Cheukting/mathqa huggingface dataset:
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 280 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 240 , b ) 277 , c ) 276 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 280 ) / 26 = 20 x = 240 m . answer : a"
Answer: a
Question (geometry): a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 13 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1560 , c ) 2832 , d ) 1299 , e ) 1236
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 13 = 1560 answer : option b"
Answer: b
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 50 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 25 , d ) 88 , e ) 78
Rationale: "we have : l = 20 ft and lb = 50 sq . ft . so , b = 2.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 5 ) ft = 25 ft . answer : c"
Answer: c
Question (general): the average weight of 24 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 ) 48.975 , b ) 42.255 , c ) 50 , d ) 51.255 , e ) 52.253
Rationale: "explanation : average weight of 24 boys = 50.25 total weight of 24 boys = 50.25 × 24 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 × 24 ) + ( 45.15 × 8 ) total boys = 24 + 8 = 32 average weight of all the boys = ( 50.25 × 24 ) + ( 45.15 × 8 ) / 32 = 48.975 answer : option a"
Answer: a
Question (general): if ' y ' is a positive integer exactly divisible by 4 or 5 but not divisible by 8 . what could possibly be the value of ' y ' ?
Options: a ) 40 , b ) 80 , c ) 20 , d ) 24 , e ) 36
Rationale: 40 and 80 are both divisible by 4 and 5 but also by 8 . so they are not the right answer . 24 and 36 are both clearly not divisible by 5 ( not correct ) 20 is both divisible by 4 and 5 but not by 8 . answer : ( c )
Answer: c
Question (physics): two goods trains each 625 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 60 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 625 + 625 = 1250 m . required time = 1250 * 6 / 125 = 60 sec . answer : option d"
Answer: d
Question (general): how many figures are required to number the pages the pages of a book containing 1000 pages ?
Options: a ) 2793 , b ) 2333 , c ) 2993 , d ) 2893 , e ) 2693
Rationale: 1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 = 4 - - - - - - - - - - - 2893 answer : d
Answer: d
Question (gain): a merchant sells an item at a 20 % discount , but still makes a gross profit of 50 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 87.5 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.5 c ( 50 % profit ) x = 1.5 / . 8 * c x = 15 / 8 c original selling price is 1.875 c which is 87.5 % profit answer c"
Answer: c
Question (geometry): the diagonal of a rhombus are 65 m and 60 m . its area is :
Options: a ) 1940 , b ) 1950 , c ) 1960 , d ) 1990 , e ) 1980
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 × 65 × 60 ) cm ( power ) 2 = 65 × 30 = 1950 cm ( power ) 2 answer is b ."
Answer: b
Question (physics): a taxi company charges $ 1.40 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.40 for the first quarter - mile , we will have $ 3.50 left to spend on quarter - mile intervals . since $ 3.50 / $ 0.15 = 23.33 , we can buy 23.33 more quarter - miles , and will travel 24.33 quarter miles in all : 24.33 × 1 / 4 = 6 miles . the correct answer is choice ( e ) ."
Answer: e
Question (general): the difference between a number and its three - fifths is 50 . what is the number ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) can not be determined , e ) none of these
Rationale: "suppose the number is n . then n - 3 ⁄ 5 n = 50 ⇒ 2 n ⁄ 5 = 50 ∴ n = 50 × 52 = 125 answer . c"
Answer: c
Question (gain): john and david can finish a job together in 6 hours . if john can do the job by himself in 8 hours , what percent of the job does david do ?
Options: a ) 35 % , b ) 45 % , c ) 25 % , d ) 30 % , e ) 20 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 24 donuts which is the job ( i picked this as a smart number ) . john on his own works 24 / 8 = 3 donuts per hour . john and david work 24 / 6 = 4 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 6 hours = 6 donuts per hour . therefore 6 donuts / 24 donuts = 1 / 4 = 25 % answer : c"
Answer: c
Question (physics): a and b finish the job in 15 days . while a , b and c can finish it in 10 days . c alone will finish the job in
Options: a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days
Rationale: "explanation : 10 = ( 15 * x ) / ( 15 + x ) 150 + 10 x = 15 x 5 x = 150 x = 30 answer : option b"
Answer: b
Question (other): in what ratio should a variety of rice costing rs . 10 per kg be mixed with another variety of rice costing rs . 13.25 per kg to obtain a mixture costing rs . 10.75 per kg ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 5 : 1 , d ) 4 : 1 , e ) 3 : 1
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 13.25 - 10.75 ) / ( 10.75 - 10 ) = 6 / 3 = 2 / 1 answer : a"
Answer: a
Question (geometry): a 9 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 10 , e ) 4 / 11
Rationale: "the longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end . the probability of this is 2 / 9 . the answer is c ."
Answer: c
Question (general): the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 1 year ?
Options: a ) 3277 , b ) 2977 , c ) 30000 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 1 answer : c"
Answer: c
Question (general): the greatest number by which the product of 3 consecutive multiples of 4 is always divisible is
Options: a ) 54 , b ) 76 , c ) 152 , d ) 384 , e ) none of these
Rationale: solution required number = product of first three multiplies of 3 = ( 4 ã — 8 ã — 12 ) = 384 . answer d
Answer: d
Question (other): if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ? .
Options: a ) 25 , b ) 27 , c ) 45 , d ) 75 , e ) 125
Rationale: if both 5 ^ 2 & 3 ^ 3 are factors , then they must be present in the number . leaving rest of the prime factors and splitting 6 ^ 2 into 3 ^ 2 * 2 ^ 3 . the number is lacking 5 ^ 2 & a 3 , so that 5 ^ 2 and 3 ^ 3 is a factor . hence the smallest number is 5 ^ 2 * 3 = 75 answer : d
Answer: d
Question (gain): rajesh spends 40 % of his monthly salary on food , 20 % of the medicines and saves 60 % of the remaining amount . if his monthly salary is rs . 15000 , how much money does he save every month ?
Options: a ) rs . 1000 , b ) rs . 2596 , c ) rs . 4320 , d ) rs . 6489 , e ) rs . 4789
Rationale: explanation : ramesh ' s monthly income = rs . 15000 he spends 40 % on food . the total money spent on food = 40 / 100 * 15000 = rs . 6000 now , his monthly remaining income = rs . 15000 – rs . 6000 = rs . 9000 out of rs . 9000 , he spends 20 % on medicines . the total money spent on medicines = 20 / 100 * 9000 = rs . 1800 now , his monthly remaining income = rs . 9000 – rs . 1800 = rs . 7200 out of rs . 7200 , he saves 600 % . amount saved = 60 / 100 * 7200 = rs . 4320 answer : c
Answer: c
Question (general): the average ( arithmetic mean ) of 14 , 32 , and 53 is 3 more than the average of 21 , 47 , and x . what is x ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "the average of 14 , 32 , and 53 is 33 . the average of 21 , 47 and x is 30 . then 21 + 47 + x = 90 . x = 22 . the answer is c ."
Answer: c
Question (physics): how long does a train 165 meters long running at the rate of 36 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 72 , c ) 55 , d ) 82.5 , e ) 62
Rationale: "explanation : t = ( 660 + 165 ) / 36 * 18 / 5 t = 82.5 answer : option d"
Answer: d
Question (general): if √ 2 n = 64 , then the value of n is :
Options: a ) 6 , b ) 12 , c ) 24 , d ) 48 , e ) none
Rationale: sol . √ 2 n = 64 ⇔ ( 2 n ) 1 / 2 ⇔ 2 n / 2 = 26 ⇔ n / 2 = 6 ⇔ n = 12 . answer b
Answer: b
Question (general): a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4500 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 31500 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4500 = > total profit = 4500 * 7 = 31500 . answer : option c"
Answer: c
Question (general): robert ' s salary was decreased by 30 % and subsequently increased by 30 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 9 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 30 % = 100 - 100 x 30 / 100 = $ 70 salary after increasing 30 % on $ 70 = 70 + 70 x 30 / 100 = $ 91 percentage of loss = 100 - 91 = 9 % answer : b"
Answer: b
Question (general): 4 + 4
Options: a ) 8 , b ) 2 , c ) 1 , d ) 5 , e ) 2
Rationale: c
Answer: c
Question (general): the total age of a and b is 20 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 20 , b ) 12 , c ) 15 , d ) 16 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 20 a - c = 20 answer is a"
Answer: a
Question (physics): if 6 cats can kill 6 rats in 6 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 6 minutes
Rationale: "it will take 6 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 6 minutes , so 100 cats can kill 100 rats in 6 minutes answer e"
Answer: e
Question (general): what is the smallest integer that is multiple of 5 , 7,20
Options: a ) 70 , b ) 35 , c ) 200 , d ) 280 , e ) 140
Rationale: "it is the lcm of 5 , 7 and 20 which is 140 . the answer is e ."
Answer: e
Question (general): in the xy - coordinate system , what is the slope of the line that goes through the point ( 7 , 3 ) and is equidistant from the two points p = ( 5 , 5 ) and q = ( 13 , 7 ) ?
Options: a ) 0.5 , b ) 0.75 , c ) 1.0 , d ) 1.25 , e ) 1.5
Rationale: "first , get the middle coordinate between ( 5,5 ) and ( 13,7 ) . . . x = 5 + ( 13 - 5 ) / 2 = 9 y = 5 + ( 7 - 5 ) / 2 = 6 second , get the slope of ( 9,6 ) and ( 7,3 ) . m = 6 - 3 / 9 - 7 = 3 / 2 = 1.5 answer : e"
Answer: e
Question (general): if x is to be chosen at random from the integers between 1 to 7 , inclusive , and y is to be chosen at random from the integers between 8 and 12 , inclusive , what is the probability that x + y will be even ?
Options: a ) 2 / 5 , b ) 3 / 7 , c ) 5 / 7 , d ) 17 / 35 , e ) 24 / 35
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 7 * 3 / 5 = 9 / 35 p ( x and y are both odd ) = 4 / 7 * 2 / 5 = 8 / 35 p ( x + y is even ) = 9 / 35 + 8 / 35 = 17 / 35 the answer is d ."
Answer: d
Question (general): hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of 1 hammers and three wrenches is one - third that of 8 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 5 / 4 , e ) 2
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 1 x + 3 y ) = 1 / 3 * ( 8 x + 5 y ) 3 ( 1 x + 3 y ) = ( 8 x + 5 y ) 3 x + 9 y = 8 x + 5 y 4 y = 5 x y = 5 x / 4 ans - d"
Answer: d
Question (general): 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 175 kg then find the average weight of all the 7 rounds ?
Options: a ) 100 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 175 / 7 = 100 kgs answer : a"
Answer: a
Question (general): a jogger running at 9 km / hr along side a railway track is 360 m ahead of the engine of a 90 m long train running at 63 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 67 sec , c ) 30 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 63 - 9 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . distance to be covered = 360 + 90 = 450 m . time taken = 450 / 15 = 30 sec . answer : c"
Answer: c
Question (gain): if price of t . v set is reduced by 18 % , then its sale increases by 72 % , find net effect on sale value
Options: a ) 41 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 18 + 72 + ( - 18 * 72 ) / 100 = - 18 + 72 - 13 = 41 answer : a"
Answer: a
Question (other): teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 155 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 177.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 155 ) / \ x â ˆ ’ 155 22.50 = > x â ˆ ’ ( 155 / 22.50 ) = 1 . = > x â ˆ ’ 155 = 22.50 . = > x = 177.50 rs . answer : c"
Answer: c
Question (general): solution for 4.75 + . 303 + . 432
Options: a ) 2.91 , b ) 5.911 , c ) 5.485 , d ) 5.986 , e ) 2.999
Rationale: "4.75 + . 303 + . 432 = 0 0 = 0 - 4.75 - 0.303 - 0.432 0 = - 5.485 answer : c"
Answer: c
Question (general): what number is 70 more than one - fourth of itself ?
Options: a ) 93 , b ) 225 , c ) 288 , d ) 324 , e ) 336
Rationale: 1 / 4 x + 70 = x that means 70 = 3 / 4 x x = ( 70 * 4 ) / 3 = 280 / 3 = 93 a is the answer .
Answer: a
Question (general): 2 / 3 rd of the boys and 3 / 4 th of the girls of a school participate in a function . if the no . of participating students is 550 , out of which 150 are girls , what is the total no . of students in the school ?
Options: a ) 500 , b ) 600 , c ) 800 , d ) 900 , e ) 1200
Rationale: let total number of boys be x and total number of girls be y . y = 400 = > x = 600 and ^ = i 50 = > y = 200 now , x + y = 800 c
Answer: c
Question (physics): length of a rectangular plot is 30 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 65 m , d ) 78 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 30 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 30 ) + x ] = 200 2 x + 30 = 100 2 x = 70 x = 35 . hence , length = x + 30 = 65 m c"
Answer: c
Question (physics): a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5 hours , then the distance covered at 40 kmph is
Options: a ) 130 km , b ) 120 km , c ) 100 km , d ) 140 km , e ) none of these
Rationale: "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5 or , x / 40 + ( 250 - x ) / 60 = 5 or , ( 3 x + 500 - 2 x ) / / 120 = 5 or 500 + x = 600 x = 100 answer : c"
Answer: c
Question (gain): how many litres of pure acid are there in 5 litres of a 30 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.9
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 5 * 30 / 100 = 1.5 answer : option a
Answer: a
Question (other): in a college students can play cricket or basketball . 500 play cricket . 220 played both and 600 played basketball . what is the total strength of college ?
Options: a ) 800 , b ) 880 , c ) 920 , d ) 950 , e ) 980
Rationale: p ( c ) = 500 p ( b ) = 600 p ( c n b ) = 220 p ( c u b ) = p ( c ) + p ( b ) - p ( c n b ) = 500 + 600 - 220 = 880 answer : b
Answer: b
Question (general): if an average hard drive had a capacity of 0.2 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 5122 , c ) 768 , d ) 2048 , e ) 1536
Rationale: "0.2 * 2 ^ 10 = 0.2 * 1024 = 204.8 the answer is d ."
Answer: d
Question (general): the cricket team of 11 members is 24 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28
Rationale: "let the average age of the whole team be x years . 11 x - ( 24 + 27 ) = 9 ( x - 1 ) = > 11 x - 9 x = 42 = > 2 x = 42 = > x = 21 . so , average age of the team is 21 years . a"
Answer: a
Question (general): what is the least number . which should be added to 0.0320 to make it a perfect square ?
Options: a ) 0.0005 , b ) 0.0004 , c ) 0.0006 , d ) 0.0002 , e ) 0.0001
Rationale: 0.0320 + 0.0004 = 0.0324 ( 0.18 ) ^ 2 answer : b
Answer: b
Question (physics): a 21 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 6 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 21 = 6 answer : b"
Answer: b
Question (general): a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 340 . how much does c have ?
Options: a ) 50 , b ) 40 , c ) 267 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 340 - - - - - - - - - - - - - - a + b + 2 c = 540 a + b + c = 500 - - - - - - - - - - - - - - - - c = 40 answer : b"
Answer: b
Question (physics): light glows for every 15 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 381 , b ) 332 , c ) 383 , d ) 334 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 13 = 331 . so total 332 times light ll glow answer : b"
Answer: b
Question (general): the average age of 29 students in a group is 15 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 31 , b ) 36 , c ) 29 , d ) 53 , e ) 57
Rationale: age of the teacher = ( 29 * 16 - 29 * 15 ) = 29 years . answer : c
Answer: c
Question (geometry): find the perimeter of a triangle with sides measuring 5 centimeters , 20 centimeters and 30 centimeters .
Options: a ) 30 cm , b ) 40 cm , c ) 50 cm , d ) 55 cm , e ) 60 cm
Rationale: "perimeter of triangle = a + b + c perimeter = 5 cm + 20 cm + 30 cm = 55 cm answer : d ."
Answer: d
Question (general): in may mrs lee ' s earnings were 30 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 34 , b ) 67 , c ) 85 , d ) 25 , e ) 38
Rationale: "lets say the family income is 100 in may , lee earned 30 family income is 70 in june , lee earned 20 % more than may , so it is ( 30 + 20 * 30 / 100 = 36 ) family income is same 70 in june lee ' s income percent is 36 * 100 / 106 ~ 34 ans is a"
Answer: a
Question (gain): a and b invests rs . 6000 and rs . 9000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 82 : 31 , c ) 24 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 9000 * 6 ) + ( 6000 * 6 ) 48000 : 90000 24 : 45 answer : c"
Answer: c
Question (general): what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 8 ?
Options: a ) 4 , b ) 0 , c ) 2 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 8 , which yields remainder of 0 upon division by 8 . answer : b"
Answer: b
Question (general): if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 2 ] ] ?
Options: a ) 3 , b ) 9 , c ) 12 , d ) 19 , e ) 25
Rationale: these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 2 ] ] = 2 ^ 2 + 2 * 2 + 4 = 12 . option c
Answer: c
Question (gain): the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 13 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 11.81 % , e ) 11.50 %
Rationale: 13 = 1.1 * x x = 11.81 % answer d )
Answer: d
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 62000 ?
Options: a ) 81000 , b ) 78468.75 , c ) 81008 , d ) 81066 , e ) 81022
Rationale: "62000 * 9 / 8 * 9 / 8 = 78468.75 answer : b"
Answer: b
Question (general): if p ( a ) = 2 / 15 , p ( b ) = 7 / 15 , and p ( a â ˆ ª b ) = 16 / 15 find p ( a | b )
Options: a ) 1 / 2 , b ) 16 / 7 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a â ˆ ª b ) / p ( b ) p ( a | b ) = ( 16 / 15 ) / ( 7 / 15 ) = 16 / 7 . b"
Answer: b
Question (physics): tanks m and b are each in the shape of a right circular cylinder . the interior of tank m has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank m is what percent of the capacity of tank b ?
Options: a ) 75 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: b . for m , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi m / b = 160 pi / 200 pi = 0.8
Answer: b