Cheukting/mathqa huggingface dataset:
Question (general): the number of diagonals of a polygon of n sides is given by the formula z = 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: "z = n ( n - 3 ) z = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Question (other): divide rs . 32000 in the ratio 3 : 9 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 8000 , 24000
Rationale: "3 / 12 * 32000 = 8000 9 / 12 * 32000 = 24000 answer : e"
Answer: e
Question (general): what will be the remainder if 2 ^ 300 is divided by 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: d 4 now if you go on calculating 2 ^ 300 , you will lose so much time and it might not even be feasible to carry out so long of calculations . thus we will make use of a trick here . we will calculate the remainder of each power of 2 till we come across a pattern . 2 ^ 1 divided by 4 leaves the remainder 2 . 2 ^ 2 divided by 4 leaves the remainder 0 . 2 ^ 3 divided by 4 leaves the remainder 0 . 2 ^ 4 divided by 4 leaves the remainder 0 . you can see that all the following powers of two will be divisible by 4 . therefore the remainder when 2 ^ 300 is divided by 4 will be 0 only .
Answer: d
Question (general): a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 5 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 351
Rationale: if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 13 / 4 solving it 28 x = 26 x + 78 x = 39 which means m ( d ) = 273 and b ( d ) = 78 so total initially is m ( d ) + b ( d ) = 351 e
Answer: e
Question (other): three numbers are in the ratio 1.5 : 2 : 3.5 and their h . c . f is 18 . the numbers are :
Options: a ) 22,36 , 63 , b ) 27,45 , 63 , c ) 27,54 , 63 , d ) 54 , 45 , 36 , e ) 27,36 , 63
Rationale: "let the required numbers be 1.5 x , 2 x and 3.5 x . then , their h . c . f = x . so , x = 18 . the numbers are 27,36 , 63 . answer : e"
Answer: e
Question (general): 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4500 , how much was it in the beginning ?
Options: a ) 5999 , b ) 6788 , c ) 6250 , d ) 4559 , e ) 6989
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 4500 x = 6250 answer : c"
Answer: c
Question (general): the tax on a commodity is diminished by 25 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 17.5 %
Rationale: "explanation : 100 * 100 = 10000 75 * 110 = 8250 10000 - - - - - - - 1750 100 - - - - - - - ? = 17.5 % e )"
Answer: e
Question (geometry): a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 48 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 8 , b ) b 22 , c ) c 27 , d ) d 40 , e ) e 51
Rationale: "l = 48 / 12 = 4 ft w = 72 / 12 = 6 ft area of paper = 24 area of cube = 4 * side ^ 2 side of cube = 2 v of cube = 8"
Answer: a
Question (general): the sum of the first 60 positive even integers is 3,750 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 4,700 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 60 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 60 positive even integers = 3750 sum of 1 st 100 odd numbers = 5050 - 3750 = 1300 so 101 + 103 + . . . . . . . 199 = 60 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 6000 + 1300 = 4700 a is the answer ."
Answer: a
Question (geometry): a wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 54.9 %
b ) 58.7 %
c ) 62.5 %
d ) 66.3 %
e ) 70.4 %
Rationale: there are a total of 6 * 6 * 6 = 216 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 4 * 4 * 4 = 64 cubes . the number of cubes with at least one side painted red is 216 - 64 = 152 cubes the probability that a cube has at least one side painted red is 152 / 216 which is about 70.4 % the answer is e .
Answer: e
Question (general): ages of two persons differ by 18 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 15,33 , c ) 16,32 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 18 ) = > 3 ( x - 6 ) = ( x + 18 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 12 = > x = 15 . so other person age is x + 18 = 33 answer : option b"
Answer: b
Question (other): the h . c . f . of two numbers is 28 and the other two factors of their l . c . m . are 12 and 15 . the larger of the two numbers is
Options: a ) 420 , b ) 430 , c ) 312 , d ) 322 , e ) none
Rationale: "solution clearly , the numbers are ( 28 x 12 ) and ( 28 x 15 ) . larger number = ( 28 x 15 ) = 420 . answer a"
Answer: a
Question (gain): in the first 8 overs of a cricket game , the run rate was only 2.3 what should be the rate in the remaining 20 overs to reach the target of 260 runs ?
Options: a ) 12.08 , b ) 12.18 , c ) 12.0 , d ) 6.19 , e ) 6.21
Rationale: "required run rate = [ 260 - ( 2.3 * 8 ) ] / 20 = 241.60 / 20 = 12.08 answer : a"
Answer: a
Question (gain): in the first 20 overs of a cricket game , the run rate was only 4.3 . what should be the run rate in the remaining 30 overs to reach the target of 264 runs ?
Options: a ) 5.93 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) 8
Rationale: "explanation : required run rate = ( 264 - ( 4.3 x 20 ) ) / 30 = 178 / 30 = 5.93 answer : a"
Answer: a
Question (gain): at what price must an article costing rs . 150 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 30 % on the cost price ?
Options: a ) 62.5 , b ) 62.0 , c ) 62.6 , d ) 216.67 , e ) 62.2
Rationale: "cp = 150 sp = 150 * ( 130 / 100 ) = 195 mp * ( 90 / 100 ) = 195 mp = 216.67 answer : d"
Answer: d
Question (physics): a man can row 8 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 5.7 , c ) 7.5 , d ) 5.74 , e ) 5.71
Rationale: "m = 8 s = 2 ds = 10 us = 6 x / 10 + x / 6 = 1 x = 3.75 d = 3.75 * 2 = 7.5 answer : c"
Answer: c
Question (geometry): all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose three faces are coloured ?
Options: a ) 4
b ) 8
c ) 16
d ) 24
e ) 2
Rationale: there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having three faces coloured = no . of corners = 8 answer : b
Answer: b
Question (gain): an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1260 ) * 100 = 25 % answer e"
Answer: e
Question (geometry): if the sides of a square are doubled in length , the area of the original square is now how many times as large as the area of the resultant square ?
Options: a ) 25 % , b ) 50 % , c ) 100 % , d ) 200 % , e ) 400 %
Rationale: let the original square have sides of length l and the new square have sides of length 2 l . the resulting areas are l ^ 2 for the original square and 4 l ^ 2 for the new square ( as the length of the side is square to get the area ) . the original square ' s area is l ^ 2 / 4 l ^ 2 or 25 % of the new square ' s area . choice a
Answer: a
Question (general): there are 16 bees in the hive , then 10 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 26
Rationale: 16 + 10 = 26 . answer is e .
Answer: e
Question (gain): the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 612 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1462 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 612 × 100 ) / ( 6 × 12 ) = rs . 850 bg = bd – td = > 612 = bd - 850 = > bd = 612 + 850 = 1462 answer : option d"
Answer: d
Question (general): if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ?
Options: a ) 8 , b ) 18 , c ) 10 , d ) 12 , e ) 14
Rationale: "we know dividend = divisor * quotient + remainder = = = > 507 = divisor * 61 + 19 = = = = = > 488 / 61 = divisor = = = > divisor = 8 ans - a"
Answer: a
Question (general): the average salary of raj and roshan is rs . 4000 but the average salary of raj , roshan and thomas is rs . 5000 . what is the salary of thomas ?
Options: a ) 4000 , b ) 5000 , c ) 6000 , d ) 7000 , e ) 8000
Rationale: total salary of raj and roshan = 2 x 4000 = 8000 total salary of raj roshan and thomas = 3 x 5000 = 15000 salary of thomas = 15000 - 8000 = rs . 7000 answer : d
Answer: d
Question (general): gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 45 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 90 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 45 . thus , 3434 ( 90 + x ) = 45 + x or 270 + 3 x = 180 + 4 x or x = 90 answer : d"
Answer: d
Question (physics): the radius of a semi circle is 35 cm then its perimeter is ?
Options: a ) 32.8 , b ) 180 , c ) 32.1 , d ) 32.2 , e ) 32.9
Rationale: "diameter 70 cm 1 / 2 * 22 / 7 * 70 + 70 = 180 answer : b"
Answer: b
Question (gain): an inspector rejects 0.06 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3333
Rationale: "let the number of meters to be examined be x then , 0.06 % of x = 2 ( 6 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 3333 answer is e"
Answer: e
Question (gain): the present worth of rs . 1404 due in two equal half - yearly installments at 8 % per annum simple interest is :
Options: a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) rs . 1600
Rationale: "time = 1 / 2 yr r = 8 % let pw = x si = 1404 - x x * 1 / 2 * 8 / 100 = 1404 - x . ( ref problm 10 of si , rs aggarwal ) x = 1404 * 25 / 26 hence x = 1350 answer : c"
Answer: c
Question (physics): a train moves with a speed of 72 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 20 , e ) none
Rationale: "solution speed = 72 kmph = ( 72 x 5 / 18 ) m / sec = 20 m / sec . answer d"
Answer: d
Question (gain): 40 % of 2 is equal to
Options: a ) 0.2 , b ) 0.8 , c ) 0.6 , d ) 0.7 , e ) 0.9
Rationale: 40 % of 2 = ( 40 / 100 ) * 2 = 0.8 answer : option b
Answer: b
Question (general): how many positive integers less than 243 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 40 , e ) 64
Rationale: "240 / 4 = 60 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 60 - 20 = 40 answer : d"
Answer: d
Question (physics): a can finish a piece of work in 5 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 days , b ) 6 days , c ) 7 days , d ) 1 days , e ) 3 days
Rationale: "a 4 days 2 / 5 + ( 2 + x ) / 10 = 1 = > x = 4 days"
Answer: a
Question (general): vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6936 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 2400
Rationale: let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6936 = x = 6936 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2400 . answer : e
Answer: e
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 59.4 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 20 + 20 + 10 + 5 + 2.5 + 1.25 + 0.6 ans b"
Answer: b
Question (geometry): a rectangular tiled patio is composed of 80 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 80 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 12 , e ) 28
Rationale: "r * c = 80 and ( 12 + 4 ) ( c - 2 ) = 80 - - > r = 12 and c = 7 . answer : d ."
Answer: d
Question (general): the maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 91 , b ) 81 , c ) 1001 , d ) 1911 , e ) none
Rationale: olution required number of students . = h . c . f of 891 and 810 . â € ¹ = â € º 81 . answer b
Answer: b
Question (general): what is the slope of a line on a standard xy - plane that passes through the point ( 1 , 3 ) and ( 4 , – 3 ) ?
Options: a ) - 1 , b ) 2 , c ) - 2 , d ) 1 / 2 , e ) - 1 / 2
Rationale: plug the values for the coordinates into the formula for the slope of a line : slope = y 2 - y 1 / x 2 - x 1 = - 3 - 3 / 4 - 1 = - 6 / 3 = - 2 correct answer c ) - 2
Answer: c
Question (general): the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 124 different signs . if the company used 122 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 124 signs ?
Options: a ) 246 , b ) 248 , c ) 492 , d ) 15,128 , e ) 30,256
Rationale: "ok let ' s take a crack at this one . so basically we have 144 ^ 2 - 142 ^ 2 so then ( 144 + 142 ) ( 144 - 142 ) ( 246 ) ( 2 ) = 492 answer : c"
Answer: c
Question (physics): pipe a can fill a tank in 5 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 67 , b ) 10 , c ) 18 , d ) 26 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 5 - 1 / x = 1 / 10 = > 1 / x = 1 / 5 - 1 / 10 = 1 / 10 = > x = 10 . answer : b"
Answer: b
Question (general): a large box contains 20 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 500 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 20 * 25 = 500 correct answer b"
Answer: b
Question (other): find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 .
Options: a ) 240 / 1587 , b ) 240 / 1545 , c ) 240 / 1547 , d ) 240 / 1542 , e ) 240 / 1512
Rationale: "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c"
Answer: c
Question (gain): if 40 % of a number is greater than 80 % of 5 by 2 , what is the number ?
Options: a ) 3 , b ) 15 , c ) 20 , d ) 2 , e ) 5
Rationale: "explanation : 40 / 100 * x - 80 / 100 * 5 = 2 40 / 100 * x - 4 = 2 40 / 100 * x = 6 x = 6 * 100 / 40 x = 15 answer : option b"
Answer: b
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 1.5 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35.75 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 1.5 x = 41.5 x dollars ; we know that harry also earned the same 41.5 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 11.5 x additional dollars . since for each additional hour he gets 3 x dollars then he worked for 11.5 x / 2 x = 5.75 additional hours , so harry worked for total of 30 + 5.75 = 35.75 hours . answer : a ."
Answer: a
Question (other): in a group of 80 people , 45 have visited iceland and 33 have visited norway . if 41 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 80 = 45 + 33 - 41 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Question (probability): seven 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 46656 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways . hence the probability is 6 / 279936 = 1 / 46656 answer : b"
Answer: b
Question (gain): the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 8000 , brokerage being 1 / 4 % , is :
Options: a ) 110.86 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 8000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 8000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 111.11 = market value of rs . 100 stock = rs . 111.11 - re . 0.25 . = market value of rs . 100 stock = rs . 110.86 . answer : a"
Answer: a
Question (other): p starts a business with rs . 4000 . after 4 months , q joins with p as his partner . after a year , the profit is divided in the ratio 2 : 3 . q ' s contribution in the capital is ?
Options: a ) rs . 7000 , b ) rs . 11000 , c ) rs . 8000 , d ) rs . 10000 , e ) rs . 9000
Rationale: solution : let ' s q ' s capital is x . p : q = ( 4000 * 12 ) : ( x : 8 ) = 2 : 3 . so q ' s share = ( 4000 * 12 / 8 x ) = 2 / 3 = > x = ( 4000 * 12 * 3 ) / ( 2 * 8 ) = rs . 9000 answer : option e
Answer: e
Question (probability): what is the probability of getting exactly 1 head in a single throw of five fair coins ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32
Rationale: "one possible case is htttt . p ( htttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 1 = 5 possible cases . p ( 1 head ) = 5 * 1 / 32 = 5 / 32 the answer is d ."
Answer: d
Question (general): - 64 * 29 + 468 = ?
Options: a ) 1430 , b ) 1302 , c ) - 2801 , d ) - 1388 , e ) none of these
Rationale: = > - 64 * ( 30 - 1 ) + 468 ; = > - ( 64 * 30 ) + 64 + 468 ; = > - 1920 + 532 = - 1388 . correct option : d
Answer: d
Question (general): there are 70 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 53 , e ) 64
Rationale: "x + ( x - 14 ) = 70 - - > x = 42 . answer : c ."
Answer: c
Question (physics): a is twice as good a work man as b and together they finish the work in 14 days . in how many days a alone can finish the work ?
Options: a ) 12 , b ) 21 , c ) 77 , d ) 99 , e ) 22
Rationale: "wc = 2 : 1 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 a can do the work in 21 days . answer : b"
Answer: b
Question (general): find the least number must be subtracted from 165826 so that remaining no . is divisible by 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "on dividing 165826 by 4 we get the remainder 2 , so 2 should be subtracted b"
Answer: b
Question (physics): hcf and lcm two numbers are 14 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 154 , d ) 264 , e ) 364
Rationale: "14 * 396 = 36 * x x = 154 answer : c"
Answer: c
Question (physics): a train 240 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 28.8 sec , b ) 20.33 sec , c ) 60 sec , d ) 48 sec , e ) 49 sec
Rationale: "total length = 240 + 240 = 480 speed = 60 km / h = ( 60 * 5 ) / 18 = 50 / 3 m / s time = ( 480 * 3 ) / 50 = 28.8 sec . answer : a"
Answer: a
Question (general): a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 2 x km .
Options: a ) 16 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 35 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 2 x / ( x / 8 ) = 16 kmph answer : a"
Answer: a
Question (general): if x and y are positive integers , and y = x ^ 2 + 8 , the greatest common divisor of a and b can not be
Options: a ) 9 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: if x is 1 , 2 , 4 , or 8 , then gcd of x and y is 1 , 2 , 4 , and 8 respectively . so , by poe the answer must be a . still : if x is a multiple of 9 , then y is 8 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : a .
Answer: a
Question (physics): a light flashes every 12 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 300 , c ) 650 , d ) 700 , e ) 750
Rationale: "1 flash = 12 sec for 1 min = 5 flashes so for 1 hour = 5 * 60 = 300 flashes . answer : b"
Answer: b
Question (gain): some of the 68 % solution of acid was removed and this was replaced with an equal amount of 11 % solution of acid . as a result , a 35 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 7 / 11 , b ) 7 / 17 , c ) 8 / 17 , d ) 8 / 19 , e ) 11 / 19
Rationale: "let x be the fraction of the original solution that was replaced . 0.68 * ( 1 - x ) + 0.11 ( x ) = 0.35 0.57 x = 0.33 x = 33 / 57 = 11 / 19 the answer is e ."
Answer: e
Question (general): how many natural numbers between 23 and 137 are divisible by 7 ?
Options: a ) 12 , b ) 17 , c ) 16 , d ) 13 , e ) 15
Rationale: "solution : these numbers are 28 , 35 , 42 , … . , 133 . this is in a . p . in which a = 28 , d = ( 35 - 28 ) = 7 and l = 133 . let the number of there terms be n . then , tn = 133 a + ( n - 1 ) d = 133 by solving this we will get n = 16 . answer c"
Answer: c