Cheukting/mathqa huggingface dataset:
Question (geometry): an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 45 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm
Rationale: "we have 45 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 22.5 and continues . so we have 45 , 22.5 , 11.25 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 45 / 1 - ( 1 / 2 ) = 90 equilateral triangle perimeter is 3 a = 3 * 90 = 270 . so option d ."
Answer: d
Question (general): if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 120 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,080
Rationale: "10 / 100 p = 120 > > p = 120 * 100 / 10 = 1200 1200 - 120 = 1080 answer : e"
Answer: e
Question (general): a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 6 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 27 , b ) 22 , c ) 24 , d ) 26 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : a"
Answer: a
Question (gain): the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 3 years ?
Options: a ) 14300 , b ) 17280 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 3 = 17280 b )"
Answer: b
Question (physics): a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 18 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : b"
Answer: b
Question (general): how many even multiples of 15 are there between 149 and 301 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "150 = 10 * 15 300 = 20 * 15 the even multiples are 15 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Question (general): what least number should be added to 1101 , so that the sum is completely divisible by 24
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1056 / 24 ) gives remainder 21 21 + 3 = 24 , so we need to add 3 . answer : option d"
Answer: d
Question (physics): a and b can do a work in 6 days , b and c in 2 days and c and a in 8 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 12 / 24 , b ) 48 / 63 , c ) 45 / 56 , d ) 48 / 19 , e ) 28 / 12
Rationale: "one day work of a and b = 1 / 6 one day work of b and c = 1 / 2 one day work of c and a = 1 / 8 2 ( a + b + c ) = 1 / 6 + 1 / 2 + 1 / 8 2 ( a + b + c ) = 19 / 24 ( a + b + c ) = 19 / 48 number of days required = 48 / 19 days . answer : d"
Answer: d
Question (gain): working alone , mary can pave a driveway in 5 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 10 % , but hillary becomes distracted and her rate decreases by 10 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 5 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 5 + ( 1 / 10 * 1 / 5 ) = 2 / 9 per hour hillary = 1 / 3 - ( 1 / 10 * 1 / 3 ) = 3 / 10 per hour together they work 2 / 9 + 3 / 10 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Question (general): how many 3 digit no ' s are between 100 - 500 , where sum of two digit is 3 rd ?
Options: a ) 24 , b ) 54 , c ) 60 , d ) 84 , e ) 94
Rationale: total permutations possible = 18 + 16 + 14 + 12 = 60 answer : c
Answer: c
Question (geometry): find the perimeter and area of a square of side 19 cm .
Options: a ) 324 , b ) 361 , c ) 400 , d ) 441 , e ) 484
Rationale: "we know that the perimeter of square = 4 ã — side side = 19 cm therefore , perimeter = 4 ã — 19 cm = 76 cm now , area of the square = ( side ã — side ) sq . units = 19 ã — 19 cm â ² = 361 cm â ² answer : b"
Answer: b
Question (general): in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 21 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 6 / 5 , d ) 3 / 4 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 21 ) = 36 / 30 = 6 / 5 . answer : c ."
Answer: c
Question (physics): the cross - section of a stream is a trapezium in shape . if the stream is 10 m wide at the top and the area of cross - section is 640 sq m , the depth of stream is 80 m and width at the bottom is ?
Options: a ) 2 m , b ) 6 m , c ) 4 m , d ) 8 m , e ) 9 m
Rationale: 1 / 2 * 80 ( 10 + b ) = 640 b = 6 m answer : b
Answer: b
Question (general): the cost of 2 books and 2 magazines is $ 26 . the cost of 1 book and 3 magazines is $ 27 . how much does 1 magazine cost ?
Options: a ) 8 , b ) 5 , c ) 7 , d ) 4 , e ) 6
Rationale: let the cost of 1 book = x , let the cost of 1 magazine = y 2 x + 2 y = 26 x = ( 26 - 2 y ) / 2 x = 13 - y again , ( 13 - y ) + 3 y = 27 13 + 2 y = 27 2 y = 14 y = 7 answer : c
Answer: c
Question (general): 6,11 , 21 , 41 , 81 , ( . . . )
Options: a ) 22 , b ) 35 , c ) 27 , d ) 32 , e ) 161
Rationale: "explanation : 6 6 × 2 - 1 = 11 11 × 2 - 1 = 21 21 × 2 - 1 = 41 41 × 2 - 1 = 81 81 × 2 - 1 = 161 answer : option e"
Answer: e
Question (general): the organizers of a fair projected a 25 percent increase in attendance this year over that of last year , but attendance this year actually decreased by 20 percent . what percent of the projected attendance was the actual attendance ?
Options: a ) 45 % , b ) 56 % , c ) 64 % , d ) 75 % , e ) 80 %
Rationale: last year attendance = 100 ( assume ) ; projected attendance = 125 ; actual attendance = 80 . the actual attendance therefore was ( actual ) / ( project ) = 80 / 125 * 100 = 64 $ of the projected attendance . answer : c .
Answer: c
Question (physics): the length of the longest tape in cm which can be used to measure exactly , the length 10 m ; 3 m 85 cm ; and 11 m 50 cm is :
Options: a ) 5 , b ) 35 , c ) 34 , d ) 36 , e ) 38
Rationale: "the three lengths in cm are 1000 , 385 & 1150 . hcf of 700 , 385 & 1295 is 5 . hence , the answer is 5 cm . answer : a"
Answer: a
Question (general): if x + y = 270 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 235 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 270 x - y = 200 2 x = 70 x = 35 y = 235 answer is b"
Answer: b
Question (physics): a and b together can do a piece of work in 6 days and a alone can do it in 11 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 66 / 5 days , d ) 21 days , e ) 22 / 5 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 11 work in 1 day b alone can do ( 1 / 6 - 1 / 11 ) = 5 / 66 work in 1 day = > complete work can be done in 66 / 5 days by b answer : option c"
Answer: c
Question (general): the average weight of 22 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 48.89 , b ) 42.25 , c ) 50 , d ) 51.25 , e ) 52.25
Rationale: explanation : average weight of 22 boys = 50.25 total weight of 22 boys = 50.25 × 22 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 16 ) + ( 45.15 × 8 ) total boys = 22 + 8 = 30 average weight of all the boys = ( ( 50.25 × 22 ) + ( 45.15 × 8 ) ) / 30 = 48.89 answer : option a
Answer: a
Question (other): profits in the partnership of bess , bill and bob are shared in the ratio 1 : 2 : 3 . if bill ' s share of the profits is $ 300 , what is bob ' s share ?
Options: a ) $ 150 , b ) $ 900 , c ) $ 600 , d ) $ 450 , e ) none
Rationale: ans is d given profit ratio , bess : bill : bob = 1 : 2 : 3 to make bill ' s portion $ 300 , multiply by $ 150 = > bess : bill : bob = $ 150 : $ 300 : $ 450 = > bob ' s share = $ 450
Answer: b
Question (general): a sporting goods store sold 60 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 204 , what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 12 , c ) 8 , d ) 4 , e ) 2
Rationale: "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 60 3 x + 4 y = 204 x = 60 - y 3 ( 60 - y ) + 4 y = 204 180 - 3 y + 4 y = 204 y = 24 answer : a"
Answer: a
Question (general): patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils . the cost of 90 pencils is how many times the selling price of 90 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.2 , e ) 1.44
Rationale: "say the cost price of 90 pencils was $ 90 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 90 - 90 p = 40 p - - > p = 9 / 13 . ( cost price ) / ( selling price ) = 1 / ( 9 / 13 ) = 13 / 9 = 1.44 . answer : e ."
Answer: e
Question (gain): tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1045 , c ) c ) 1055 , d ) d ) 1060 , e ) e ) 1235
Rationale: cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 75 × 9 = 675 . total cost he has to pay = 560 + 675 = 1235 . e )
Answer: e
Question (physics): it takes joey the postman 1 hours to run a 6 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 ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 6 miles an hour let the other half be x miles an hour now , avg speed = 8 mile an hour 2 * 6 * x / 6 + x = 8 12 x = 8 x + 48 = > x = 12 b"
Answer: b
Question (general): if ( a - b - c + d = 18 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 36 .
Rationale: "eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 12 ( 2 ) simplify - b + d = 6 b - d = - 6 ( b - d ) ^ 2 = ( - 6 ) ^ 2 = 36 my answer : e"
Answer: e
Question (physics): a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 60 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 55
Rationale: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 60 hours = 3,600 / 60 seconds = 60 seconds ; time to cover 1 kilometer at regular speed is 60 + 5 = 65 seconds = 65 / 3,600 hours = 1 / 55 hours ; so , we get that to cover 1 kilometer 1 / 55 hours is needed - - > regular speed 55 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e"
Answer: e
Question (probability): what is the probability of getting 53 mondays in a leap year ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: "in a leap year contains 52 monday ' s since 52 weeks are present and 2 days extra it may be sunday and monday 2 . monday and tuesday 3 . tuesday and thursday 4 . thursday and friday similary 7 alternatives are possible . among this only 2 are possible cases so 2 / 7 answer : b"
Answer: b
Question (general): if a and b are positive integers and ( 5 ^ a ) ^ b = 5 ^ 2 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 3125 , b ) 625 , c ) 5 , d ) 25 , e ) 125
Rationale: "5 ^ ab = 5 ^ 2 therefore ab = 2 either a = 1 or 2 or b = 2 or 1 therefore 5 ^ a * 5 ^ b = 5 ^ ( a + b ) = 5 ^ 3 = 125 e"
Answer: e
Question (other): if w is the set of all the integers between 10 and 332 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 111 , b ) 28 , c ) 160 , d ) 213 , e ) 107
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 330 , the smallest is 12 ) : 330 - 12 = 318 step 2 . divide by 3 : 318 / 3 = 106 step 3 . add 1 : 106 + 1 = 107 . so there are 107 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 330 , the smallest is 12 ) : 330 - 12 = 318 step 2 . divide by 2 : 318 / 2 = 159 step 3 . add 1 : 159 + 1 = 160 . so there are 160 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 107 multiples of 3 and the 160 multiples of 2 : 107 + 160 = 267 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 107 + 160 = 267 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 25 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 330 - 12 = 318 step 2 . divide by 6 : 318 / 6 = 53 step 3 . add 1 : 53 + 1 = 54 . so there are 54 multiples of 6 within the range : we counted 54 numbers twice . subtract the 54 multiples of 6 from the sum of the multiples of 2 and 3 : = 107 + 160 - 54 = 267 - 54 = 213 therefore , the final number of multiples of 2 , 3 or 6 is 213 . hence , this is the correct answer . ( d )"
Answer: d
Question (physics): a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 12 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 2345
b ) 3456
c ) 4567
d ) 5678
e ) 6789
Rationale: the tank is emptied at this rate : 12 + 6 - 3 = 15 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 15 = 3456 minutes . the answer is b .
Answer: b
Question (gain): an investment yields an interest payment of $ 231 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 28,300 , b ) $ 30,800 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 35,100
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 230 = > p = ( 231 * 4 * 10 ^ 2 ) / 3 = 77 * 4 * 10 ^ 2 = 308 * 10 ^ 2 = 30800 answer b"
Answer: b
Question (general): if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x × 7.50 = x = 80 kg . ∴ reduction in consumption = 20 % . answer b"
Answer: b
Question (general): there are cats got together and decided to kill the mice of 999975 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 995,1005 , d ) 791,1009 , e ) 931,1009
Rationale: 999975 can be written as 1000000 â € “ 25 = 10002 â € “ 52 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 5 ) * ( 1000 - 5 ) = ( 1005 ) * ( 995 ) given that number of cats is less than number if mice . so number of cats is 995 and number of mice were 1005 answer c
Answer: c
Question (general): how many positive integers less than 50 have a reminder 01 when divided by 5 ?
Options: a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 5 . so , there are total of 10 numbers . answer : a ."
Answer: a
Question (physics): natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3.5 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 2.125 , b ) 2.375 , c ) 2.625 , d ) 2.675 , e ) 2.825
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3.5 km / hour x / 3 = 3.5 x = 10.5 km the average speed while climbing = distance / time = 10.5 / 4 = 2.625 km / h the answer is c ."
Answer: c
Question (other): how many positive integers d between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Question (general): the number of the members of a club is more than 50 and less than 80 . when 5 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "the number of members is 7 k + 5 = 8 j + 5 the only number in this range which satisfies this is 61 . 61 / 9 = 6 ( 9 ) + 7 the answer is d ."
Answer: d
Question (general): in a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 3 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ?
Options: a ) 63 , b ) 64.28 , c ) 65 , d ) 66 , e ) 68
Rationale: given : - violets - c / 3 carnations - c tulip - c / 9 rose - c / 9 total flowers in terms of c = c / 3 + c + c / 9 + c / 9 = 14 c / 9 percentage of carnations = c / 14 c / 9 * 100 = 64.28 % answer b
Answer: b
Question (general): a batsman scored 90 runs which included 4 boundaries and 6 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 500 / 11 , c ) 42.22 % , d ) 55 % , e ) 35 %
Rationale: "explanation : number of runs made by running , = > 90 − ( 4 × 4 + 6 × 6 ) . = > 90 − 52 = > 38 hence , the required percentage is : - = > 38 / 90 * 100 = > 42.22 % answer : c"
Answer: c
Question (physics): a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 9 : 30 am in the same direction at the rate of 84 km / h . at what time will the second train catch the first train ?
Options: a ) 11 : 00 , b ) 11 : 30 , c ) 12 : 00 , d ) 12 : 30 , e ) 1 : 00
Rationale: "in thirty minutes the first train travels 35 km . the second train catches the first train at a rate of 84 km / h - 70 km / h = 14 km / h . the second train will catch the first train in 35 / 14 = 2.5 hours , so at 12 : 00 noon . the answer is c ."
Answer: c
Question (general): two brother x and y appeared for an exam . the probability of selection of x is 1 / 5 and that of b is 2 / 7 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 30 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 5 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 5 ) ã — ( 2 / 7 ) = 2 / 35 answer : a ) 2 / 35"
Answer: a
Question (geometry): the volumes of two cones are in the ratio 1 : 30 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 6 : 5 , b ) 6 : 9 , c ) 6 : 2 , d ) 2 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 30 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 6 / 5 i . e . h 1 : h 2 = 6 : 5 answer : a"
Answer: a
Question (general): the average of runs of a cricket player of 10 innings was 42 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 86 , c ) 28 , d ) 76 , e ) 80
Rationale: "average after 11 innings = 46 required number of runs = ( 46 * 11 ) - ( 42 * 10 ) = 506 - 420 = 86 . answer : b"
Answer: b
Question (general): in a survey of parents , exactly 9 / 10 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 27 % , b ) 21 % , c ) 19 % , d ) 18 % , e ) 16 %
Rationale: "fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 10 * 2 / 5 = 2 / 50 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 2 / 50 = 19 / 100 = 19 % the answer is c ."
Answer: c
Question (general): cereal a is 8 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 2 , d ) 1 : 4 , e ) 1 : 3
Rationale: "( 8 / 100 ) a + ( 2 / 100 ) b = ( 4 / 100 ) ( a + b ) 4 a = 2 b = > a / b = 1 / 2 answer is c ."
Answer: c
Question (other): the ratio of boarders to day students at a school was originally 2 to 5 . however , after a number of new boarders join the initial 120 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90
Rationale: "let x be the number of new boarders . the ratio changed from 2 : 5 = 4 : 10 up to 1 : 2 = 5 : 10 . 120 / ( 120 + x ) = 4 / 5 x = 30 the answer is a ."
Answer: a