Cheukting/mathqa huggingface dataset:
Question (physics): the length of the bridge , which a train 145 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 230 m , c ) 245 m , d ) 250 m , e ) 270 m
Rationale: "let the length of the bridge : l the equation now is l + 145 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 230 m answer : b"
Answer: b
Question (geometry): how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 135 , b ) 125 , c ) 120 , d ) 110 , e ) 140
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 19 - 1 then 18 * ( 18 - 3 ) / 2 = 135 correct option : a"
Answer: a
Question (other): sachin is younger than rahul by 7 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ?
Options: a ) 22.5 years , b ) 24.5 years , c ) 12.5 years , d ) 28.5 years , e ) 29.5 years
Rationale: "let rahul ' s age be x years . then , sachin ' s age = ( x - 7 ) years . therefore ( x - 7 ) / x = 7 / 9 9 x - 63 = 7 x 2 x = 63 x = 31.5 hence , sachin ' s age = ( x - 7 ) = 24.5 years . answer : b"
Answer: b
Question (physics): a train running at the speed of 72 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 279 , c ) 277 , d ) 272 , e ) 180
Rationale: "speed = 72 * 5 / 18 = 20 m / sec length of the train = speed * time = 20 * 9 = 180 m answer : e"
Answer: e
Question (general): find the 12 th term of an arithmetic progression whose first term is 2 and the common difference is 8 .
Options: a ) 45 , b ) 38 , c ) 44 , d ) 90 , e ) 96
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 2 + ( 12 - 1 ) * 8 , = 2 + 88 = 90 . answer : d"
Answer: d
Question (general): a set consists of 20 numbers , all are even or multiple of 5 . if 9 numbers are even and 12 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 20 = 9 + 12 - { both } + 0 ; { both } = 1 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : b ."
Answer: b
Question (general): united telephone charges a base rate of $ 6.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 20 minutes , b ) 110 minutes , c ) 120 minutes , d ) 140 minutes , e ) 160 minutes
Rationale: "lets take number of minutesx . given that , 6 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 120 minutes ans c"
Answer: c
Question (other): the ratio of three numbers is 1 : 3 : 4 and the sum of their squares is 2600 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 3 x , 4 x then , x ^ 2 + 9 x ^ 2 + 16 x ^ 2 = 2600 26 x ^ 2 = 2600 x ^ 2 = 100 x = 10 answer is a"
Answer: a
Question (gain): a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18000 . a ' s share is ?
Options: a ) rs . 7500 , b ) rs . 7200 , c ) rs . 6000 , d ) rs . 5750 , e ) rs . 6750
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18000 = 6000 answer : c"
Answer: c
Question (general): the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 365
Rationale: "let the smallest number be x . then larger number = ( x + 1365 ) x + 1365 = 6 x + 15 = 5 x = 1350 x = 270 smaller number = 270 . answer : b"
Answer: b
Question (physics): in a 100 m race , sam beats john by 4 seconds . on the contrary , if sam allowed john to start 24 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 4 seconds , b ) 25 seconds , c ) 19 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: "their difference is 4 second but this difference is 0 if john allows sam to start the race from 24 m ahead . that means jhon was 24 m away from finishing line when they started together . so he will cover 24 m in 4 seconds . so his speed = 24 / 4 = 6 metre / second . so time taken = 100 / 4 = 25 seconds . so sam took = 19 seconds . correct answer = c"
Answer: c
Question (general): the contents of a certain box consist of 14 apples and 20 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 20 oranges , so to get to 6 oranges , we should remove 20 - 6 = 14 oranges . answer c
Answer: c
Question (gain): a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 500 , what is the reduced price for kg ?
Options: a ) 25 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 500 * ( 25 / 100 ) = 125 - - - - 5 ? - - - - 1 = > rs . 25"
Answer: a
Question (gain): there are two concentric circles with radii 8 and 6 . if the radius of the outer circle is increased by 25 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ?
Options: a ) 225 , b ) 250 , c ) 275 , d ) 300 , e ) 325
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 64 pi . the area of the small circle is 36 pi . the area a 1 between the circles is 28 pi . when the big circle ' s radius increases , the new area is 100 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 91 pi . the ratio of a 2 / a 1 is 91 / 28 = 3.25 which is an increase of 225 % . the answer is a ."
Answer: a
Question (physics): the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 100 meters ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 100 meters = 100 / 5 = 20 seconds . the answer is d .
Answer: d
Question (general): 3 people decided to put a down payment on a car for 3500 dollars . how much money do they each have to pay , given that that they have to pay the same amount , and they can not use any bills below $ 1 ?
Options: a ) $ 1166 , b ) $ 1168 , c ) $ 1166.6 , d ) $ 1167 , e ) none of the above
Rationale: to keep the amount exact when dividing for 3 , we have to work backwards through division . dividing 3500 by 3 will give us 1166.66 then by subtracting . 66 , we get 1166 , and we multiply it by 3 to get 3498 . to get enough for the down payment , we add 3 to 3498 . dividing the result by 3 gives us our answer . correct option : d
Answer: d
Question (physics): a biker covered half the distance between two towns in 2 hr 30 min . after that he increased his speed by 2 km / hr . he covered the second half of the distance in 2 hr 20 min . find the distance between the two towns and the initial speed of the biker .
Options: a ) 140 , b ) 120 , c ) 130 , d ) 150 , e ) 160
Rationale: let x km / hr be the initial speed of the biker , then his speed during the second part of the trip is x + 2 km / hr . half the distance between two cities equals 23060 ⋅ x km and 22060 ⋅ ( x + 2 ) km . from the equation : 23060 ⋅ x = 22060 ⋅ ( x + 2 ) we get x = 28 km / hr . the intial speed of the biker is 28 km / h . half the distance between the two towns is 2 h 30 min × 28 = 2.5 × 28 = 70 . so the distance is 2 × 70 = 140 km . answer is a .
Answer: a
Question (geometry): the diagonal of a square is 40 m . the area of the square is :
Options: a ) 600
b ) 900
c ) 800
d ) 500
e ) 400
Rationale: arear = 1 / 2 × ( diagonal ) ( power ) 2 = ( 1 / 2 × 40 × 40 ) m ( power ) 2 = 1600 / 2 = 800 m ( power ) 2 answer is c .
Answer: c
Question (general): on dividing 16698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 154 , c ) 187 , d ) 741 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 16698 - 14 ) / 89 = 187 answer ( c )"
Answer: c
Question (other): a box contains 4 black , 3 red and 6 green marbles . 2 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 24 / 78 , b ) 24 / 709 , c ) 24 / 76 , d ) 24 / 71 , e ) 24 / 72
Rationale: explanation : total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random . therefore , n ( s ) = 13 c 2 = 78 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 4 c 2 + 3 c 2 + 6 c 2 = 6 + 3 + 15 = 24 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 24 / 78 answer : a
Answer: a
Question (general): when an amount was distributed among 14 boys , each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys . what was the amount ?
Options: a ) 5000 , b ) 5030 , c ) 5010 , d ) 5040 , e ) 5020
Rationale: let the total amount be rs . x the , x / 14 - x / 18 = 80 < = > 2 x / 126 = 80 < = > x / 63 = 63 x 80 = 5040 . hence the total amount is 5040 answer is d .
Answer: d
Question (general): sum of the squares of 3 no . is 156 and the sum of their products taken two at a time is 50 . find the sum ?
Options: a ) 18 , b ) 16 , c ) 19 , d ) 21 , e ) 15
Rationale: ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 156 + 2 * 50 a + b + c = â ˆ š 256 = 16 answer b
Answer: b
Question (physics): two trains of length 150 m and 250 m are 150 m apart . they start moving towards each other on parallel tracks , at speeds 36 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 55 / 3 , b ) 55 / 7 , c ) 55 / 6 , d ) 55 / 8 , e ) 55 / 9
Rationale: "relative speed = ( 36 + 72 ) * 5 / 18 = 6 * 5 = 30 mps . the time required = d / s = ( 150 + 150 + 250 ) / 30 = 550 / 30 = 55 / 3 sec . answer : a"
Answer: a
Question (general): farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15.502 % , b ) 25.7014 % , c ) 12.502 % , d ) 21.7014 % , e ) none
Rationale: "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 3840 ) x 100 = 13.02083 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 13.02083 % x ( 100 / 60 ) = 21.7014 % and the answer is not there in the options . the correct answer is ( d ) ."
Answer: d
Question (gain): a , b and c started a business with capitals of rs . 6000 , rs . 8000 , and rs . 10000 respectively . at the end of the year , the profit share of b is rs 1000 . the difference between the profit shares of a and c is
Options: a ) rs . 400 , b ) rs . 450 , c ) rs . 500 , d ) rs . 550 , e ) rs . 650
Rationale: ratio of investments of a , b and c is 6000 : 8000 : 10000 = 3 : 4 : 5 . and also given that , profit share of ‘ b ’ is rs . 1000 . now required difference is 5 – 3 = 2 parts . therefore , required difference = 2 / 4 ( 1000 ) = rs . 500 . answer : c
Answer: c
Question (other): the probability that a computer company will get a computer hardware contract is 4 / 5 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ?
Options: a ) 7 / 20 , b ) 9 / 25 , c ) 11 / 30 , d ) 13 / 35 , e ) 17 / 40
Rationale: "let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 4 / 5 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 5 / 6 = ( 4 / 5 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 11 / 30 . hence , the required probability is 11 / 30 . the answer is c ."
Answer: c
Question (geometry): the length of a rectangle is five times of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 16 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 11 units ?
Options: a ) 180 sq . units
b ) 11 sq . units
c ) 110 sq . units
d ) 140 sq . units
e ) 220 sq . units
Rationale: given that the area of the square = 16 sq . units = > side of square = â ˆ š 16 = 4 units the radius of the circle = side of the square = 4 units length of the rectangle = 5 * 4 = 20 units given that breadth = 11 units area of the rectangle = lb = 20 * 11 = 220 sq . units answer : e
Answer: e
Question (physics): second saturday and every sunday is a holiday . how many working days will be there in a month of 30 days beginning on a saturday ?
Options: a ) 24 , b ) 23 , c ) 18 , d ) 21 , e ) 22
Rationale: explanation : mentioned month begins on a saturday and has 30 days sundays = 2 nd , 9 th , 16 th , 23 rd , 30 th = > total sundays = 5 every second saturday is holiday . 1 second saturday in every month total days in the month = 30 total working days = 30 - ( 5 + 1 ) = 24 . answer : option a
Answer: a
Question (gain): if 80 % of 90 is greater than 70 % of a number by 30 , what is the number ?
Options: a ) 70 , b ) 60 , c ) 10 , d ) 75 , e ) 85
Rationale: "explanation : 80 / 100 * 90 - 70 / 100 * x = 30 72 - 70 / 100 * x = 30 72 - 30 = 70 / 100 * x 42 = 70 / 100 * x 42 * 100 / 70 = x 60 = x answer : option b"
Answer: b
Question (geometry): a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 40 inches . find b .
Options: a ) 8 , b ) 6 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 40 ( 2 ^ 3 * 5 ) , sob = 2 ^ 3 or 2 ^ 3 * 5 ( 8 or 40 ) . combining 2 premises shows the answer is b ( 6 ) ."
Answer: b
Question (general): find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1345 , b ) 1197 , c ) 1540 , d ) 1600 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 6 x + 15 5 x = 985 x = 197 large number = 197 + 1365 = 1197 b"
Answer: b
Question (geometry): a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be ?
Options: a ) 7744
b ) 8844
c ) 5544
d ) 4444
e ) 3444
Rationale: length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a
Answer: a
Question (geometry): a rectangular courtyard , the sides of which are in the ratio of 4 : 3 , cost rs . 600 for paving at 50 p per m 2 ; find the length of the diagonal of the courtyard ?
Options: a ) 17 m
b ) 45 m
c ) 54 m
d ) 77 m
e ) 34 m
Rationale: 1 m 2 - - - - 1 / 2 ? - - - - - 600 = > 1200 m 2 4 x * 3 x = 1200 = > x = 10 answer : b
Answer: b
Question (geometry): if the area of a circle decreases by 42 % , then the radius of a circle decreases by
Options: a ) 20 % , b ) 18 % , c ) 24 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 42 ) % = ( 100 − 10 √ 58 ) % = 100 - 76 = 24 % answer c"
Answer: c
Question (general): a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c"
Answer: c
Question (general): when x is multiplied by 3 , the result is 20 more than the result of subtracting x from 20 . what is the value of x ?
Options: a ) 10 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 20 = 20 - x or , 4 x = 40 or , x = 10 . answer : a"
Answer: a
Question (general): solution for 2.75 + . 003 + . 158
Options: a ) 2.91 , b ) 2.911 , c ) 2.938 , d ) 2.986 , e ) 2.999
Rationale: "2.75 + . 003 + . 158 = 0 0 = 0 - 2.75 - 0.003 - 0.158 0 = - 2.911 answer : b"
Answer: b
Question (physics): jane makes toy bears . when she works with an assistant , she makes 70 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 80 % b"
Answer: b
Question (gain): ravi and sunil are partners in a business . ravi invests rs . 9,000 for 8 months and sunil invested rs . 12000 for 9 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 9000 * 8 ) : ( 15000 * 8 ) = 72000 : 108000 = 2 : 3 answer : b"
Answer: b
Question (general): a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 238 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 33 , c ) 55 , d ) 42 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 238 = > . 1 x + 3 / 4 x = 238 = > x = 280 280 - 238 = pure gala = 42 . answer d"
Answer: d
Question (gain): the purchase price of an article is $ 48 . in order to include 25 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 50 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: cost price of article = 48 $ % of overhead cost = 25 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 25 = 50 % answer a
Answer: a
Question (physics): a car is running at a speed of 90 kmph . what distance will it cover in 15 second ?
Options: a ) 100 m , b ) 255 m , c ) 375 m , d ) can not be determined , e ) none of these
Rationale: "explanation : given : speed = 108 kmph = ( 90 x ( 5 / 18 ) ) m / sec = 25 m / sec distance covered in 15 second = ( 25 x 15 ) m = 375 m . answer : c"
Answer: c
Question (general): what should be the least number to be added to the 51234 number to make it divisible by 9 ?
Options: a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2
Rationale: "the least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits . sum of digits = 15 . nearest multiple of 9 greater than sum of digits = 18 . hence 3 has to be added . answer : c"
Answer: c
Question (general): in a 120 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 49 , b ) 47 , c ) 25 , d ) 43 , e ) 41
Rationale: "solution simple out of 120 20 % are male i . e 24 and 25 % are female i . e 30 , so total homeowner is 54 . now min number homeowner is 24 and max is 54 so question ask us to find least and 25 has least value among all option . so ans is 25 . answer : c"
Answer: c
Question (general): 8 k 8 + k 88 - - - - - - - - 16 t 6 if k and t represent non - zero digits within the integers above , what is t ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 17
Rationale: 8 k 8 k 88 - - - - - - - - 16 t 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * * ) . after that it ' s easy to get that k = 7 and t = 6 . answer : a .
Answer: a
Question (physics): the distance between delhi and mathura is 110 kms . a starts from delhi with a speed of 20 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 25 kmph at 8 p . m . from delhi . when will they meet ?
Options: a ) 08 a . m . , b ) 09 a . m . , c ) 12 a . m . , d ) 10 a . m . , e ) 07 a . m .
Rationale: "d 10 a . m . d = 110 – 20 = 90 rs = 20 + 25 = 45 t = 90 / 45 = 2 hours 8 a . m . + 2 = 10 a . m ."
Answer: d
Question (general): what is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 27 , c ) 30 , d ) 21 , e ) 18
Rationale: "explanatory answer useful result pertaining to remainders you can solve this problem if you know this rule about remainders . let a number x divide the product of a and b . the remainder will be the product of the remainders when x divides a and when x divides b . using this rule , the remainder when 33 divides 1044 is 21 . the remainder when 33 divides 1047 is 24 . the remainder when 33 divides 1050 is 27 . the remainder when 33 divides 1053 is 30 . ∴ the remainder when 33 divides 1044 * 1047 * 1050 * 1053 is 21 * 24 * 27 * 30 . note : the remainder when a number is divided by a divisor ' d ' will take values from 0 to ( d - 1 ) . it can not be equal to or more than ' d ' . the value of 21 * 24 * 27 * 30 is more than 33 . when the value of the remainder is more than the divisor , final remainder will be the remainder of dividing the product by the divisor . i . e . , the final remainder is the remainder when 33 divides 21 * 24 * 27 * 30 . when 33 divides 21 * 24 * 27 * 30 , the remainder is 30 . choice c"
Answer: c