y = ?
Options: a ) 1 , b ) - 1 , c ) 3 , d ) 5 , e ) 13
Rationale: "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 3 hence answer should be c"
Answer: c
Problem: there were 35 students in a hostel . if the number of students increases by 7 , the expenses of the mess increase by rs . 42 per day while the average expenditure per head diminishes by re 1 . find the original expenditure of the mess .
Options: a ) rs . 480 , b ) rs . 520 , c ) rs . 420 , d ) rs . 460 , e ) none of these
Rationale: let d be the average daily expenditure original expenditure = 35 × d new expenditure = 35 × d + 42 new average expenditure will be : ( 35 × d + 42 ) / 42 = d - 1 on solving , we get d = 12 therefore original expenditure = 35 × 12 = 420 answer : c
Answer: c
Problem: two numbers are in the ratio of 1 : 2 . if 8 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 8 ) / ( y + 8 ) = 3 / 5 = > x = 16 and y = 32 answer : d"
Answer: d
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 200 papers and 20 % discount after first 1000 papers , how much will it cost to buy 2500 sheets of xerox paper ?
Options: a ) $ 125 , b ) $ 106 , c ) $ 135 , d ) $ 90 , e ) $ 100
Rationale: "30 sec approach - solve it using approximation 2500 sheet at full price , 5 cent = 125 2500 sheet at max discount price , 4 cent = 100 your ans got to be between these two . ans b it is ."
Answer: b
Problem: a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 3 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 1 / 5 days , e ) 9 days
Rationale: "work done by a in 3 days = 3 / 10 remaining work = 7 / 10 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 7 / 10 * 6 / 1 = 21 / 5 = 4 1 / 5 days . answer : d"
Answer: d
Problem: how many integers between 265,205 and 758,805 have tens digit 1 and units digit 3 ?
Options: a ) 4,629 , b ) 4,639 , c ) 3,946 , d ) 4,926 , e ) 4,936
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 265,205 and 758,805 is 758,805 - 265,205 = 493,600 - one number per each hundred gives 133,900 / 100 = 4,936 numbers . answer : e ."
Answer: e
Problem: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 60 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) a ) 12.5 % , b ) b ) 13 % , c ) c ) 13.15 % , d ) d ) 14 % , e ) e ) 15 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.6 x 1.25 = 0.755 decrease in price = ( 0.125 / 1 ) × 100 = 12.5 % a )"
Answer: a
Problem: a batsman scored 160 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 64 % , b ) 66 % , c ) 60 % , d ) 68 % , e ) 70 %
Rationale: "explanation : number of runs made by running = 160 - ( 3 x 4 + 8 x 6 ) = 160 - ( 60 ) = 100 now , we need to calculate 100 is what percent of 160 . = > 100 / 160 * 100 = 68 option d"
Answer: d
Problem: a train covers a distance of 6 km in 10 min . if it takes 12 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 220 m , e ) 280 m
Rationale: "speed = ( 6 / 10 * 60 ) km / hr = ( 36 * 5 / 18 ) m / sec = 10 m / sec . length of the train = 10 * 12 = 120 m . answer : a"
Answer: a
Problem: 60 % of the employees of a company are men . 60 % of the men in the company speak french and 50 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 96 % , d ) 90 % , e ) 65 %
Rationale: "no of employees = 100 ( say ) men = 60 women = 40 men speaking french = 0.6 * 60 = 36 employees speaking french = 0.5 * 100 = 50 therefore women speaking french = 50 - 36 = 14 and women not speaking french = 40 - 14 = 26 % of women not speaking french = 26 / 40 * 100 = 65 % answer e"
Answer: e
Problem: an error 2 % in excess is made while measuring the side ofa square . the % of error in the calculated area of the square is ?
Options: a ) 4 %
b ) 4.04 %
c ) 4.23 %
d ) 4.56 %
e ) 5 %
Rationale: 100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b
Answer: b
Problem: in a group of donkeys and pigs , the numbers of legs are 16 more than twice the number of heads . the number of donkeys is
Options: a ) 6 , b ) 8 , c ) 11 , d ) 12 , e ) 13
Rationale: let the number of donkeys be x and the number of pigs be y . then , 4 x + 2 y = 2 ( x + y ) = 16 or 2 x + ( 2 x + 2 y ) = ( 2 x + 2 y ) + 16 or 2 x = 16 or x = 8 . answer : b
Answer: b
Problem: a furniture dealer purchased a desk for $ 240 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 160 , d ) $ 90 , e ) $ 100
Rationale: "purchase price = 240 selling price = x 240 + 0.4 * x = x 0.6 * x = 240 x = 400 profit = 400 - 240 = 160 answer : c"
Answer: c
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 12375 . what is the share of c ?
Options: a ) rs . 2250 , b ) rs . 3375 , c ) rs . 6750 , d ) rs . 5625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 12375 ] = rs . 3375 answer : option b"
Answer: b
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 60 % at 20 % profit . find his % profit on total .
Options: a ) 24 % , b ) 20 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 40 x 20 % + 60 x 20 % = 20 this profit will remain same for any total quantity unless the % of products remains the same . hence ' b ' is the answer"
Answer: b
Problem: how many positive integers less than 30 have no common prime factor with 30 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "30 = 2 * 3 * 5 . so , the number must be less than 30 and not have primes 2 , 3 , or 5 . this means that the number could be : 1 , 7 , 11 , 13 , 17 , 19 , 23 , or 29 . total of 8 numbers . answer : d ."
Answer: d
Problem: a 300 m long train crosses a platform in 38 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 350 , c ) 889 , d ) 276 , e ) 333
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 38 = 50 / 3 3 x + 900 = 1900 = > x = 333 m . answer : e"
Answer: e
Problem: two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 36 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 18.4 sec , b ) 77 sec , c ) 76 sec , d ) 20 sec , e ) 66 sec
Rationale: "relative speed = ( 42 + 36 ) * 5 / 18 = 21.7 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 21.7 = 18.4 sec . answer : a"
Answer: a
Problem: tough and tricky questions : mixture problems . a drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke . what is the ratio of rum to coke in the resulting mixture ?
Options: a ) 2 : 5 , b ) 5 : 15 , c ) 3 : 5 , d ) 4 : 7 , e ) 14 : 5
Rationale: answer = b ) 5 : 15 . . . . . . . . . . . . . . . . . . . . . . . . rum . . . . . . . . . . . . . . . . . . . . . coke . . . . . . . . . . . . . . . . . total first drink . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . 6 ( ratio 1 : 2 ) second drink . . . . . . . 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . . . . 32 ( ratio 1 : 3 ) total . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 . . . . . . . . . . . . . . . . . . . . 38 ratio = 10 : 30 = 5 : 15 b
Answer: b
Problem: excluding stoppages , the speed of a bus is 70 km / hr and including stoppages , it is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 118 min , b ) 10 min , c ) 18 min , d ) 16 min , e ) 25 min
Rationale: "due to stoppages , it covers 30 km less . time taken to cover 30 km = 30 / 70 * 60 = 25 min . answer : e"
Answer: e
Problem: 49 x 49 x 49 x 49 = 7 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) 20
Rationale: "solution 49 * 49 * 49 * 49 = ( 72 * 72 * 72 * 72 ) = 7 ( 2 + 2 + 2 + 2 ) = 78 so , the correct answer is 8 answer c"
Answer: c
Problem: calculate 12351 ÷ ? = 69
Options: a ) 179 , b ) 119 , c ) 129 , d ) 173 , e ) 156
Rationale: "answer let 12351 ÷ ? = 69 then x = 12351 / 69 = 179 . option : a"
Answer: a
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is ?
Options: a ) 153600 , b ) 153629 , c ) 151299 , d ) 153129 , e ) 152109
Rationale: "let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m ^ 2 = 153600 m ^ 2 . answer : a"
Answer: a
Problem: if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursa day , how much coal will be required for 8 engines , each running 13 hours a day , it is being given that 3 engines of former type consume as much as 4 engines of latter type ?
Options: a ) 23 , b ) 25 , c ) 26 , d ) 28 , e ) 30
Rationale: explanation : let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal consumed ( direct proportion ) more working hours , more coal consumed ( direct proportion ) less rate of consumption , less coal consumed ( direct proportion ) number of engines 9 : 8 working hours 8 : 13 } : : 24 : x rate of consumption ( 1 / 3 ) : ( 1 / 4 ) ( 9 * 8 * ( 1 / 3 ) * x ) = ( 8 * 13 * ( 1 / 4 ) * 24 ) < = > 24 x = 624 < = > x = 26 . answer : c
Answer: c
Problem: it takes 40 identical printing presses 15 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 21 , e ) 24
Rationale: 40 printing presses can do 1 / 15 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 15 = 1 / 20 of the job each hour . the answer is c .
Answer: c
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 400 sq . ft , how many feet of fencing will be required ?
Options: a ) 60 feet , b ) 50 feet , c ) 40 feet , d ) 30 feet , e ) 5 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 400 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 20 = 60 feet answer : option a"
Answer: a
Problem: one night 20 percent of the female officers on a police force were on duty . if 100 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 250 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 100 number of female officers on duty on that night = 100 / 2 = 50 ( 20 / 100 ) * f = 50 = > f = 250 answer c"
Answer: c
Problem: if a certain number of people can dig earth 100 m deep , 25 m long , and 30 m broad in 12 days , then find the number of days the same number of people will require to dig earth 75 m deep , 20 m long and 50 m broad .
Options: a ) 12 , b ) 18 , c ) 6 , d ) 1 , e ) 17
Rationale: explanation : more number of days means – more length , more depth and more width . hence , it ’ s a direct proportion . ( 100 * 25 * 30 ) : ( 75 * 20 * 50 ) : : 12 : x 75000 : 75000 : : 12 : x x = 12 answer a
Answer: a
Problem: a mixture of 125 gallons of wine and water contains 20 % water . how much water must be added to the mixture in order to increase the percentage of water to 25 % of the new mixture ?
Options: a ) 10 glas , b ) 8.5 gals , c ) 8 gals , d ) 6.66 gals , e ) 8.33 gals
Rationale: "in 125 gallons of the solution there are 0.2 ∗ 125 = 250 gallons of water . we want to add ww gallons of water to 125 gallons of solution so that 25 + w gallons of water to be 25 % of new solution : 25 + w = 0.25 ( 125 + w ) - - > w = 25 / 3 ≈ 8.33 answer : e ."
Answer: e
Problem: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 61.5 . when one student dropped the class , the average of the remaining scores increased to 64.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 24 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 61.50 = 984 total score of 15 students is 15 * 64 = 960 so , the score of the person who left is 24 ( 984 - 960 ) answer will be ( b )"
Answer: b
Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 4 : 40 : 90 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 200 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 1300
b ) 1500
c ) 1600
d ) 1700
e ) 1800
Rationale: soap : alcohol initial ratio soap : alcohol : water - - > 4 : 40 : 90 initial soap : alcohol = 4 / 40 = 4 : 40 after doubled soap : alcohol = 2 * 4 / 40 = 8 : 40 initial soap : water = 4 / 90 = 4 : 90 after halved soap : water : 1 / 2 * 4 / 90 = 2 / 90 = 2 : 90 after soap : alcohol : water - - > 8 : 40 : 360 - - > 1 : 5 : 45 given alcohol 200 cubic centimeter . ratio is 40 : 200 : 1800 ( 1 : 5 : 45 ) for 200 cubic centimeter of alcohol - - - 1800 cubic cm water is required . answer - e
Answer: e
Problem: there is enough provisions for 2400 women in an army camp for 100 days . if there were 1200 men less , how long will the provision last ?
Options: a ) 170 , b ) 180 , c ) 190 , d ) 200 , e ) 210
Rationale: "we have , m 1 d 1 = m 2 d 2 2400 * 100 = 1200 * d 2 d 2 = 2400 * 100 / 1200 = 200 days . answer : d"
Answer: d
Problem: a thief steals a car at 2.30 pm and drives it at 60 kmph . the theft is discovered at 3 pm and the owner sets off in another car at 75 kmph when will he overtake the thief
Options: a ) 3.3 pm , b ) 5.5 pm , c ) 4.9 pm , d ) 5 pm , e ) 5.2 pm
Rationale: let the thief is overtaken x hrs after 2.30 pm distance covered by the thief in x hrs = distance covered by the owner in x - 1 / 2 hr 60 x = 75 ( x - ½ ) x = 5 / 2 hr thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm answer is d .
Answer: d
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 100 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 1 hour 40 minutes , e ) 2 hours 40 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 100 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 100 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 100 + 60 ) = 160 minutes on the road . e . 2 hours 40 minutes"
Answer: e
Problem: if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 60 km , d ) 40 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 15 15 x = 10 x + 200 5 x = 200 x = 40 km . answer : d"
Answer: d
Problem: nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1.5 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "d its is . let price = x ( x - 1.5 ) 8 = 6 x x = 6 hence total money = 6 * 6 = 36"
Answer: d
Problem: there are 40 doors marked with numbers 1 to 40 . there are 40 individuals marked 1 to 40 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , and 40 . if every individual in the group gets one turn , then how many doors are open at the end ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 for a total of 6 doors . the answer is d .
Answer: d
Problem: for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 7.2 – 7.2 * ?
Options: a ) 1.2 , b ) 0.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: since y * is defined as the greatest positive even integer less than or equal to y , then 7.2 * = 6 ( the greatest positive even integer less than or equal to 7.2 is 6 ) . hence , 7.2 – 7.2 * = 7.2 - 6 = 1.2 answer : a .
Answer: a
Problem: p and q started a business investing rs 85000 and rs 10000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 17 : 5 , b ) 17 : 3 , c ) 17 : 6 , d ) 17 : 2 , e ) 17 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 85000 : 10000 = 85 : 10 = 17 : 2 option d"
Answer: d
Problem: a bag contains 5 white marbles and 5 black marbles . if each of 5 girls and 5 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 126 , b ) 1 / 120 , c ) 1 / 24 , d ) 4 / 25 , e ) 1 / 2
Rationale: "consider a case when all girls select black marbles . . . so girl 1 will chose 1 black marble out of 10 . . and black marble will be chosen from 5 black marbles girl 1 will have a probability of picking black marble 5 / 10 girl 2 will have to pick a black marble out of 4 and total remaining no . of marbles 9 = 4 / 9 so we have probability of all girls selecting black marbles as 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 * 1 / 6 = 1 / 252 since girls can also select white marbles so we will have 2 cases so probability of girls selecting all same colour marbles is 2 * 1 / 252 or 1 / 126 ans is a"
Answer: a
Problem: if the radius of a circle that centers at the origin is 5 , how many m points on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : m = c"
Answer: c
Problem: the angle between the minute hand and the hour hand of a clock when the time is 8.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 75 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 8 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 8 − 30 / 5 ) + 30 / 2 = 30 ( 8 − 6 ) + 15 = 30 × 2 + 15 = 75 ° answer is d ."
Answer: d
Problem: ravi and sunil are partners in a business . ravi invests rs . 10,000 for 8 months and sunil invested rs . 12000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 80000 : 120000 = 2 : 3 answer : b"
Answer: b
Problem: dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 3 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "dan can complete 1 / 15 of the job per hour . in 3 hours , dan completes 3 ( 1 / 15 ) = 1 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 4 / 5 / 1 / 10 = 8 hours . the answer is d ."
Answer: d
Problem: alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,800 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,100 , c ) 1,900 , d ) 2,550 , e ) 3,400
Rationale: assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 3800 therefore x = 2600 / 4 = 650 price of 28 inch + 30 inch = 850 + 1050 = 1900 option c
Answer: c
Problem: 1 , 3,5 , 7,9 , . 50 find term of sequnce
Options: a ) 1234 , b ) 1367 , c ) 1789 , d ) 1568 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Problem: how many multiples of 3 are there between 81 and 358 ?
Options: a ) 94 , b ) 95 , c ) 93 , d ) 97 , e ) 98
Rationale: "3 * 27 = 81 3 * 119 = 357 total multiples of 3 = ( 119 - 27 ) + 1 = 93 answer is c ."
Answer: c
Problem: a trader bought a car at 10 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 110 , c ) 112 , d ) 126 , e ) 115
Rationale: "original price = 100 cp = 80 s = 80 * ( 140 / 100 ) = 126 100 - 126 = 26 % answer : d"
Answer: d
Problem: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 30 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 16.66 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 30 = 62 - - > c = 5 / 9 * 30 = 16.66 . increase = 16.66 degrees . answer : b ."
Answer: b
Problem: a train covers a distance of 18 km in 10 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 120 m , b ) 180 m , c ) 270 m , d ) 220 m , e ) 280 m
Rationale: "speed = ( 18 / 10 * 60 ) km / hr = ( 108 * 5 / 18 ) m / sec = 30 m / sec . length of the train = 30 * 9 = 270 m . answer : c"
Answer: c
Problem: the smallest value of n , for which n + 1 is not a prime number , is
Options: a ) 5 , b ) 6 , c ) 8 , d ) 3 , e ) 10
Rationale: "( 1 + 1 ) = 2 . ( 2 + 1 ) = 3 . ( 3 + 1 ) = 4 . ( 4 + 1 ) = 5 . which is not prime , n = 3 . answer : d"
Answer: d
Problem: a number divided by 24 leaves remainder 56 what is the remainder when same number divided by 7
Options: a ) 9 , b ) 7 , c ) 5 , d ) 3 , e ) 1
Rationale: "add 24 + 56 = 80 now 80 divided by 7 so we get 3 as reaminder answer : d"
Answer: d
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 42.5 % , e ) ca n ' t be calculated
Rationale: the owner buys 100 kg but actually gets 114 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 114 - 80 ) / 80 * 100 = ~ 42.5 % answer : d .
Answer: d
Problem: 9548 + 7314 = 3362 + ( ? )
Options: a ) 8300 , b ) 8400 , c ) 13500 , d ) 8700 , e ) 9000
Rationale: 9548 16862 = 3362 + x + 7314 x = 16862 - 3362 - - - - - = 13500 16862 - - - - - c )
Answer: c
Problem: john had a stock of 620 books in his bookshop . he sold 50 on monday , 82 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 54.84 % , b ) 36.5 % , c ) 46.5 % , d ) 56.5 % , e ) 66.5 %
Rationale: "let n be the total number of books sold . hence n = 50 + 82 + 64 + 78 + 135 = 280 let m be the books not sold m = 620 - n = 620 - 280 = 340 percentage books not sold / total number of books = 340 / 620 = 0.55 = 54.84 % correct answer a"
Answer: a
Problem: a sum of money is distributed among w , x , y , z in the proportion of 1 : 6 : 2 : 4 . if x gets $ 1500 more than y , what is the w ' s share ?
Options: a ) $ 1500 , b ) $ 150 , c ) $ 375 , d ) $ 200 , e ) $ 450
Rationale: let the shares of w , x , y , z are 1 a , 6 a , 2 a , 4 a 6 a - 2 a = 1500 4 a = $ 1500 , a = 375 w ' s share = 1 a = $ 375 answer is c
Answer: c
Problem: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are :
Options: a ) 500 , b ) 387 , c ) 298 , d ) 267 , e ) 191
Rationale: "explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark answer : a ) 500"
Answer: a
Problem: what is 15 percent of 58 ?
Options: a ) 6.9 , b ) 7.4 , c ) 8.7 , d ) 9.3 , e ) 10.4
Rationale: "( 15 / 100 ) * 58 = 8.7 the answer is c ."
Answer: c
Problem: if equation | x / 4 | + | y / 4 | = 2.5 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 50 , c ) 100 , d ) 400 , e ) 200
Rationale: the equation can be reduced to intercept form as | x / 10 | + | y / 10 | = 1 , so these are lines in four quadrants with x and y intercept as 10 , so it is a rhombus with diagonals of 20 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 20 * 20 = 200 . answer e .
Answer: e
Problem: if 60 honey bees make 60 grams of honey in 60 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 60
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 60 : : 60 : x honey 60 : 1 = > 1 x 60 x x = 60 x 1 x 60 = > x = 60 . answer : e"
Answer: e
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 7 - sided polygon ) ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 7
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 / 4 = 1 / 2 . the answer is a ."
Answer: a
Problem: find the remainder when 3 ^ 27 is divided by 5 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5
Rationale: "solution : 3 ^ 27 = ( ( 3 ^ 4 ) ^ 6 ) * ( 3 ^ 3 ) = ( 81 ^ 6 ) * 27 then unit digit of ( 81 ^ 6 ) is 1 so on multiplying with 27 , unit digit in the result will be 7 . now , 7 when divided by 5 gives 2 as remainder . answer b"
Answer: b
Problem: a is twice as good a work man as b and together they finish a piece of work in 16 days . the number of days taken by a alone to finish the work is :
Options: a ) 36 days , b ) 24 days , c ) 46 days , d ) 16 days , e ) 14 days
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 16 divide 1 / 14 in the ratio 2 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 14 x 2 / 3 ) = 1 / 24 hence , a alone can finish the work in 24 days . answer b"
Answer: b
Problem: a cube of edge 15 cm is imersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in waer level .
Options: a ) 11.25 cm .
b ) 12.25 cm
c ) 13.25 cm
d ) 14.25 cm
e ) none of these
Rationale: sol . increase in volume = volume of the cube = ( 15 * 15 * 15 ) cm ³ . ∴ rise in water level = [ volume / area ] = [ 15 * 15 * 15 / 20 * 15 ] cm = 11.25 cm . answer a
Answer: a
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 7 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.55 % , c ) 14.44 % , d ) 13.33 % , e ) 12.22 %
Rationale: "( 100 % + 7 % ) * ( 100 % - 19 % ) = 1.07 * . 81 = 0.8667 1 - 0.8667 = 13.33 % lost = - 13.33 % the answer is d the organization has lost 13.33 % of its total volunteers from fall to spring ."
Answer: d
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many e cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer e = 44 . d"
Answer: d
Problem: half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 150 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 7
Rationale: "there are total 150 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 75 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 150 = 25 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 75 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 150 = 75 + 25 - b + ( 75 - b - 1 ) b = 12 answer ( b )"
Answer: b
Problem: if 144 / 0.144 = 14.4 / x , then the value of x is :
Options: a ) 0.0414 , b ) 0.144 , c ) 0.0144 , d ) 0.414 , e ) none of them
Rationale: = 144 / 0.144 = 14.4 / x = 144 x 1000 / 144 = 14.4 / x = x = 14.4 / 1000 = 0.0144 answer is c .
Answer: c
Problem: ravi and kavi start a business by investing â ‚ ¹ 6000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .
Options: a ) 2 : 12 , b ) 5 : 12 , c ) 7 : 12 , d ) 1 : 12 , e ) 3 : 12
Rationale: "ratio of profit = ratio of investments = 6000 : 72000 = 1 : 12 answer : d"
Answer: d
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 40 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 40 = 60 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 60 / 100 ) * 100 = ( 0.6 ) * 100 = 60 % . e"
Answer: e
Problem: it takes joey the postman 1 hours to run a 7 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 8 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 8 , e ) 15
Rationale: "let his speed for one half of the journey be 7 miles an hour let the other half be x miles an hour now , avg speed = 8 mile an hour 2 * 7 * x / 7 + x = 8 14 x = 8 x + 56 = > x = 8 d"
Answer: d
Problem: a man buys rs . 20 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is ?
Options: a ) 14 , b ) 15 , c ) 61 , d ) 17 , e ) 18
Rationale: "dividend on rs . 20 = rs . ( 9 / 100 ) x 20 = rs . 9 / 5 . rs . 12 is an income on rs . 100 . rs . 9 / 5 is an income on rs . [ ( 100 / 12 ) x ( 9 / 5 ) ] = rs . 15 ? answer : b"
Answer: b
Problem: the speed at which a man can row a boat in still water is 6 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 110 meters ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 52 , e ) 56
Rationale: "the speed of the boat downstream = 6 + 3 = 9 km / hr 9 km / hr * 5 / 18 = 2.5 m / s the time taken to cover 110 meters = 110 / 2.5 = 44 seconds . the answer is b ."
Answer: b
Problem: 24 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 36 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 24 ã — 13.5 = 324 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 324 â  „ 9 = 36 answer b"
Answer: b