Cheukting/mathqa huggingface dataset:
Question (general): the price of 2 saris and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) rs . 2400 , b ) rs . 2490 , c ) rs . 2500 , d ) rs . 2550 , e ) rs . 2600
Rationale: let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . a
Answer: a
Question (other): two numbers are in ratio 4 : 5 and their lcm is 180 . the smaller number is
Options: a ) 9 , b ) 15 , c ) 36 , d ) 45 , e ) none
Rationale: solution : let two numbers be 4 x and 5 x ; their lcm = 180 and hcf = x ; now , 1 st number * 2 nd number = lcm * hcf or , 4 x * 5 x = 180 * x ; or , 20 x = 180 ; or , x = 9 ; then , the smaller number = 4 * 9 = 36 . answer : option c
Answer: c
Question (physics): how many cubes of 25 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 177 cm
b ) 100 cm
c ) 86 cm
d ) 64 cm
e ) 87 cm
Rationale: number of cubes = 100 â ˆ — 100 â ˆ — 100 / 25 â ˆ — 25 â ˆ — 25 = 64 note : 1 m = 100 cm answer : d
Answer: d
Question (physics): if an object travels at two feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 3778 , c ) 7200 , d ) 1800 , e ) 2881
Rationale: "explanation : if an object travels at 2 feet per second it covers 2 x 60 feet in one minute , and 2 x 60 x 60 feet in one hour . answer = 7200 answer : c ) 7200"
Answer: c
Question (physics): an apple orchard grows red and green apples . on the first day of harvest , 496 apples are collected . there are 3 times as many red apples as there are green apples . how many green apples were harvested ?
Options: a ) 99 , b ) 112 , c ) 118 , d ) 124 , e ) 130
Rationale: let x be the number of green apples . there were 496 total apples ; there are three times as many red apples as green apples . therefore , x + 3 x = 496 4 x = 496 x = 124 answer : d
Answer: d
Question (general): what is the tenth digit to the right of the decimal point , in the decimal expansion of ( 1 / 5 ) ^ 10
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: actually 1 / 5 = 0.2 = 2 * 10 ^ - 1 so 2 ^ 10 * 10 ^ - 10 2 has sequence 24 , 86 . hence digit will be 4 answer is c
Answer: c
Question (other): 100 liters of a mixture contains milk and water in the ratio 7 : 3 . 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 : 8 , b ) 8 : 3 , c ) 3 : 8 , d ) 8 : 7 , e ) 7 : 1
Rationale: "quantity of milk in 100 liters if mix = 100 * 7 / 10 = 70 liters quantity of milk in 110 liters of new mix = 80 + 10 = 80 liters quantity of water in it = 110 - 80 = 30 liters ratio of milk and water in new mix = 80 : 30 = 8 : 3 answer is b"
Answer: b
Question (other): two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 16 : 5 , b ) 14 : 5 , c ) 16 : 7 , d ) 19 : 5 , e ) none of these
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres as 6 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5 . answer : d"
Answer: d
Question (other): a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 36 / 49 . how many marbles are in the bag ?
Options: a ) 24 , b ) 48 , c ) 84 , d ) 72 , e ) 80
Rationale: ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 36 / 49 - - > ( x - 12 ) ^ 2 = 36 / 49 x ^ 2 square rooting u have x - 12 / x = 6 / 7 or 7 x - 6 x = 84 or x = 84 c
Answer: c
Question (general): 288 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 32 , d ) 39 , e ) 43
Rationale: "explanation : 288 ã · ? ã — 15 = 405 - 270 = 135 ( 288 ã — 15 ) / ? = 135 ? = ( 288 ã — 15 ) / 135 = 32 answer : option c"
Answer: c
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 7 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 7 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 2 = 160 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 2 = 10 . thus there are 160 - 10 = 150 such numbers . answer : b ."
Answer: b
Question (general): a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 8 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 89.60 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80
Rationale: "correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.08 ( $ 1120 ) = $ 89.60 . the correct answer is b ."
Answer: b
Question (general): what is the remainder of g = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , g = when divided by 10 , the remainder must be 7 . d"
Answer: d
Question (other): what is the value of ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) ?
Options: a ) 1 / 6 , b ) 2 , c ) 5 / 2 , d ) 6 , e ) 32
Rationale: using the identity ( loga b ) ( logb c ) = loga c repeatedly , we obtain ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) = log 2 64 = 6 correct answer d
Answer: d
Question (geometry): how many 2 x 2 x 2 cubes could fit in a box of 7 x 9 x 4 ?
Options: a ) 31 , b ) 32 , c ) 30 , d ) 33 , e ) 29
Rationale: the answer is a ) 31 . a 2 x 2 x 2 cube has an area of 8 . a 7 x 9 x 4 box has an area of 252 . if you divide 252 by 8 , you get 31.5 . since that means you can only fit 31 entire cubes in the box , the answer is 31 .
Answer: a
Question (gain): by selling a book for 300 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 250 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 300 × 100 / 120 = 250 option ' b '"
Answer: b
Question (physics): the h . c . f . of two numbers is 15 and their l . c . m . is 420 . if one of the numbers is 375 , then the other is :
Options: a ) 12.21 , b ) 283 , c ) 16.8 , d ) 318 , e ) 32.4
Rationale: "other number = ( 15 x 420 ) / 375 = 16.8 . answer : c"
Answer: c
Question (general): what is the sum of all the multiples of 10 between 0 and 85 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 360 , e ) 440
Rationale: "the multiples of 10 between 0 and 85 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 . if these are all added together , the result is 360 . final answer : d"
Answer: d
Question (general): find large number from below question the difference of two no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1456 , b ) 1563 , c ) 1546 , d ) 1643 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Question (general): if | x + 2 | = 10 , what is the sum of all the possible values of x ?
Options: a ) - 16 , b ) - 13 , c ) - 4 , d ) - 2 , e ) 12
Rationale: "there will be two cases x + 2 = 10 or x + 2 = - 10 = > x = 8 or x = - 12 sum of both the values will be - 12 + 8 = - 4 answer : c"
Answer: c
Question (general): in a group of cows and chickens , the number of legs was 18 more than twice the number of heads . the number of cows was :
Options: a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 18 more than twice the number of heads . therefore , 2 × ( x + y ) + 18 = 4 x + 2 y . or , 2 x + 2 y + 18 = 4 x + 2 y . or , 2 x + 18 = 4 x [ subtracting 2 y from both sides ] . or , 18 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 18 = 2 x . or , x = 9 [ dividing by 2 on both sides ] . therefore , the number of cows = 9 . correct answer : c ) 9"
Answer: c
Question (physics): before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 3.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 42 , d ) 2 , e ) 30
Rationale: pete covered 3.5 * 60 = 210 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 210 = 1 / 42 . answer : c .
Answer: c
Question (general): what least number should be subtracted from 642 so that the remainder when divided by 5 , 7 , and 9 will leave in each case the same remainder 4 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "the lcm of 5 , 7 , and 9 is 315 . the next multiple is 2 * 315 = 630 . 630 + { remainder } = 630 + 4 = 634 , which is 8 less than 642 . answer : c ."
Answer: c
Question (physics): 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 6 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 14 m / h - - > 7 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 7 ^ 2 d ^ 2 = 65 = ~ 8 answer option c"
Answer: c
Question (physics): a train 250 m long running at 72 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 150 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 20 = 400 â € “ 250 = 150 m answer : a"
Answer: a
Question (gain): raman ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he loss .
Options: a ) 75 , b ) 65 , c ) 45 , d ) 25 , e ) 85
Rationale: explanation : let the origianl salary = rs . 100 it will be 150 % of ( 50 % of 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = 75 so new salary is 75 , it means his loss is 25 % option d
Answer: d
Question (general): if 80 % of a number is equal to four - third of another number , what is the ratio of first number to the second number ?
Options: a ) 5 : 3 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 80 % of a = 4 / 3 b then 80 a / 100 = 4 b / 3 4 a / 5 = 4 b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is a"
Answer: a
Question (physics): two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 11 minutes , b ) 17 minutes , c ) 18 minutes , d ) 10 minutes , e ) 16 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 45 = ( 5 + 6 - 2 ) / 90 = 9 / 90 = 1 / 10 so , the tank becomes full in 10 minutes . answer : d :"
Answer: d
Question (general): 223.124 x 11.98 ã · 6.001 + 11.11 = ?
Options: a ) 983.578 , b ) 459.121 , c ) 781.189 , d ) 656.112 , e ) 457.358
Rationale: "explanation : ? = 223.124 x 11.98 ã · 6.001 + 11.11 â ‰ ˆ ( 223.124 x 12 / 6 ) + 11.11 â ‰ ˆ 446.248 + 11.11 â ‰ ˆ 457.358 answer : option e"
Answer: e
Question (physics): pipe p can fill a tank in 6 hours , pipe q in 12 hours and pipe r in 24 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 2.4 hours , c ) 3 hours , d ) 3.4 hours , e ) 4.5 hours
Rationale: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 6 + 1 / 12 + 1 / 24 ) = 7 / 24 all the three pipes together will fill the tank = 24 / 7 = 3.4 hours answer d"
Answer: d
Question (general): 4 friends , peter , john , quincy , and andrew , are pooling their money to buy a $ 1200 item . peter has twice as much money as john . quincy has $ 20 more than peter . andrew has 15 % more than quincy . if they put all their money together and spend the $ 1200 , they will have $ 11 left . how much money does peter have ?
Options: a ) $ 320 , b ) $ 160 , c ) $ 200 , d ) $ 410 , e ) $ 325
Rationale: p = 2 j ; q = p + 20 ; a = 1.15 ( q ) p + j + q + r - 1200 = 11 p + 0.5 p + p + 20 + 1.15 ( p + 20 ) = 1211 p + 0.5 p + p + 20 + 1.15 p + 23 = 1211 p + 0.5 p + p + 1.15 p + 43 = 1211 p + 0.5 p + p + 1.15 p = 1168 3.65 p = 1168 p = 320 answer : a
Answer: a
Question (physics): a man travelled from the village to the post - office at the rate of 25 kmph and walked back at the rate of 4 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village
Options: a ) 20 , b ) 87 , c ) 276 , d ) 198 , e ) 171
Rationale: explanation : average speed = ( 2 × a × b ) / ( a + b ) here a = 25 b = 4 average speed = 2 × 25 × 4 / ( 25 + 4 ) = 200 / 29 kmph . distance covered in 5 hours 48 minutes = speed × time distance = ( 200 / 29 ) × ( 29 / 5 ) = 40 kms distance covered in 5 hours 48 minutes = 40 kms distance of the post office from the village = ( 40 / 2 ) = 20 km . answer : a
Answer: a
Question (general): 893.7 – 573.07 – 95.007 = ?
Options: a ) 225.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 893.7 - ( 573.07 + 95.007 ) = 893.7 - 668.077 = 225.623 . answer a"
Answer: a
Question (physics): one man traveled a distance of 61 km in 9 hrs . he traveled partly on footat 4 km / hr and partly on bicycle ta 9 km / hr . the distance traveled on foot is ?
Options: a ) 11 km , b ) 13 km , c ) 16 km , d ) 18 km , e ) 19 km
Rationale: let the distance travelled on foot be x km . then , distance travelled on bicycle = ( 61 - x ) km . so , x + ( 61 - x ) = 9 4 9 9 x + 4 ( 61 - x ) = 9 x 36 5 x = 80 x = 16 km . c
Answer: c
Question (gain): ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 64500 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 17.3 , d ) 99 , e ) 88
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 64500 profit ( % ) = ( 64500 - 55000 ) / 55000 * 100 = 17.3 % answer : c"
Answer: c
Question (general): in the coordinate plane , points ( x , 3 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 3 / 5 , then x + y =
Options: a ) 9 , b ) 8 , c ) 7 , d ) 5 , e ) 6
Rationale: "line k passes through the origin and has slope 3 / 5 means that its equation is y = 3 / 5 * x . thus : ( x , 3 ) = ( 3 , 5 ) and ( 5 , y ) = ( 3 , 5 ) - - > x + y = 3 + 5 = 8 . answer : b"
Answer: b
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 30 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 14.28 %
Rationale: "0.1 m = 0.70 e = > e / m = 1 / 7 * 100 = 14.28 % so answer is e . m - # of motorists e - # of motorists exceeding speed"
Answer: e
Question (probability): a question paper has 2 parts , a & b , each containing 6 questions . if a student has to choose 4 from part a & 3 from part b , in how many ways can he choose the questions ?
Options: a ) 100 , b ) 200 , c ) 350 , d ) 150 , e ) 140
Rationale: "there 6 questions in part a out of which 4 question can be chosen as = 6 c 4 . similarly , 3 questions can be chosen from 6 questions of part b as = 6 c 3 . hence , total number of ways , = 6 c 4 * 6 c 3 = [ 6 ! / ( 2 ! 4 ! ) ] * [ 6 ! / ( 3 ! * 3 ! ) ] = { 15 } * { 6 * 5 * 4 * 3 / ( 3 * 2 * 1 ) } = 300 . d"
Answer: d
Question (other): a man invests some money partly in 12 % stock at 132 and partly in 10 % stock at 80 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 11 : 8 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 12 % stock at 132 , investment = rs . ( 132 / 12 ) = rs . 11 . for an income of rs . 1 in 10 % stock at 80 , investment = rs . ( 80 / 10 ) = rs . 8 . ∴ ratio of investments = 11 : 8 = 11 : 8 answer c"
Answer: c
Question (general): george baked a total of 150 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2
Rationale: "3 / 5 of the 150 pizzas cooked on saturday = 90 pizzas 3 / 5 of the remaining pizzas on sunday = 36 pizzas we ' re left with ( 150 - 90 - 36 ) = 24 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 8 7 6 2 1 = 24 w = 6 b"
Answer: b
Question (physics): a train 200 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : c . speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 200 m at 50 / 3 m / sec = 200 * 3 / 50 sec = 12 sec"
Answer: c
Question (general): at veridux corporation , there are 200 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 65
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 200 â € “ 90 = 110 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 200 â € “ 40 = 160 must be associates . now , in the â € œ associate â €  row , 135 + e = 160 , which means e = 25 â € ” the other 25 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 25 = 90 , which means b = 65 . there are fifteen female managers in this company . thus , the answer = ( e ) ."
Answer: e
Question (general): find the value of ( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: "( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) 11 / 9 + 12 / 7 = > ( 77 + 108 ) / 63 = > 185 / 63 answer is e ."
Answer: e
Question (general): the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 49 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 49 has the form 4 k + 1 , so the units digit of 93 ^ 49 is 3 . the units digit of powers of 5 is always 5 . 3 + 5 = 8 , so the units digit is 8 . the answer is d ."
Answer: d
Question (geometry): a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 2 , 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π , b ) 15.25 π , c ) 262 √ π , d ) 52 π , e ) 64 π
Rationale: "the distance between the two points is sqrt ( 61 ) . radius = sqrt ( 61 ) / 2 area = pi * ( sqrt ( 61 ) / 2 ) ^ 2 b . 15.25 π"
Answer: b
Question (gain): if the cost price of 20 articles is equal to the selling price of 15 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 33.33 % profit , c ) 20 % loss , d ) 20 % profit , e ) 5 % profit
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 20 articles = 20 * 1 = $ 20 the selling price of 15 articles = cost price of 20 articles = $ 15 . now , we know the selling price of 15 articles . let us find the cost price of 15 articles . cost price of 15 articles = 15 * 1 = $ 15 . therefore , profit made on sale of 15 articles = selling price of 15 articles - cost price of 15 articles = 20 - 15 = $ 5 . as the profit is in the positive , the merchant has made a profit of $ 5 . therefore , % loss = loss / cp * 100 % loss = 5 / 15 * 100 = 33.33 % profit . b"
Answer: b
Question (general): how many positive integers less than 255 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 43 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 42 , as all the other choices are very far away . the numbers 244 and 248 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice d is correct here .
Answer: d
Question (general): if 2 x + y = 10 , 2 y + z = 20 and 2 x + z = 30 . where x , y , and z are real number . what is the value of 2 x ?
Options: a ) 3 / 2 , b ) sqrt ( 15 ) , c ) sqrt ( 6 ) / 2 , d ) 15 , e ) 18
Rationale: "explanation : let , 2 x = a , 2 y = b and 2 z = c then from the question : 2 x + y = 2 x * 2 y = ab = 10 similarly , bc = 20 , ac = 30 ab / bc = 1 / 2 = > a / c = 1 / 2 and ac = 30 ( a / c ) * ac = 1 / 2 * 30 = 15 a = sqrt ( 15 ) answer : b"
Answer: b
Question (gain): in a factory , there are 50 % technicians and 50 % non - technicians . if the 50 % of the technicians and 50 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 50 % , b ) 57 % , c ) 52 % , d ) 22 % , e ) 42 %
Rationale: "total = 100 t = 50 nt = 50 50 * ( 50 / 100 ) = 25 50 * ( 50 / 100 ) = 25 25 + 25 = 50 = > 100 - 50 = 50 % answer : a"
Answer: a