Cheukting/mathqa huggingface dataset:
Question (physics): the length of a room is 6.5 m and width is 2.75 m . what is the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre .
Options: a ) rs . 18725 , b ) rs . 16725 , c ) rs . 30725 , d ) rs . 10725 , e ) rs . 20725
Rationale: "area = 6.5 * 2.75 sq . metre . cost for sq . metre . = rs . 600 hence , total cost = 6.5 * 2.75 * 600 = rs . 10725 answer : d"
Answer: d
Question (general): the number of diagonals of a polygon of n sides is given by the formula v = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "v = n ( n - 3 ) v = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Question (general): what is the least common multiple of 12,27 and 40
Options: a ) 8521 , b ) 1080 , c ) 368 , d ) 8979 , e ) 6584
Rationale: "factors of 12 = 2 * 2 * 3 factors of 27 = 3 * 3 * 3 factors of 40 = 2 * 2 * 2 * 5 thus the l . c . m is 2 ^ 3 * 3 ^ 3 * 5 = 1080 the answer is b"
Answer: b
Question (physics): saturn travels around the sun at an approximate speed of 5.82 miles per second . this speed is how many kilometers per hour ? ( 1 km = 0.6 miles )
Options: a ) 30,560 , b ) 31,650 , c ) 32,740 , d ) 33,830 , e ) 34,920
Rationale: the speed is 5.82 miles / s . then 5.82 / 0.6 = 9.7 km / s 9.7 * 3600 = 34,920 kph the answer is e .
Answer: e
Question (general): total 30 cows 10 cow gives each 2 liter milk 10 cow gives each 3 / 4 liter milk 10 cow gives each 1 / 4 liter milk this is split into 3 son per each 10 cows & 10 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "10 cow 2 liter each = 20 liter 10 cow 3 / 4 liter each = 3 / 4 = 0.758 * 10 = 7.5 10 cow 1 / 4 liter each = 1 / 4 = 0.25 * 10 = 2.5 add 20 + 7.5 + 2.5 = 30 milk split into 3 son each 10 liter then 30 / 3 = 10 answer : a"
Answer: a
Question (gain): if 15 % of 30 % of 50 % of a number is 108 , then what is the number ?
Options: a ) 4000 , b ) 3050 , c ) 4400 , d ) 4800 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 108 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 108 = > a = 10 * 20 * 10 * 2 = 4800 . answer : d"
Answer: d
Question (general): andy solves problems 75 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 52 , c ) 51 , d ) 50 , e ) 49
Rationale: "125 - 75 + 1 = 51 ' c ' is the answer"
Answer: c
Question (physics): if a boat goes 7 km upstream in 42 minutes and the speed of the stream is 6 kmph , then the speed of the boat in still water is
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) none of these
Rationale: explanation : rate upstream = ( 7 / 42 ) * 60 kmh = 10 kmph . speed of stream = 6 kmph . let speed in still water is x km / hr then , speed upstream = ( x ï ¿ ½ 6 ) km / hr . x - 6 = 10 or x = 16 kmph answer : e
Answer: e
Question (physics): a worker earns $ 20 on the first day and spends $ 15 on the second day . the worker earns $ 20 on the third day and spends $ 15 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 80 ?
Options: a ) 24 , b ) 25 , c ) 27 , d ) 30 , e ) 32
Rationale: "every two days , the net total is $ 5 . after 24 days , the worker will have $ 60 . on day 25 , the worker will receive $ 20 for a net total of $ 80 . the answer is b ."
Answer: b
Question (other): 6 ) a marketing firm determined that , of 260 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 45
Rationale: "180 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 180 = > 4 x = 120 = > x = 30 answer - c"
Answer: c
Question (physics): 26 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 39 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 26 ã — 13.5 = 351 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 351 â  „ 9 = 39 answer b"
Answer: b
Question (physics): a train is running at a speed of 40 km / hr and it crosses a post in 22.5 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 22.5 s distance covered , d = vt = ( 400 / 36 ) ã — 22.5 = 250 m distance covered is equal to the length of the train = 250 m correct answer is 250 metres e"
Answer: e
Question (gain): at a florist shop on a certain day , all corsages sold for either $ 20 or $ 30 . if 10 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 20 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 500 , d ) $ 800 , e ) $ 1000
Rationale: "let , no . of corsages @ $ 20 = x , no . of corsages @ $ 30 = y and revenue = r so , 20 x + 30 y = r . . . . . . . . . ( 1 ) now , given the situation , 20 ( x + 10 ) + 30 ( y - 10 ) = r - . 2 r = > 20 x + 200 + 30 y - 300 = . 8 r = > 20 x + 30 y = . 8 r + 100 . . . . . . . . . . . . ( 2 ) so , r = . 8 r + 100 = > r = 500 the answer is c ."
Answer: c
Question (physics): it is currently 8 : 12 pm . at what time in the morning was it exactly 205,106 minutes ago ?
Options: a ) 9 : 14 , b ) 9 : 16 , c ) 9 : 42 , d ) 9 : 44 , e ) 9 : 46
Rationale: convert 205,106 minutes to hours by dividing by 60 : 205,106 / 60 = 3,418 r 26 . that is 3,418 hours and 26 minutes . convert 3,418 hours to days by dividing by 24 : 3,418 / 24 = 142 r 10 . that is 142 days and 10 hours . now , 142 days previous was 8 : 12 pm . another 10 hours previous was 10 : 12 am . another 26 minutes previous was 9 : 46 am ( subtract the 12 minutes of 10 : 12 from 26 to get 14 . then subtract 14 from 60 to get 46 ) . e
Answer: e
Question (geometry): a circular ground whose diameter is 70 metres , has a 2.8 metre - broad garden around it . what is the area of the garden in square metres ?
Options: a ) 540.72 , b ) 740.64 , c ) 640.64 , d ) 620.45 , e ) 725.26
Rationale: "req . area = ï € [ ( 37.8 ) 2 â € “ ( 35 ) 2 ] = 22 â  „ 7 ã — ( 72.8 ã — 2.8 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = 22 ã — 72.8 ã — 0.4 = 640.64 sq m answer c"
Answer: c
Question (other): a 70 kg metal bar made of alloy of tin and silver lost 7 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 7 kg when 70 kg alloy is immersed . this is a loss of ( 7 / 70 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Question (gain): what is the rate percent when the simple interest on rs . 720 amount to rs . 180 in 4 years ?
Options: a ) 6.25 , b ) 7.25 , c ) 8.25 , d ) 9.25 , e ) 10.25
Rationale: "180 = ( 720 * 4 * r ) / 100 r = 6.25 % answer : a"
Answer: a
Question (general): when 242 is divided by a certain divisor the remainder obtained is 15 . when 698 is divided by the same divisor the remainder obtained is 27 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?
Options: a ) 11 , b ) 17 , c ) 13 , d ) 23 , e ) 37
Rationale: let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27 . now 242 - 15 = 227 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 27 = 671 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 227 + 671 ) + 15 + 27 = x ( k + l ) + 42 when we divide this number by x then remainder will be equal to remainder of ( 42 divided by x ) = 5 hence x = 42 - 5 = 37 hence e
Answer: e
Question (general): if 25 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 4 : 3 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 25 % of a = 1 / 3 b then 25 a / 100 = 1 b / 3 a / 4 = b / 3 a / b = 4 / 3 a : b = 4 : 3 answer is a"
Answer: a
Question (general): gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 15 times as heavy as water ?
Options: a ) 3 : 2 , b ) 3 : 8 , c ) 5 : 7 , d ) 3 : 7 , e ) 3 : 6
Rationale: "let us say , water weighs 1 kg / 1 liter . then gold weighs 19 kgs and copper weighs 9 kgs . assume x kgs of gold and y kgs of copper required to get the required alloy . we use weighted average formula = ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 therefore , 15 = x . 19 + y . 9 x + y 15 = x . 19 + y . 9 x + y 15 x + 15 y = 19 x + 9 y 4 x = 6 y ⇒ x / y = 3 : 2 so gold and copper should be mixed in the ratio 3 : 2 . answer : a"
Answer: a
Question (physics): find the cost of fencing around a circular field of diameter 32 m at the rate of rs . 2 a meter ?
Options: a ) 201 , b ) 132 , c ) 772 , d ) 592 , e ) 261
Rationale: "2 * 22 / 7 * 16 = 100.5 100.5 * 2 = rs . 201 answer : a"
Answer: a
Question (general): how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 40 percent alcohol ?
Options: a ) 7 / 2 , b ) 5 , c ) 100 / 3 , d ) 8 , e ) 39 / 4
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 40 % of ( 100 + x ) or 20 + x = ( 100 + x ) 2 / 5 100 + 5 x = 200 + 2 x 3 x = 100 x = 100 / 3 ans : c"
Answer: c
Question (general): a bookseller has two display windows . she plans to display 3 new fiction books in the left window , and 3 new non - fiction books in the right window . assuming she can put the 4 fiction books in any order , and separately , the 3 non - fiction books in any order , how many total configurations will there be for the two display windows ?
Options: a ) 24 , b ) 72 , c ) 144 , d ) 36 , e ) 420
Rationale: the left window will have permutations of the 3 fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 the right window will have permutations of the 3 non - fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 any of the 24 displays of the left window could be combined with any of the 6 displays of the right window , so the total number of configurations is 6 * 6 = 36 answer : d .
Answer: d
Question (general): find a two digit number , given that the sum of the digits is 11 and the difference of the digits is 5 . ?
Options: a ) 78 , b ) 53 , c ) 89 , d ) 83 , e ) 99
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 83 meets this description sum of digits - - - 8 + 3 = 11 difference of digits - - - 8 - 3 = 5 answer d ."
Answer: d
Question (general): what is the remainder when 43 ^ 87 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 87 has the form 4 k + 3 so the units digit of 43 ^ 87 is 7 . the remainder when dividing by 5 is 2 . the answer is c ."
Answer: c
Question (physics): if julie rows 32 km upstream and 72 km down steam taking 4 hours each , then the speed of the stream
Options: a ) 1.5 kmph , b ) 0.5 kmph , c ) 0.4 kmph , d ) 1.6 kmph , e ) 2.5 kmph
Rationale: speed upstream = 32 / 4 = 8 kmph speed down stream = 72 / 8 = 9 kmph speed of stream = ½ ( 9 - 8 ) = 0.5 kmph answer : b
Answer: b
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of odd all the integers between 10 and 100 ?
Options: a ) 1345 , b ) 1576 , c ) 2475 , d ) 2578 , e ) 1895
Rationale: "numbers are 11 , 13,15 - - - - - - - , 97,99 average of the set : ( largest + smallest ) / 2 = ( 99 + 11 ) / 2 = 55 ; # of terms : ( largest - smallest ) / 2 + 1 = ( 99 - 11 ) / 2 + 1 = 45 the sum = 45 * 55 = 2475 answer : c"
Answer: c
Question (other): two numbers are in the ratio of 7 : 6 . if 18 be subtracted from each , they are in the ratio of 6 : 5 . find the numbers ?
Options: a ) 5,9 , b ) 7,9 , c ) 4,7 , d ) 7,6 , e ) 6,9
Rationale: "( 7 x - 18 ) : ( 6 x - 18 ) = 6 : 5 x = 1 = > 7,6 answer : d"
Answer: d
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 / 7 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 ) 11 / 30 , b ) 29 / 42 , 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 / 7 x = 6 / 7 x so if gold card balance is transferred then the rest unspent will be 6 / 7 x - x / 6 = 29 / 42 x so the ans is b"
Answer: b
Question (general): of all the homes on gotham street , 1 / 3 are termite - ridden , and 4 / 7 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: "the fraction of homes which are termite - infested but not collapsing is 3 / 7 * 1 / 3 = 1 / 7 the answer is e ."
Answer: e
Question (general): if the average ( arithmetic mean ) of x + 2 , x + 3 , and x + 4 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 2 + x + 3 + x + 4 ) / 3 = 0 = > 3 x + 9 = 0 = > x = - 3 answer b"
Answer: b
Question (general): 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 6
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 35 , e ) 2 ^ 7
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 answer e"
Answer: e
Question (general): 54671 - 14456 - 31466 = ?
Options: a ) 2449 , b ) 5449 , c ) 8749 , d ) 8449 , e ) 6468
Rationale: "c if we calculate we will get 8749"
Answer: c
Question (general): what is the minimum value of | x - 4 | + | x + 5 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 10
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 5 | > = 0 - - > minimum occurs at x = - 5 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 5 - - > result = 9 + 0 + 10 = 19 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 9 + 1 = 10 x = 5 - - > result = 1 + 10 + 0 = 11 so minimum value of the expression occurs at x = 4 and the resultant value = 10 answer : e"
Answer: e
Question (physics): sravan travelled for 15 hours . he covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph . find the distance travelled by sravan ?
Options: a ) 520 , b ) 540 , c ) 550 , d ) 560 , e ) 440
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 45 + ( x / 2 ) / 30 = 15 = > x / 90 + x / 60 = 15 = > ( 2 x + 3 x ) / 180 = 15 = > x = 540 km answer : b
Answer: b
Question (physics): 50 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 100 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 50 = 66.67 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 66.67 = 100 litres . answer c"
Answer: c
Question (general): a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 10 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 18.25 , b ) 20.75 , c ) 22.25 , d ) 24.25 , e ) 26.75
Rationale: "let x be the length of the size 8 shoe . then 0.1 x = 9 / 4 x = 90 / 4 inches the size 15 shoe has a length of 90 / 4 + 7 / 4 = 97 / 4 = 24.25 inches the answer is d ."
Answer: d
Question (physics): a student travels from his house to school at 10 km / hr and reaches school 2 hours late . the next day he travels 18 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
Options: a ) 65.0 , b ) 67.5 , c ) 70.0 , d ) 72.5 , e ) 75.0
Rationale: "let x be the distance from his house to the school . x / 10 = x / 18 + 3 9 x = 5 x + 270 4 x = 270 x = 67.5 km the answer is b ."
Answer: b
Question (general): excluding stoppages , the average speed of a bus is 75 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 28 min
Rationale: "in 1 hr , the bus covers 75 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 75 - 40 ) km i . e 35 km at 75 km / hr . stoppage time = 35 / 75 hrs = 28 min answer : e"
Answer: e
Question (geometry): find the area of a parallelogram with base 26 cm and height 16 cm ?
Options: a ) 297 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 416 cm 2 , e ) 286 cm 2
Rationale: "area of a parallelogram = base * height = 26 * 16 = 416 cm 2 answer : d"
Answer: d
Question (gain): by selling an article at rs . 600 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 360 , b ) s . 480 , c ) s . 500 , d ) s . 450 , e ) s . 550
Rationale: "sp = 600 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / 125 ] = 480 loss = 25 % = 25 % of 480 = rs . 120 sp = cp - loss = 480 - 120 = rs . 360 answer : a"
Answer: a
Question (other): a man invests some money partly in 15 % stock at 105 and partly in 8 % stock at 40 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 7 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 15 % stock at 105 , investment = rs . ( 105 / 15 ) = rs . 7 . for an income of rs . 1 in 8 % stock at 40 , investment = rs . ( 40 / 8 ) = rs . 5 . ∴ ratio of investments = 7 : 5 = 7 : 5 answer c"
Answer: c
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 600 per sq . metre .
Options: a ) rs . 12375 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 600 × 20.625 ) = 12375 . answer a"
Answer: a
Question (gain): a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 15,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 4,500 , c ) s . 5,700 , d ) s . 6,500 , e ) s . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 15000 x 3 / 10 = rs . 4,500 . b"
Answer: b
Question (general): if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 14 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: @ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 14 . then 4 n < 14 and n < 3.5 . the largest possible integer is n = 3 . the answer is c .
Answer: c
Question (general): if x ^ 2 – 4 x = 5 , then one possible value of x – 2 =
Options: a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 5
Rationale: "x ^ 2 – 4 x = 5 i . e . x ^ 2 – 4 x - 5 = 0 i . e . x ^ 2 – 5 x + x - 5 = 0 i . e . ( x - 5 ) ( x + 1 ) = 0 i . e . x = 5 or - 1 i . e . x - 2 = 5 - 2 or - 1 - 2 i . e . x - 2 = 3 or - 3 answer : option c"
Answer: c
Question (physics): if 9 workers can build 9 cars in 9 days , then how many days would it take 7 workers to build 7 cars ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "9 workers can build 1 car per day on average . 1 worker can build 1 / 9 of a car per day . 7 workers can build 7 / 9 car per day . the time required to build 7 cars is 7 / ( 7 / 9 ) = 9 days the answer is d ."
Answer: d
Question (other): the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.20 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.55 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 20 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : c"
Answer: c
Question (general): a bakery has 6 employees . it pays annual salaries of $ 19,000 to each of 2 employees , $ 21,000 to 1 employee , and $ 22,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 20,200 , b ) $ 20,500 , c ) $ 20,800 , d ) $ 21,000 , e ) $ 21,400
Rationale: average = 2 ( 19000 ) + ( 21000 ) + 3 ( 22000 ) / 6 = $ 20,833 the answer is c .
Answer: c
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 300 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ?
Options: a ) 65 , b ) 13.42 , c ) 18 , d ) 16 , e ) 14
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 300 / 5 = 60 sq m l b = 60 i . e . , l * l / 3 = 60 l 2 = 180 = > l = 13.42 answer : b"
Answer: b
Question (gain): the s . i . on a certain sum of money for 5 years at 10 % per annum is half the c . i . on rs . 5000 for 2 years at 12 % per annum . the sum placed on s . i . is ?
Options: a ) 1585 , b ) 1454 , c ) 1656 , d ) 2458 , e ) 1272
Rationale: c . i . = [ 5000 * ( 1 + 12 / 100 ) 2 - 5000 ] = ( 5000 * 28 / 25 * 28 / 25 - 5000 ) = rs . 1272 . sum = ( 636 * 100 ) / ( 5 * 10 ) = rs . 1272 answer : e
Answer: e