Cheukting/mathqa huggingface dataset:
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1245 , find the loss % ?
Options: a ) 17 % , b ) 16 % , c ) 19 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 255 100 - - - - ? = > 17 % answer : a"
Answer: a
Question (gain): a person buys an article at $ 500 . at what price should he sell the article so as to make a profit of 20 % ?
Options: a ) 560 , b ) 449 , c ) 600 , d ) 740 , e ) 460
Rationale: "c 600 cost price = $ 500 profit = 20 % of 500 = $ 100 selling price = cost price + profit = 500 + 100 = 600"
Answer: c
Question (gain): ramu bought an old car for rs . 36400 . he spent rs . 8000 on repairs and sold it for rs . 68400 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 18 % , d ) 54 % , e ) 13 %
Rationale: "total cp = rs . 36400 + rs . 8000 = rs . 44400 and sp = rs . 68400 profit ( % ) = ( 68400 - 44400 ) / 44400 * 100 = 54 % answer : d"
Answer: d
Question (gain): i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a gain ?
Options: a ) a ) 657 , b ) b ) 200 , c ) c ) 438 , d ) d ) 290 , e ) e ) 427
Rationale: "x = price of a book sold at loss x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 price of book sold at gain = 480 - 280 = 200 answer : b"
Answer: b
Question (physics): a ladder 25 m long reaches a window of building 20 m above the ground . then the distance of the foot of the ladder from the building is ?
Options: a ) 35 m , b ) 45 m , c ) 30 m , d ) 15 m , e ) 25 m
Rationale: let it forms a right angled triangle and follow c ^ 2 = a ^ 2 + b ^ 2 then 25 ^ 2 = 20 ^ 2 + b ^ 2 b ^ 2 = 625 - 400 b = 15 answer : d
Answer: d
Question (general): when positive integer n is divided by positive integer j , the remainder is 10 . if n / j = 134.08 , what is value of j ?
Options: a ) 125 , b ) 56 , c ) 78 , d ) 112 , e ) 175
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 10 so , 134.08 = 134 + 10 / j so , j = 125 ans a"
Answer: a
Question (general): when positive integer n is divided by positive integer j , the remainder is 18 . if n / j = 204.03 , what is value of j ?
Options: a ) 600 , b ) 200 , c ) 400 , d ) 800 , e ) 1000
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.03 here 204 is the quotient . given that remainder = 18 so , 204.03 = 204 + 18 / j so , j = 600 answer : a"
Answer: a
Question (general): if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 4 + 8 = ?
Options: a ) 125 , b ) 126 , c ) 127 , d ) 128 , e ) 129
Rationale: 2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 4 ^ 3 + 8 ^ 2 = 128 answer : d
Answer: d
Question (gain): a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 30 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.4 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 6 hours ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.3 ( 6 ) = 1.8 gallons at the start , the amount of water is 0.7 ( 6 ) = 4.2 gallons after 6 hours , the amount of water is 4.2 - 0.4 ( 6 ) = 1.8 gallons the concentration of water is 1.8 / ( 1.8 + 1.8 ) = 1.8 / 3.6 = 50 % the answer is e ."
Answer: e
Question (gain): by selling 20 pencils for a rupee a man loses 35 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 14 , e ) 10
Rationale: 65 % - - - 20 130 % - - - ? 65 / 130 * 20 = 10 answer : e
Answer: e
Question (general): 1804 x 1804 = ?
Options: a ) a ) 3254416 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1804 x 1804 = ( 1804 ) 2 = ( 1800 + 4 ) 2 = ( 1800 ) 2 + ( 4 ) 2 + ( 2 x 1800 x 4 ) = 3240000 + 16 + 14400 . = 3254416 . a )"
Answer: a
Question (gain): in order to obtain an income of rs . 500 from 30 % stock at rs . 90 , one must make an investment of
Options: a ) rs . 1550 , b ) rs . 1430 , c ) rs . 1450 , d ) rs . 1400 , e ) rs . 1500
Rationale: "explanation : market value = rs . 90 required income = rs . 500 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 30 ( ie , 30 % of the face value 100 ) , investment = rs . 90 to obtain rs . 15000 , investment = 90 / 30 ã — 500 = rs . 1500 answer : option e"
Answer: e
Question (general): if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Question (general): the value of ( 2.502 + 0.064 ) ^ 2 - ( 2.502 - 0.064 ) ^ 2 / 2.502 * 0.064
Options: a ) . 25 , b ) . 235 , c ) 4 , d ) 3 , e ) 2
Rationale: "( 2.502 + 0.064 ) 2 - ( 2.502 - 0.064 ) 2 / 2.502 * 0.064 = ( a + b ) 2 - ( a - b ) / ab = 4 ab / ab = 4 answer : c"
Answer: c
Question (general): a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 320 . how much does c have ?
Options: a ) 50 , b ) 78 , c ) 267 , d ) 20 , e ) 27
Rationale: a + b + c = 500 a + c = 200 b + c = 320 - - - - - - - - - - - - - - a + b + 2 c = 520 a + b + c = 500 - - - - - - - - - - - - - - - - c = 20 answer : d
Answer: d
Question (general): what is 10 - 8 + 6 - 4 + . . . + ( - 18 ) ?
Options: a ) - 8 , b ) 10 , c ) 12 , d ) - 4 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 18 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , - 14 , - 16 , and - 18 . now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) + ( - 14 ) - ( - 16 ) + ( - 18 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 = 58 - 62 = - 4 hence the correct answer choice is d ."
Answer: d
Question (physics): car a runs at the speed of 70 km / hr & reaches its destination in 10 hr . car b runs at the speed of 35 km / h & reaches its destination in 10 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 11 : 8 , c ) 13 : 7 , d ) 15 : 7 , e ) 2 : 1
Rationale: "sol . distance travelled by car a = 70 × 10 = 700 km distance travelled by car b = 35 × 10 = 350 km ratio = 700 / 350 = 2 : 1 answer : e"
Answer: e
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 50 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 120 , c ) 140 , d ) 147 , e ) 98
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 50 t t = 2.8 distance travelled by car x from the time car y began traveling until both cars stopped is 35 x 2.8 = 98 miles answer : - e"
Answer: e
Question (physics): a and b together can do a work in 4 days . if a alone can do it in 14 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 6 , c ) 77 , d ) 55 , e ) 21
Rationale: 1 / 4 – 1 / 12 = 1 / 6 = > 6 answer : b
Answer: b
Question (general): sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 6 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 2 / 3 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 6 x = 5 / 6 x so if gold card balance is transferred then the rest unspent will be 5 / 6 x - x / 6 = 2 / 3 x so the ans is a"
Answer: a
Question (other): find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 2 = 2 / 1 = 2 : 1 answer is b"
Answer: b
Question (physics): city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 5 : 30 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 7 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 5 : 30 pm + 2 hrs = 7 : 30 pm answer : b . 7 : 30
Answer: b
Question (geometry): the perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 87 cm 2 , b ) 28 cm 2 , c ) 98 cm 2 , d ) 26 cm 2 , e ) 40 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 32 / 2 = 40 cm 2 answer : e"
Answer: e
Question (physics): you cook a pot of beef stew for you and your roommate . normally it lasts 7 days between the two of you . if 3 guests are now staying with you and your roommate , how many days will the beef stew now last if everyone eats it ?
Options: a ) 2.8 , b ) 1 , c ) 3.5 , d ) 14 , e ) 1.6
Rationale: first set up a ratio with all the relevant values and also the unknown variable : 2 * 7 = 5 * x now solve by multiplying 2 by 7 and then dividing that product by 5 : 2 * 7 = 14 14 / 5 = x x = 2.8 the value of x represents the amount of days a bot of beef stew will last for 5 total people . answer : a
Answer: a
Question (physics): a person can swim in still water at 12 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 10 km ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 2 us = 12 - 2 = 10 d = 10 t = 10 / 10 = 1 answer : a"
Answer: a
Question (physics): a train running at the speed of 54 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 135 , b ) 278 , c ) 255 , d ) 150 , e ) 287
Rationale: "speed = ( 54 * 5 / 18 ) m / sec = ( 15 ) m / sec length of the train = ( speed x time ) = ( 15 * 9 ) m = 135 m . answer : a"
Answer: a
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 44 kg , then the weight of b is :
Options: a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 34 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 44 x 2 ) = 88 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 168 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 33 . b ’ s weight = 33 kg . answer : c"
Answer: c
Question (other): the duplicate ratio of 3 : 4 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 9 : 16 , e ) 1 : 13
Rationale: "3 ^ 2 : 4 ^ 2 = 9 : 16 answer : d"
Answer: d
Question (gain): in the first 15 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 35 overs to reach the target of 275 runs ?
Options: a ) 5.55 , b ) 6.25 , c ) 6.75 , d ) 7.02 , e ) 6.48
Rationale: required run rate = 275 - ( 3.2 x 15 ) / 35 = 227 / 35 = 6.48 option e
Answer: e
Question (general): a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 1800 in january , how many cars does he need to sell in february in order to double his january earnings ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: 1000 + 200 x = 3600 x = 13 cars . the answer is a .
Answer: a
Question (physics): the area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is ?
Options: a ) 7 , b ) 7.67 , c ) 8.75 , d ) 8.98 , e ) 8.28
Rationale: "( 4 * 3.5 ) / 2 = 7 answer : a"
Answer: a
Question (physics): working alone , a can complete a certain kind of job in 12 hours . a and d , working together at their respective rates , can complete one of these jobs in 4 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "let total time taken by s to complete the job = s total time taken by a to complete the job = 12 work done by a in an hour 1 / a = 1 / 12 working together a and d can complete the job in 4 hours 1 / a + 1 / d = 1 / 4 = > 1 / d = 1 / 4 - 1 / 12 = 1 / 4 - 1 / 12 = 1 / 6 = > d = 6 hours answer d"
Answer: d
Question (geometry): the perimeter of a triangle is 35 cm and the inradius of the triangle is 4.5 cm . what is the area of the triangle ?
Options: a ) 22 , b ) 75 , c ) 78 , d ) 54 , e ) 23
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 4.5 * 35 / 2 = 78.75 cm 2 answer : c"
Answer: c
Question (general): a ’ s speed is 22 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 22 , b ) 1 / 19 , c ) 3 / 19 , d ) 2 / 19 , e ) 3 / 22
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 22 meters , b covers 19 meters in that time . so if the race is 22 meters long , when a reaches the finish line , b would be 3 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 3 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 22 meters ) would be the same as the time required by b ( to cover 19 meters ) to reach the finish line . so b should get a head start of 3 / 22 th of the race . answer ( e )"
Answer: e
Question (general): the average weight of 8 girls increases by 3 kg when a new girl comes in place of one of them weighing 70 kg . what might be the weight of the new girl ?
Options: a ) 94 kg , b ) 95 kg , c ) 96 kg , d ) 97 kg , e ) 98 kg
Rationale: total weight increased = 8 x 3 kg = 24 kg . weight of new person = 70 + 24 kg = 94 kg answer : a
Answer: a
Question (general): if t = 5 / 9 * ( k - 32 ) , and if t = 35 , then what is the value of k ?
Options: a ) 92 , b ) 95 , c ) 98 , d ) 101 , e ) 104
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 35 ) / 5 + 32 = 95 the answer is b ."
Answer: b
Question (physics): from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 6 kilometers per hour , while ferry q takes a route that is two times longer . if ferry p is slower than ferry q by 3 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the distance traveled by ferry p is 18 km . then the distance traveled by ferry q is 36 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 36 / 9 = 4 hours , which is 1 hour more than ferry p . the answer is a ."
Answer: a
Question (general): 48.95 - 32.006 = ?
Options: a ) 16.089 , b ) 16.35 , c ) 16.89 , d ) 16.944 , e ) none of them
Rationale: "48.950 - 32.006 - - - - - - - - - 16.944 answer is d"
Answer: d
Question (gain): the effective annual rate of interest corresponding to a nominal rate of 8 % per annum payable half - yearly is ?
Options: a ) 6.06 % , b ) 8.16 % , c ) 6.08 % , d ) 6.09 % , e ) 6.19 %
Rationale: amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 4 / 100 ) 2 ] = rs . 108.16 effective rate = ( 108.16 - 100 ) = 8.16 % answer : b
Answer: b
Question (general): a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 50 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 10 * 4 = 40 now half on their horses so remaining on the walk so 5 men 5 men has 10 legs so , 10 + 40 = 50 legs walking answer : a"
Answer: a
Question (general): 15.06 * 0.0000001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 1.506 e - 06 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 9 digits should be there . option c"
Answer: c
Question (physics): if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 60 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 24 and 60 ) so : 240 = 80 * t 1 = 3 hrs 240 = 24 * t 2 = 10 hrs 240 = 60 * t 3 = 4 hrs t = t 1 + t 2 + t 3 = 17 hrs d = rt ( 240 * 3 ) = r * 17 r = 42.35 answer : c"
Answer: c
Question (general): in 1990 the budgets for projects q and v were $ 540000 and $ 780000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30000 and the budget for v was decreased by $ 10000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: let the no of years it takes is x . 540 + 30 x = 780 - 10 x - - > 40 x = 240 and x = 6 . thus , it happens in 1996 . e .
Answer: e
Question (gain): a shopkeeper sells 500 metres of cloth for rs . 15000 at a loss of rs . 10 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 40 , b ) s . 12 , c ) s . 96 , d ) s . 50 , e ) s . 13
Rationale: "sp per metre = 15000 / 500 = rs . 30 loss per metre = rs . 10 cp per metre = 30 + 10 = rs . 40 answer : a"
Answer: a
Question (geometry): a larger cube has 216 cubic inch as a volume and in the cube there are 216 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 216 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 64 , c ) 81 , d ) 1080 , e ) 120
Rationale: "volume of larger cube = 216 = 6 ^ 3 side of larger cube = 6 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 6 ^ 2 = 216 surface area of 27 smaller cubes = 216 * 6 * 1 = 1296 difference = 1296 - 216 = 1080 answer : d"
Answer: d
Question (general): in a colony the municipality decided to number the houses and the shops . they want to number the shops with the numbers containing 3 between 1 - 100 . the houses are 10 - 20 floored and at the back of the houses 8 feet is left for fire exit . how many shops can be numbered ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: 3 numbers containing 3 - - - > 3 , 1323 , . . . = 10 numbers - - - - > 30 , 3132 . . . = 10 numbers total = 20 - 1 = 19 answer : a
Answer: a
Question (general): a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 196 what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 12 , c ) 8 , d ) 2 , e ) 4
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 = 64 3 x + 4 y = 196 x = 64 - y 3 ( 64 - y ) + 4 y = 196 192 - 3 y + 4 y = 196 y = 4 answer : e"
Answer: e
Question (general): the average ( arithmetic man ) of 3 integers a , b , and c is exactly half the median . if a < b < c and a = 0 , what is the value of c / b ?
Options: a ) 2 , b ) 3 / 2 , c ) 4 , d ) 5 , e ) can not be determined from the information given .
Rationale: the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 1 b / 2 - - > since a = 0 , then ( 0 + b + c ) / 3 = 1 b / 2 - - > c = 3 b / 2 - - > c / b = 3 / 2 . answer : b .
Answer: b
Question (general): in a room with 10 people , 7 people have exactly 1 friend in the room and 6 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 49 / 45
Rationale: "( 7 / 10 ) ( 8 / 9 ) + ( 6 / 10 ) ( 7 / 9 ) if you choose one of the 7 with one other friend , then you have a 8 / 9 chance of not picking their friend 2 nd . if you choose one of the 6 with 2 friends , you have a 7 / 9 chance of not picking one of their friends second . add them up . 56 / 90 + 42 / 90 98 / 90 = 49 / 45 e . 49 / 45"
Answer: e
Question (physics): dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 46 of gas ?
Options: a ) 124 , b ) 256 , c ) 368 , d ) 424 , e ) 512
Rationale: "46 / 4 = 11.5 gallons 11.5 * 32 = 368 miles the answer is c ."
Answer: c
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 6 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 6 / 16 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 6 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 6 / 5 = 6 - - > total time for both of them would be 10 + 6 = 16 - - > deluxe / total = 6 / 16 . answer : a ."
Answer: a