Cheukting/mathqa huggingface dataset:
Question (gain): a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 50 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: 50 % is 10 % - points above 40 % and 30 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 3 : 1 . so the team played a total of 30 + 10 = 40 games . the answer is a .
Answer: a
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 29.85 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 16 ) = 76 cm parameter of the square = 76 cm i . e . 4 a = 76 a = 19 diameter of the semicircle = 19 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 19 ) = 1 / 2 ( 22 / 7 ) ( 19 ) = 418 / 14 = 29.85 cm to two decimal places answer : d"
Answer: d
Question (other): the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 9 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 5 , b ) 1 : 6 , c ) 1 : 7 , d ) 1 : 8 , e ) 1 : 9
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 5 : 9 , thus the smaller number must have a ratio of 1 . the ratio of the smaller number to the larger number is 1 : 9 . the answer is e ."
Answer: e
Question (general): if | 5 x - 10 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 3 , d ) - 3 , e ) 4
Rationale: "| 5 x - 10 | = 100 5 x - 10 = 100 or 5 x - 10 = - 100 5 x = 110 or 5 x = - 90 x = 22 or x = - 18 sum = 21 - 18 = 3 answer is c"
Answer: c
Question (physics): a is twice as good a workman as b and together they finish a piece of work in 18 days . in how many days will a alone finish the work ?
Options: a ) 31 days , b ) 25 days , c ) 27 days , d ) 29 days , e ) 19 days
Rationale: "if a takes x days to do a work then b takes 2 x days to do the same work . - - > 1 / x + 1 / 2 x = 1 / 18 - - > 3 / 2 x = 1 / 18 - - > x = 27 days . hence , a alone can finish the work in 27 days . answer : c ."
Answer: c
Question (physics): it takes avery 2.5 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 15 minutes . , b ) 30 minutes . , c ) 1 hour and 30 minutes . , d ) 1 hour and 40 minutes , e ) 2 hours
Rationale: "avery ' s efficiency is 100 / 2.5 = 40 % tom ' s = 100 / 5 = 20 % they worked together for 1 hour and finished 60 % of the job remaining = 40 % tom will complete 20 % in 60 minutes , 40 % in 120 minutes time taken by tom to finish the remaining on his own = 120 minutes answer : e"
Answer: e
Question (gain): a , b and c invests rs . 4000 , rs . 2000 and rs . 6000 in a business . after one year a removed his money ; b and c continued the business for two more year . if the net profit after 3 years be rs . 3300 , then a ' s share in the profit is ?
Options: a ) 6000 , b ) 4000 , c ) 2000 , d ) 600 , e ) 300
Rationale: 4 * 12 : 2 * 36 : 4 * 36 2 : 3 : 6 2 / 11 * 3300 = 600 answer : d
Answer: d
Question (general): the avg weight of a , b & c is 80 kg . if d joins the group , the avg weight of the group becomes 82 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 81 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 95
Rationale: a + b + c = 3 * 80 = 240 a + b + c + d = 4 * 82 = 328 - - - - ( i ) so , d = 88 & e = 88 + 3 = 91 b + c + d + e = 81 * 4 = 324 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 328 – 324 = 4 a = e + 4 = 91 + 4 = 95 answer : e
Answer: e
Question (geometry): the base of a triangle is 15 cm and height is 12 cm . the height of another triangle of double the area having the base 20 cm is :
Options: a ) 22 cm
b ) 20 cm
c ) 18 cm
d ) 10 cm
e ) none of these
Rationale: explanation : area of triangle , a 1 = 1 / 2 ∗ base ∗ height = 1 / 2 ∗ 15 ∗ 12 = 90 cm 2 area of second triangle = 2 ∗ a 1 = 180 cm 2 1 / 2 ∗ 20 ∗ height = 180 = > height = 18 cm option c
Answer: c
Question (geometry): rectangular tile each of size 20 cm by 30 cm must be laid horizontally on a rectangular floor of size 100 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 40 , b ) 15 , c ) 25 , d ) 32 , e ) 45
Rationale: "area of tile = 20 * 30 = 600 area of floor = 100 * 150 = 15000 no of tiles = 15000 / 600 = 25 so , the no of tile = 25 answer : c"
Answer: c
Question (gain): 5000 was divided into two parts such a way that when first part was invested at 3 % and the second at 5 % , the whole annual interest from both the investments is rs . 144 , how much was put at 3 % ?
Options: a ) 10600 , b ) 11600 , c ) 12600 , d ) 10680 , e ) 20600
Rationale: "( x * 3 * 1 ) / 100 + [ ( 5000 - x ) * 5 * 1 ] / 100 = 144 3 x / 100 + ( 25000 – 5 x ) / 100 = 144 = > x = 10600 answer : a"
Answer: a
Question (general): if x is 30 percent more than y and y is 40 percent less than z , then x is what percent of z ?
Options: a ) 78 % , b ) 250 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %
Rationale: "z = 100 ; y = 60 so x = 78 x as % of z = 78 / 100 * 100 = > 78 % answer will be ( a )"
Answer: a
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 12 seconds . find the length of the train .
Options: a ) 150 , b ) 278 , c ) 179 , d ) 200 , e ) 191
Rationale: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 12 = 200 meter answer : d"
Answer: d
Question (general): if y > 0 , ( 7 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 7 y / 20 + 6 y / 20 = 13 y / 20 = 65 % answer c"
Answer: c
Question (gain): the value of a machine depreciates at 21 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 257615 , b ) $ 437615 , c ) $ 127615 , d ) $ 117615 , e ) $ 157615
Rationale: "the value of the machine after two years = 0.79 * 0.79 * 1 , 50,000 = $ 96,000 sp such that a profit of $ 24,000 is made = 93,615 + 24,000 = $ 1 , 17,615 d"
Answer: d
Question (gain): what is the cp of rs 100 stock at 9 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 91.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 9 + 1 / 5 91.2 thus the cp is rs 91.2 . answer : c"
Answer: c
Question (physics): the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 8000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,000
Rationale: x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 8000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 8000 ) * t = = = > 3 d = ts + 8000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 8000 t - 2 d = - 2 st + 8000 t 2 d = 2 st - 8000 t d = st - 4000 t x 13 : d = s * t st - 4000 t = s * t s - 4000 = s - 2000 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 8000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 8000 2 = 4000 d = s * t d = 4000 * ( 1 / 2 ) d = 2000 answer : e
Answer: e
Question (general): the average of 15 numbers is 75 . average of the first 8 of them is 68 and that of the last 8.00001 is 77 . find the 8.000001 th number ?
Options: a ) 51 , b ) 87 , c ) 35 , d ) 75 , e ) 68
Rationale: sum of all the 15 numbers = 15 * 75 = 1,125 sum of the first 8 of them = 8 * 68 = 544 sum of the last 8 of them = 8 * 77 = 616 so , the 8 th number = 544 + 616 - 1,125 = 35 . answer : c
Answer: c
Question (physics): a train covers a distance of 12 km in 10 minutes . if it takes 5 seconds to pass a telegraph post , then the length of the train is
Options: a ) 110 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 100 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 5 ) m = 100 m answer : option e"
Answer: e
Question (general): mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 48456 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) none of these
Rationale: ∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 48456 ⁄ 12 = 4038 answer a
Answer: a
Question (general): what is the sum of all the multiples of 10 between 0 and 100 ?
Options: a ) 500 , b ) 620 , c ) 550 , d ) 340 , e ) 440
Rationale: "the multiples of 10 between 0 and 100 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 and 100 . if these are all added together , the result is 550 . final answer : c"
Answer: c
Question (geometry): the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 336 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 336 , 2 ( 7 / 5 ) w + 2 w = 336 solve the above equation to find : w = 70 m and l = 98 m . correct answer c ) 70"
Answer: c
Question (gain): difference of two numbers is 1650 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2490 , 4150 , e ) 2475 , 4125
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1650 5 * y / 3 – y = 1650 2 * y / 3 = 1650 y = [ ( 1650 * 3 ) / 2 ] = 2475 . one number = 2475 , second number = 5 * y / 3 = 4125 . answer e ."
Answer: e
Question (general): a certain no . when divided by 140 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 11
Rationale: "explanation : 140 + 25 = 165 / 15 = 11 ( remainder ) e"
Answer: e
Question (physics): a room of 6 m 00 cm long and 8 m 00 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 12 , b ) 200 , c ) 600 , d ) 800 , e ) 20
Rationale: "explanation : area of the room = 600 * 800 sq cm size of largest square tile = h . c . f of 600 cm and 800 cm = 200 cm area of 1 tile = 200 * 200 sq cm no . of tiles required = ( 600 * 800 ) / ( 200 * 200 ) = 12 answer : a ) 12"
Answer: a
Question (gain): an inspector rejects 0.07 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2857 , d ) d ) 3000 , e ) e ) 3100
Rationale: "let the number of meters to be examined be x then , 0.07 % of x = 2 ( 7 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 2857 answer is c"
Answer: c
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 154 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 176.50 , 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 . 154 ) / \ x â ˆ ’ 154 22.50 = > x â ˆ ’ ( 154 / 22.50 ) = 1 . = > x â ˆ ’ 154 = 22.50 . = > x = 176.50 rs . answer : c"
Answer: c
Question (general): mother , her daughter and her grand child weighs 110 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 110 kg daughter + child = 60 kg mother = 110 - 60 = 50 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 50 = 10 kg so now daughter = 110 - ( mother + child ) = 110 - ( 50 + 10 ) = 50 kg answer : e"
Answer: e
Question (general): in a simultaneous throw of a pair of dice , find the probability of getting a total more than 10
Options: a ) 5 / 13 , b ) 2 / 15 , c ) 1 / 12 , d ) 3 / 17 , e ) 6 / 19
Rationale: "total number of cases = 6 * 6 = 36 favourable cases = [ ( 5,6 ) ( 6,5 ) , ( 6,6 ) ] = 3 so probability = 3 / 36 = 1 / 12 answer is c"
Answer: c
Question (general): when a student joe , weighing 42 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5.5 kg , b ) 6 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg
Rationale: after two persons leave the group the average remains the same . that means the weight of the two persons = 42 + 30 = 72 so , the average the two persons = 36 that gives the answer 42 - 36 = 6 answer b
Answer: b
Question (general): the sum of two numbers is 44 . 5 times one number is equal to 6 times the other . the smaller of the two numbers is
Options: a ) 10 , b ) 12 , c ) 16 , d ) 22 , e ) 20
Rationale: sol . let the numbers be x and ( 44 - x ) . then , 5 x = 6 ( 44 - x ) ⇔ 11 x = 264 ⇔ x = 24 . so , the numbers are 24 and 20 . answer e
Answer: e
Question (physics): youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 4 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 6 , c ) 10 , d ) 15 , e ) 20
Rationale: "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 240 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 240 - - - - > 40 x = 240 - - > x = 6 option b"
Answer: b
Question (physics): a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 5 days . b can do the work alone in ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 30 , e ) 114
Rationale: suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 5 6 / x = 1 / 5 = > x = 30 so , b takes 15 hours to finish the work . answer : d
Answer: d
Question (geometry): the mass of 1 cubic meter of a substance is 200 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: 200 kg - 1 cubic meter ; 200,000 g - 1 cubic meter ; 200,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 200,000 = 10 / 2 = 5 cubic centimeters . answer : e .
Answer: e
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 244 ft , b ) 88 ft , c ) 122 ft , d ) 178 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 8 x breadth = 680 breadth = 85 feet area to be fenced = 2 b + l = 2 ( 85 ) + 8 = 178 feet answer : d ) 178 ft"
Answer: d
Question (physics): a train 400 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 77 kmph , c ) 54 kmph , d ) 71 kmph , e ) 90 kmph
Rationale: "s = 400 / 16 * 18 / 5 = 90 kmph answer : e"
Answer: e
Question (physics): ravi can do a piece of work in 50 days while prakash can do it in 75 days . in how many days will they finish it together ?
Options: a ) 30 days , b ) 35 days , c ) 25 days , d ) 27 days , e ) 29 days
Rationale: 1 / 50 + 1 / 75 = 5 / 150 30 / 1 = 30 days answer : a
Answer: a
Question (other): the marks obtained by polly and sandy are in the ratio 3 : 5 and those obtained by sandy and willy are in the ratio of 5 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 2 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 4 , e ) 6 : 5
Rationale: "polly : sandy = 3 : 5 sandy : willy = 5 : 2 polly : sandy : willy = 3 : 5 : 2 polly : willy = 3 : 2 the answer is b ."
Answer: b
Question (gain): add 10 % of 30 and 15 % of 50 .
Options: a ) 9.5 , b ) 10.5 , c ) 11.5 , d ) 12 , e ) 15
Rationale: "10 % of 30 + 15 % of 50 30 * 10 / 100 + 50 * 15 / 100 3 + 7.5 = 10.5 answer b"
Answer: b
Question (geometry): smita was making a cube with dimensions 5 * 5 * 5 using 1 * 1 * 1 cubes . what is the number of cubes needed to make a hollow cube looking of the same shape ?
Options: a ) 98
b ) 104
c ) 100
d ) 61
e ) 51
Rationale: cube use to make perfect 5 * 5 * 5 = 125 no need of cube to make hollow = ( 5 - 2 ) * ( 5 - 2 ) * ( 5 - 2 ) = 27 so total cube need to make hollow cube is = 125 - 27 = 98 answer : a
Answer: a
Question (general): the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 50 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 50 * 5 = 250 lowest is 40 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 40 = 160 . on the fifth day it is 250 - 160 = 90 range is therefore 90 - 40 = 50 answer d"
Answer: d
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 36 , what is the total amount ?
Options: a ) 166 , b ) 140 , c ) 178 , d ) 177 , e ) 169
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 36 35 - - - ? = > 140 answer : b"
Answer: b
Question (gain): a retailer sold 2 houses at each $ 10000 . on 1 st house he got 30 % profit and on 2 nd house he loss 10 % then find his net profit or loss ?
Options: a ) 15 % , b ) 17 % , c ) 21 % , d ) 19 % , e ) 25 %
Rationale: a = 30 % b = - 10 % profit % = 30 - 10 + ( - 300 / 100 ) = 17 % answer is b
Answer: b
Question (general): the remainder when e = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . + 3 ^ 200 is divided 13 .
Options: a ) 12 , b ) 7 , c ) 0 , d ) 5 , e ) 3
Rationale: e = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . . . . . . . . . + 3 ^ 200 is a geometric progression having common ratio as ' 3 ' and number of terms as ' 201 ' . since sum to n terms in gp = a ( r ^ n - 1 ) / ( r - 1 ) where a = first term and r = common ration hence , 1 * ( 3 ^ 201 - 1 ) / ( 3 - 1 ) rem of ( 3 ^ 201 - 1 ) / 2 divided by 13 3 ^ 201 - 1 / 26 wkt , 3 ^ 3 = 27 = 26 + 1 { ( 26 + 1 ) ^ 67 - 1 } / 26 { 1 - 1 } / 26 = > 0 . c
Answer: c
Question (gain): today joelle opened an interest - bearing savings account and deposited $ 6000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 6715 , b ) $ 5615 , c ) $ 6415 , d ) $ 6615 , e ) $ 6315
Rationale: interest for 1 st year = 6000 * 5 / 100 = 300 interest for 2 nd year = 6300 * 5 / 100 = 315 total = 6000 + 300 + 315 = 6615 answer : d
Answer: d
Question (physics): a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 196 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 196 km time taken = distance / speed = 196 / 28 = 7 hours answer : option e"
Answer: e
Question (physics): a train 900 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 200 m , b ) 379 m , c ) 400 m , d ) 589 m , e ) 600 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 900 + x ) / 60 = 65 / 3 x = 400 m . answer : c"
Answer: c
Question (gain): jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 54,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 54,000 i . e . rs . 27,000 answer : a"
Answer: a
Question (physics): 600 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 15 , b ) 11 , c ) 10 , d ) 8 , e ) 7
Rationale: "600 * 20 = 800 * x x = 15 . answer : a"
Answer: a
Question (other): the hcf of two numbers is 52 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 624 , b ) 450 , c ) 480 , d ) 504 , e ) 555
Rationale: "explanation : hcf of the two numbers = 52 hcf will be always a factor of lcm 52 is factor of lcm other two factors are 11 & 12 then the numbers are ( 52 * 11 ) and ( 52 x 12 ) = 572 and 624 answer : option a"
Answer: a