regisss/math_qa huggingface dataset:
Problem: a company purchased raw material worth 1 / 4 of it capital , 1 / 10 of the remaining is spent on machinery . how much fraction of the capital was left with the company after its expenditures on raw material and machinery ?
Options: a ) 1 / 5 , b ) 2 / 8 , c ) 5 / 9 , d ) 27 / 40 , e ) 15 / 30
Rationale: the amount spent by the company on raw material is 1 / 4 , so remaining is 3 / 4 . 1 / 10 of the remaining is spent on machinery , 1 / 10 * 3 / 4 = 3 / 40 total amount spent on raw material and machinery is 1 / 4 + 3 / 40 to make the denominator common we use 40 , so 1 / 4 is 10 / 40 10 / 40 + 3 / 40 = 13 / 40 is spent on raw material and machinery remaining 27 / 40 is left with the company answer is d
Answer: d
Problem: if x = y = 2 z and xyz = 256 then what is the value of x ?
Options: a ) 12 , b ) 8 , c ) 16 , d ) 6 , e ) 2
Rationale: given that x = y = z . so , x = y , x = 2 z , y = 2 z . given xyz = 256 = > ( 2 z ) * ( 2 z ) * z = 256 = > 4 z ^ 3 = 256 = > z = 4 then x = 2 z = 2 ( 4 ) = 8 answer : b
Answer: b
Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 5184 , what is the area of the side face of the box ?
Options: a ) 123 , b ) 167 , c ) 178 , d ) 199 , e ) 288
Rationale: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 5184 l * 1.5 l * 2 l = 5184 l = 12 side face area = l * d = l * 2 l = 12 * 2 * 12 = 288 e is the answer"
Answer: e
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed r of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = r ans = c"
Answer: c
Problem: if a ã — b = 2 a - 3 b + ab , then 4 ã — 5 + 5 ã — 4 is equal to :
Options: a ) 31 , b ) 32 , c ) 43 , d ) 45 , e ) 26
Rationale: "explanation : 4 ã — 5 + 5 ã — 4 = ( 2 ã — 4 - 3 ã — 5 + 4 ã — 5 ) + ( 2 ã — 5 - 3 ã — 4 + 5 ã — 4 ) = ( 8 - 15 + 20 + 10 - 12 + 20 ) = 31 . answer : a"
Answer: a
Problem: my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 100 years . can you tell my grandson age in years ?
Options: a ) 50 years , b ) 20 years , c ) 5 years , d ) 10 years , e ) 90 years
Rationale: let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 120 years , g + s + m = 100 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows : g + 365 g / 52 + 12 g = 100 or 52 g + 365 g + 624 g = 5,200 or g = 5,200 / 1,041 = 5 years answer : c
Answer: c
Problem: what is the difference between the place values of two sevens in the numeral 54179759 ?
Options: a ) 699990 , b ) 99990 , c ) 99980 , d ) 69300 , e ) none of these
Rationale: explanation : required difference = 70000 - 700 = 69300 answer is d
Answer: d
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 34 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 22.67 litres , c ) 11 litres , d ) 07 litres , e ) 38.67 litres
Rationale: "262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) solve the equation . 262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) 8936.9 + 3 , 104.35 x = 47 , 581.3 + 1 , 399.45 x 8936.9 + 1 , 704.9 x = 47 , 581.3 1 , 704.9 x = 38 , 644.40 x ≈ 22.67 answer is b ."
Answer: b
Problem: the equation of line s is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line s ?
Options: a ) 48 , b ) 50 , c ) 60 , d ) 75 , e ) 100
Rationale: this can be solve in two steps and without any complex calculation . given : equation of line s as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 75,0 ) . this can be considered a right angle triangle with right angle at ( 0,0 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 0,0 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c
Answer: c
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.0 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 5.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2 + ( 3.6 / . 4 ) * . 35 = 2 + 9 * . 35 = 5.15 $ answer a"
Answer: a
Problem: to a sugar solution of 10 liters containing 50 % sugar , 10 liter of water is added . the percentage of sugar in the new solution is ?
Options: a ) 25 % , b ) 30 % , c ) 15 % , d ) 20 % , e ) 18 %
Rationale: "quantity of sugar = 50 * 10 / 100 = 5 kg new percentage = 5 / 20 * 100 = 25 % answer is a"
Answer: a
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 2 / 3 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 144 , c ) 175 , d ) 216 , e ) 264
Rationale: total paint initially = 360 gallons paint used in the first week = ( 2 / 3 ) * 360 = 240 gallons . remaning paint = 120 gallons paint used in the second week = ( 1 / 5 ) * 120 = 24 gallons total paint used = 264 gallons . option e
Answer: e
Problem: a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 8 , e ) 9
Rationale: let the ten ' s and unit digit be x and 8 respectively . x then , 10 x + 8 + 18 = 10 x 8 + x x x 10 x 2 + 8 + 18 x = 80 + x 2 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 option b
Answer: b
Problem: how many numbers from 10 to 47 are exactly divisible by 3 ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 , . 12 numbers . 10 / 3 = 3 and 47 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits a )"
Answer: a
Problem: a 7 % stock yields 10 % . the market value of the stock is :
Options: a ) rs 60 , b ) rs 70 , c ) rs 90 , d ) rs 75 , e ) rs 50
Rationale: "explanation : for an income of rs . 10 , investment = rs . 100 . for an income of rs 7 , investment = rs . 100 / 10 x 7 = rs 70 market value of rs . 100 stock = rs . 70 answer is b"
Answer: b
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 360 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 744 , c ) 788 , d ) 298 , e ) 930
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 360 62 % - - - - - - - - ? = > 930 answer : e"
Answer: e
Problem: a light flashes every 6 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 650 , d ) 700 , e ) 750
Rationale: "1 flash = 6 sec for 1 min = 10 flashes so for 1 hour = 10 * 60 = 600 flashes . answer : b"
Answer: b
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 6 : 4 . if 60 % of the toyota bought and 40 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 52 % , e ) 72 %
Rationale: "let total no of vehicles bought be 100 , toyota 60 and honda 40 , so total number of suv ' s bought for toyota and honda respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : d"
Answer: d
Problem: a clothing store purchased a pair of pants for $ 81 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 5.4 , c ) $ 4.4 , d ) $ 1.2 , e ) $ 5.0
Rationale: "sale price ( sp ) = 81 + markup ( mp ) - - > mp = sp - 81 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 81 3 sp / 4 = 81 sp = 108 now a discount of 20 % is given so new sp is . 8 * 108 = 86.4 profit = 86.4 - 81 = 5.4 $ answer is b"
Answer: b
Problem: find the average of all prime numbers between 80 and 100
Options: a ) 88 , b ) 60 , c ) 80 , d ) 89.6 , e ) 92
Rationale: "prime numbers between 80 and 100 are 83 , 89 , 97 required average = ( 83 + 89 + 97 ) / 3 = 269 / 3 = 89.6 answer is d"
Answer: d
Problem: a certain number when divided by 65 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 65 + 25 = 90 / 15 = 6 ( remainder ) c"
Answer: c
Problem: a train 240 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 4 , b ) 6 , c ) 12 , d ) 9 , e ) 13
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 240 * 3 / 55 ] sec = 13 sec answer : e"
Answer: e
Problem: the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 70 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 31 % , e ) 100 %
Rationale: "let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.7 * 10 = 17 percentage by which wage earned by charles is more than that earned by robin = ( 17 - 13 ) / 13 * 100 % = 4 / 13 * 100 % = 31 % answer d"
Answer: d
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 3 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 3 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 3 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 3 / 7 x 1 / 5 = 3 / 35 answer : a"
Answer: a
Problem: two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 60 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 767 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 60 km more than the other , 25 x – 20 x = 60 5 x = 60 x = 12 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 12 = 540 km . answer : a"
Answer: a
Problem: a set consists of 18 numbers , all are even or multiple of 5 . if 6 numbers are even and 12 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: { total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 18 = 6 + 12 - { both } + 0 ; { both } = 0 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : a .
Answer: a
Problem: what is the units digit of 17 ^ 83 × 13 ^ 52 × 11 ^ 87 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 5 correct option : b"
Answer: b
Problem: during a certain two - week period , 50 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 9 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 ) 10 a , c ) 20 a , d ) 25 a , e ) 28 a
Rationale: "movies : 50 % comedies . 50 % remaining genre . now in this 50 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 9 x . total 10 x . 10 x = 50 ; x = 5 action movies : 5 % drama movies : 45 % we can say that out of 100 z , : comedies : 50 z action : 5 z drama : 45 z now action movies were a this means : a = 5 z . z = ( a / 5 ) comedies : 50 z = 50 * ( a / 5 ) 10 a b is the answer ."
Answer: b
Problem: a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 200 , b ) 276 , c ) 230 , d ) 240 , e ) 250
Rationale: "let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b"
Answer: b
Problem: a and b can do a work in 4 hours and 12 hours respectively . a starts the work at 6 am and they work alternately for one hour each . when will the work be completed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 78
Rationale: "work done by a and b in the first two hours , working alternately = first hour a + second hour b = 1 / 4 + 1 / 12 = 1 / 3 . total time required to complete the work = 2 * 3 = 6 days . answer : d"
Answer: d
Problem: john had a stock of 1300 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 69.0 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1300 - n = 1300 - 402 = 898 percentage books not sold / total number of books = 898 / 1300 = 0.69 = 69 % correct answer d"
Answer: d
Problem: a farm is made up of brown and white goats . the number of male brown goats is 35 % less than the total number of brown goats . the total number of female goats is 20 times more than the number of female brown goats . if the total population of male goats is half the population of the female goats , what percentage of male goats are brown ?
Options: a ) 30.1 , b ) 20.5 , c ) 15.2 , d ) 10.2 , e ) 28.6
Rationale: since we are dealing in percentage let us pick 100 as the number of brown male goats . that means that the total number of brown goats is = 135 ( number of male brown goats is 35 % less than the total number of brown goats ) , therefore the number of brown female goats is 35 . the total number of female goats is 15 x the number of brown female goats = 35 * 20 = 700 female goats . male goats total population is half the population of the female goats = 700 / 2 = 350 therefore percentage of male horses goats that are brown = 100 / 350 * 100 = 28.6 correct option is e
Answer: e
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 4 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 4 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 4 = 3 / 4 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 3 / 4 = 3 / 8 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 3 / 4 * 5 / 8 = 1 / 2 ans d"
Answer: d
Problem: the average of 7 consecutive numbers is 20 . the largest of these numbers is
Options: a ) 12 , b ) 27 , c ) 23 , d ) 28 , e ) 11
Rationale: let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c
Answer: c
Problem: ( 128.5 x 25 ) + ( 13.8 x 50 ) = ? x 50
Options: a ) 78.05 , b ) 556.02 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 25 ) + ( 13.8 x 50 ) / 50 = 3212.5 + 690 / 50 = 78.05 answer : option a"
Answer: a
Problem: a bookseller sells his books at a 15 % markup in price . if he sells a book for $ 23.00 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 21.00 , d ) $ 19.60 , e ) $ 20.00
Rationale: "let the cost price of book = x selling price of book = 23 $ markup % = 15 ( 115 / 100 ) x = 23 = > x = 20 answer e"
Answer: e
Problem: there are 20 poles with a constant distance between each pole . a car takes 24 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 41.4543 , b ) 41.4545 , c ) 41.45128 , d ) 41.41288 , e ) 41.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 24 seconds 1 pole ( 24 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 24 / 11 ) seconds = 41.4545 seconds answer : b"
Answer: b
Problem: a person walks from one end to the other of a 100 - meter long moving walkway at a constant rate in 50 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 63 , b ) 66 , c ) 69 , d ) 72 , e ) 75
Rationale: let v be the speed of the person and let x be the speed of the walkway . 50 ( v + x ) = 100 then 150 ( v + x ) = 300 150 ( v - x ) = 100 when we add the two equations : 300 v = 400 v = 4 / 3 time = 100 / ( 4 / 3 ) = 75 seconds the answer is e .
Answer: e
Problem: what will be the compound interest on a sum of rs . 23,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 9313.34 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 23000 * ( 1 + 12 / 100 ) 3 ] = 23000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 32313.34 c . i . = ( 32313.34 - 23000 ) = rs . 9313.34 answer : a"
Answer: a
Problem: the radius of a wheel is 16.8 cm . what is the distance covered by the wheel in making 300 resolutions ?
Options: a ) 754 m , b ) 316.512 m , c ) 311.512 m , d ) 311.518 m , e ) 313.512 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 300 resolutions . = 300 * 2 * 22 / 7 * 16.8 = 31651.2 cm = 316.512 m answer : b"
Answer: b
Problem: evaluate : 6302.5 + 630.25 + 63.025 + 6.3025 + 0.63025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 7002.70775
Rationale: "6302.5 630.25 63.025 6.3025 + 0.63025 - - - - - - - - - - - - - - - 7002.70775 answer is e ."
Answer: e
Problem: what is the sum of all the prime numbers from 20 to 40 ?
Options: a ) 279 , b ) 100 , c ) 278 , d ) 120 , e ) 191
Rationale: "explanation : 23 + 29 + 31 + 37 = 120 answer : d"
Answer: d
Problem: evaluate 30 ! / 28 !
Options: a ) 720 , b ) 600 , c ) 870 , d ) 910 , e ) 650
Rationale: "we have 30 ! / 28 ! = 30 * 29 * 28 ! / 28 ! = 30 * 29 = 870 answer is c"
Answer: c
Problem: at present the ratio between the ages of arun and deepak is 2 : 5 . after 10 years arun ' s age will be 30 years . what is the age of the deepak ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 45
Rationale: "let the present age of arun and deepak be 4 x and 3 x 2 x + 10 = 30 2 x = 20 x = 10 deepak ' s age = 5 x = 50 years answer is c"
Answer: c
Problem: 100 liters of a mixture contains milk and water in the ratio 4 : 1 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 7 : 5 , b ) 9 : 2 , c ) 6 : 1 , d ) 5 : 4 , e ) 11 : 4
Rationale: "quantity of milk in 100 liters if mix = 100 * 4 / 5 = 80 liters quantity of milk in 110 liters of new mix = 80 + 10 = 90 liters quantity of water in it = 110 - 90 = 20 liters ratio of milk and water in new mix = 90 : 20 = 9 : 2 answer is b"
Answer: b
Problem: there are 8 baskets numbered from 1 to 8 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 640 , b ) 680 , c ) 720 , d ) 760 , e ) 800
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 8 * 9 / 2 = 36 apples . the total number of apples taken by 10 children is 10 * 36 = 360 the number of apples left in the end is 1000 - 360 = 640 apples . the answer is a ."
Answer: a
Problem: a rectangular floor that measures 6 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 15 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 225 , e ) $ 1,920
Rationale: "the width of the rectangular floor ( 6 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 10 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 6 / 2 ) * ( 10 / 2 ) = 15 . the total cost is 15 * 15 = $ 225 . the answer is , therefore , d ."
Answer: d
Problem: on multiplying a numberz by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number z is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Problem: the average age of 40 passengers in a ferry is 35 . what is the average age of the new group formed when combining the passengers with the 5 crew members of ferry whose average age is 25 ?
Options: a ) 36.45 , b ) 38.89 , c ) 39.67 , d ) 40.12 , e ) 41.88
Rationale: sum of ages of passengers = 40 x 35 = 1400 sum of ages of crew = 25 x 5 = 125 sum of ages of new group formed = 1525 average = 1525 / 45 = 38.89 answer : b
Answer: b
Problem: one side of the bottom layer of a triangular pyramid has 12 balls . how many are there in the whole pyramid ? note that the pyramid is equilateral and solid .
Options: a ) 286
b ) 364
c ) 504
d ) 164
e ) 165
Rationale: as there are 12 balls along one side , it means that there are 12 layers of balls . the top most layer has 1 ball . the second layer has 3 ( 1 + 2 ) balls . the third layer has 6 ( 1 + 2 + 3 ) balls . the fourth layer has 10 ( 1 + 2 + 3 + 4 ) balls . the fifth layer has 15 ( 1 + 2 + 3 + 4 + 5 ) balls . similarly , there are 21 , 28 , 36 , 45 , 55 , 66 and 78 balls in the remaining layers . hence , the total number of balls are = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 balls answer : b
Answer: b
Problem: in a company of 15 employees , 6 employees earn $ 37,000 , 5 employees earn $ 42,000 , and the 4 highest - paid employees earn the same amount . if the average annual salary for the 15 employees is $ 45,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 56,250 , b ) $ 57,750 , c ) $ 59,250 , d ) $ 60,750 , e ) $ 62,250
Rationale: "6 * 37,000 + 5 * 42,000 + 4 x = 15 * 45,000 4 x = 675,000 - 222,000 - 210,000 4 x = 243,000 x = 60,750 the answer is d ."
Answer: d
Problem: what is the units digit of ( 493 ) ( 915 ) ( 381 ) ( 756 ) ( 22 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 1 . imo b ."
Answer: b
Problem: a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 25 % 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 ) 38 % , c ) 36 % , d ) 33.33 % , e ) 35 %
Rationale: "anyway , in this question , there is no discount but the mark up is given as 25 % of the selling price . so it is not 25 % of $ 150 but instead , 40 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 25 % of s = s s = 200 profit = 50 which is calculated on cost price in % terms . so 50 / 150 * 100 = 33.33 % is profit . d"
Answer: d
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 90 kmph and 108 kmph . in how much time will the trains cross each other ?
Options: a ) 80 / 8 , b ) 80 / 7 , c ) 80 / 5 , d ) 80 / 3 , e ) 80 / 11
Rationale: "relative speed = ( 90 + 108 ) * 5 / 18 = 11 * 5 = 55 mps . the time required = d / s = ( 100 + 100 + 200 ) / 55 = 400 / 55 = 80 / 11 sec . answer : e"
Answer: e
Problem: how many 4 digit odd numbers do not use any digit more than once
Options: a ) 1720 , b ) 2160 , c ) 224 , d ) 2460 , e ) none of these
Rationale: the way i solved it is a b c d ( thousand , hundreds , tens , units ) d can be 1 3 5 7 9 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities c can be anything execpt a and b so 8 possibilities b can be anything execpt ( a d c ) so 7 possibilities total ways are 8 * 7 * 8 * 5 = 2240 ans e
Answer: e
Problem: how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 9 inches than that of a rectangular sheet of paper measuring 4.5 inches by 11 inches ?
Options: a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
Rationale: "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 9 is twice 4.5 then the area will be double which means 100 % greater . the answer is c ."
Answer: c
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 36 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 19 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 36 pints will require 9 / 17 * 36 = 19 pints . . c"
Answer: c
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3000 . if the price of the car in 1996 was $ 22000 , what is the car ' s price in 2002 ?
Options: a ) $ 21,700 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 3000 = $ 21700 correct option : a
Answer: a
Problem: the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 850 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 18,700
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 850 ã — 22 ) = rs . 18700 answer : option e"
Answer: e
Problem: at a conference table , 6 employees gather around a table . one of the employees is the manager and he sits at the head of the table . two of the employees sit on either side of the table . how many different seating arrangements can be made with these 6 employees ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: head ' s sit is fixed . now 5 people is left with 5 seats . 5 people can sit on 5 seats in 5 ! ways or 120 ways . ans is d
Answer: d
Problem: if q and t are positive integers , qt + q + t can not be
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let qt + t + q = x add 1 on both sides : qt + t + q + 1 = x + 1 tq + 1 ) + q + 1 = x + 1 ( q + 1 ) ( t + 1 ) = x + 1 minimum value of ( q + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > qt + t + s can not be 6 answer : b
Answer: b
Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 1 red and 2 green balls ?
Options: a ) 70 / 323 , b ) 50 / 323 , c ) 52 / 969 , d ) 60 / 323 , e ) 25 / 321
Rationale: "sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue and 1 red and 2 green balls were drawn from bag = 6 c 1 * 5 c 1 * 8 c 2 = 840 probability = 840 / 3876 = 70 / 323 ans - a"
Answer: a
Problem: a toy factory stores its toys in either a big box or a small box . the big box can store 35 toys while the small box can store 14 toys . if the factory is to store 86 newly manufactured toys , what is the least number of toys that will be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 4
Rationale: total toys to be stored 86 the big box can store 35 small box can store 14 storing 85 toys in big box 85 / 35 = 2 r 16 store remainder in small box 16 / 14 = 1 r 2 least number of toys that will be left unboxed = 2 answer : a
Answer: a
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 3,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6.43 % , b ) 6.89 % , c ) 7.69 % , d ) 8.21 % , e ) 8.75 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 6500 = 1 / 13 which is about 7.69 % the answer is c ."
Answer: c
Problem: a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 35 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 1050 km , b ) 1150 km , c ) 1250 km , d ) 1550 km , e ) 850 km
Rationale: "d = 30 * 5 = 150 rs = 35 – 30 = 5 t = 150 / 5 = 30 d = 35 * 30 = 1050 km answer : a"
Answer: a
Problem: total dinning bill for 9 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 26.96 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 9 = 26.96 answer : d"
Answer: d
Problem: a sum of money at simple interest amounts to rs . 805 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 688 , d ) s . 700 , e ) s . 718
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 805 - 117 ) = rs . 688 . answer : option c"
Answer: c
Problem: a shopkeeper fixes the marked price of an item 25 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 11.59 % , b ) 12.59 % , c ) 13.59 % , d ) 14.59 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 125 required gain = 8 % , so selling price = rs 108 discount = 125 - 108 = 17 discount % = ( 17 / 135 ) * 100 = 12.59 % option b"
Answer: b
Problem: a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 550.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 7.85 , b ) $ 11.30 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 550 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 550 / 70 ~ 7.85 a
Answer: a
Problem: a candidate got 30 % of the votes polled and he lost to his rival by 1760 votes . how many votes were cast ?
Options: a ) 4000 , b ) 4100 , c ) 4200 , d ) 4300 , e ) 4400
Rationale: "let x be the total number of votes . 0.3 x + 1760 = 0.7 x 0.4 x = 1760 x = 1760 / 0.4 = 4400 the answer is e ."
Answer: e
Problem: if 4 / p = 8 & 4 / q = 18 then p - q = ?
Options: a ) 5 / 18 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 4 / 8 , q = 4 / 18 = > q = 2 / 9 therefore p - q = ( 1 / 2 ) - ( 2 / 9 ) = 5 / 18 answer : a"
Answer: a
Problem: tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many q minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , q = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Problem: a student completes a 3 part exam as follows . the student completes section a in 10 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 5 : 2 , b ) 4 : 1 , c ) 4 : 3 , d ) 3 : 2 , e ) 2 : 1
Rationale: the time spent on section b and section c is 25 minutes each . the ratio of c to a is 25 : 10 = 5 : 2 the answer is a .
Answer: a
Problem: a person ' s present age is two - fifth of the age of his father . after 8 years , he will be one - half of the age of his father . how old is the father at present ?
Options: a ) a ) 40 , b ) b ) 48 , c ) c ) 32 , d ) d ) 45 , e ) e ) 28
Rationale: "let the father ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 8 = 1 / 2 ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) x = 40 answer is a"
Answer: a
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 21 liters of drink a to convert it to drink b ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "in 21 liters of drink a , there are 12 liters of milk and 9 liters of juice . with 12 liters of milk , we need a total of 16 liters of juice to make drink b . we need to add 7 liters of juice . the answer is e ."
Answer: e
Problem: the l . c . m . of two numbers is 54 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 40 , d ) 45 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 54 or x = 9 . the numbers are 18 and 27 . hence , required sum = ( 18 + 27 ) = 45 . answer : option d"
Answer: d
Problem: simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on rs . 4000 for 2 years at 10 % per annum . the sum placed on simple interest is
Options: a ) rs 1650 , b ) rs 1750 , c ) rs 1850 , d ) rs 1950 , e ) none of these
Rationale: "explanation : c . i . = ( 4000 × ( 1 + 10 / 100 ) 2 − 4000 ) = 4000 ∗ 11 / 10 ∗ 11 / 10 − 4000 = 840 so s . i . = 840 / 2 = 420 so sum = s . i . ∗ 100 / r ∗ t = 420 ∗ 100 / 3 ∗ 8 = rs 1750 option b"
Answer: b
Problem: a car is purchased on hire - purchase . the cash price is $ 21 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly instalments . interest is charged at 12 % p . a . what is the monthly instalment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 505 , d ) $ 506 , e ) $ 507
Rationale: explanation : cash price = $ 21 000 deposit = 10 % × $ 21 000 = $ 2100 loan amount = $ 21000 − $ 2100 = $ 18900 i = p * r * t / 100 i = 11340 total amount = 18900 + 11340 = $ 30240 regular payment = total amount / number of payments answer : b
Answer: b
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 12 plants . there are 11 gapes between the two corner trees ( 11 x 2 ) metres and 1 metre on each side is left . therefore length = ( 22 + 2 ) m = 24 m . answer : c"
Answer: c
Problem: the radius of a wheel is 25.4 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 724 m , b ) 798.3 m , c ) 287 m , d ) 278 m , e ) 927 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 25.4 = 79829 cm = 798.3 m answer : b"
Answer: b
Problem: divide $ 2000 among b , c in the ratio 4 : 16 . how many $ that c get ?
Options: a ) $ 1200 , b ) $ 1400 , c ) $ 1600 , d ) $ 1800 , e ) $ 2000
Rationale: sum of ratio terms = 4 + 16 = 20 c = 2000 * 16 / 20 = $ 1600 answer is c
Answer: c
Problem: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 15 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 600 , c ) 887 , d ) 299 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 15 < = > ( 25 / 10 * 1 / 100 * x ) = 15 < = > x = 600 . answer : b )"
Answer: b
Problem: what is the smallest integer that is multiple of 5 , 7,8
Options: a ) a ) 70 , b ) b ) 35 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 5 , 7 and 8 which is 280 . the answer is d ."
Answer: d
Problem: the smallest 6 digit number exactly divisible by 111 is ?
Options: a ) 100009 , b ) 100010 , c ) 100011 , d ) 100015 , e ) 100017
Rationale: the smallest 6 - digit number 100000 . 111 ) 100000 ( 900 999 - - - - - 100 - - - required number = 100000 + ( 111 - 100 ) = 100011 option c
Answer: c
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 - ounce cans of the concentrate are required to prepare 272 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 67 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 272 * 6 = 1632 oz so orange juice concentrate : water : : 408 oz : 1224 oz no . of 12 oz can = 408 oz / 12 oz = 34 answer b , 34 cans"
Answer: b
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 432 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 432 , 2 ( 7 / 5 ) w + 2 w = 432 solve the above equation to find : w = 90 m and l = 126 m . correct answer e ) 90"
Answer: e
Problem: a train 160 m long is running at 30 kmph . in how much time will it pass a platform 120 m long ?
Options: a ) 15.89 seconds , b ) 24.36 seconds , c ) 15.96 seconds , d ) 14.93 seconds , e ) 22.23 seconds
Rationale: distance travelled = 160 + 120 m = 280 m speed = 30 * 5 / 8 = 75 / 4 m time = 280 * 4 / 75 = 14.93 seconds answer : d .
Answer: d
Problem: difference between the length and breadth of a rectangle is 23 m . ifits perimeter is 206 m , then its area is ? ?
Options: a ) 1220 m ^ 2
b ) 1520 m ^ 2
c ) 2520 m ^ 2
d ) 2600 m ^ 2
e ) 3420 m ^ 2
Rationale: we have : ( l - b ) = 23 and 2 ( l + b ) = 206 or ( l + b ) = 103 . solving the two equations , we get : l = 63 and b = 40 . area = ( l x b ) = ( 63 x 40 ) m 2 = 2520 m ^ 2 c
Answer: c
Problem: the salaries of a and b together amount to $ 2000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 1500 , e ) $ 1200
Rationale: "let a ' s salary is x b ' s salary = 2000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 2000 - x ) x = $ 1500 answer is d"
Answer: d
Problem: what is the least value of p , so that 123 p 578 is divisible by 11
Options: a ) 7 , b ) 8 , c ) 6 , d ) 5 , e ) 4
Rationale: "explanation : 123 p 578 1 + 3 + 5 + 8 = 17 2 + p + 7 = 17 = > 9 + p = 17 = > p = 17 - 9 = > p = 8 answer : option b"
Answer: b
Problem: a train covers a distance of 12 km in 10 min . if it takes 11 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 m , b ) 189 m , c ) 220 m , d ) 178 m , e ) 188 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 11 = 220 m . answer : c"
Answer: c
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if his company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) 234 , b ) 600 , c ) 388 , d ) 278 , e ) 129
Rationale: "explanation : number of shares = = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = = rs . 600 answer : b ) rs . 600"
Answer: b
Problem: a man sold 18 toys for rs . 27300 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1300
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 27300 . gain = sp â € “ cp 3 x = 27300 â € “ 18 x 21 x = 27300 x = rs . 1300 . answer : option e"
Answer: e
Problem: what is the square root of 3,969 ?
Options: a ) a ) 18 , b ) b ) 9 , c ) c ) 45 , d ) d ) 63 , e ) e ) 81
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 63 * 63 = 3,969 3969 divided by x = 63 x = 63 ( d ) 63"
Answer: d
Problem: if 5 < x < 11 and y = x + 7 , what is the greatest possible integer value of x + y ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: x + y = x + x + 7 = 2 x + 7 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 10.5 then x + y = 10.5 + 17.5 = 28 . the answer is c .
Answer: c
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.75 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 2.80 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80
Rationale: total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.8 therefore , x = $ 2.80 . answer b
Answer: b
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30,000 , a receives :
Options: a ) s . 12,000 , b ) s . 12,200 , c ) s . 12,400 , d ) s . 12,600 , e ) s . 12,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 30000 x 21 / 50 ) = rs . 12,600 . d"
Answer: d
Problem: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2080 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2600 , c ) 2507 , d ) 3200 , e ) 11500
Rationale: "p - 2080 = ( p * 5 * 4 ) / 100 p = 2600 answer : b"
Answer: b