Cheukting/mathqa huggingface dataset:
Question (general): of 70 players on a football team , 49 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: total = 70 thrower = 49 rest = 70 - 49 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 49 + 14 = 63 so c . 63 is the right answer
Answer: c
Question (other): jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the numbers will be 3 ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21
Rationale: method - 1 probability that the number on first die is 3 = 1 / 6 probability that the number on second die is 3 = 1 / 7 probability that both dice result in odd numbers = ( 1 / 6 ) * ( 1 / 7 ) = 1 / 42 answer : option d
Answer: d
Question (general): a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "add 44 + 12 = 56 now 56 divided by 12 so we get 8 as reaminder answer : b"
Answer: b
Question (physics): a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 16 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.5 , e ) 4
Rationale: time = 8 / 4 + 8 / 8 = 3 hours the answer is c .
Answer: c
Question (general): change the below lagarithm log 255 = 1 / 2 to exponential form
Options: a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 11
Rationale: solution : log 255 = 251 / 2 = 5 answer is a
Answer: a
Question (geometry): the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle ?
Options: a ) 10 cm , b ) 40 cm , c ) 20 cm , d ) 30 cm , e ) 50 cm
Rationale: "let the breadth of the given rectangle be x then length is 2 x . thus area of the given rect is \ fn _ jvn { \ color { black } 2 x ^ { 2 } } after dec 5 cm from length and inc 5 cm breadth , new lenght becomes 2 x - 5 and breadth is x + 5 . thus new area = ( 2 x - 5 ) ( x + 5 ) = \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 5 x - 25 } since new area is 75 units greater than original area thus \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 75 = 2 x ^ { 2 } + 5 x - 25 } 5 x = 75 + 25 5 x = 100 therefore x = 20 hence length of the rectangle is 40 cm . answer : b"
Answer: b
Question (gain): by selling 16 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 12 , d ) 89 , e ) 81
Rationale: "90 % - - - 16 120 % - - - ? 90 / 120 * 16 = 12 answer : c"
Answer: c
Question (physics): if it takes a machine 2 ⁄ 3 minute to produce one item , how many items will it produce in 1 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 90 , d ) 120 , e ) 180
Rationale: "1 item takes 2 / 3 min so it takes 60 min to produce x 2 x / 3 = 60 the x = 90 answer : c"
Answer: c
Question (general): a batsman makes a score of 65 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 17 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above
Rationale: let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 65 = 17 x or x = ( 65 – 48 ) = 17 . answer a
Answer: a
Question (gain): an article is bought for rs . 675 and sold for rs . 1200 , find the gain percent ?
Options: a ) 87 % , b ) 88 % , c ) 78 % , d ) 75 % , e ) 73 %
Rationale: "675 - - - - 525 100 - - - - ? = > = 78 % answer : c"
Answer: c
Question (physics): the distance between two cities a and b is 1410 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 pm , b ) 07 pm , c ) 11 pm , d ) 05 am , e ) 03 am
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1410 . therefore , 60 x + 75 ( x - 1 ) = 1410 . = > x = 3 . so , they meet at ( 8 + 11 ) i . e , 7 pm . answer : b"
Answer: b
Question (gain): tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4000 . they earned a profit of rs . 4230 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 2000 , b ) 2200 , c ) 2309 , d ) 2350 , e ) 3250
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 4230 = 2350 d"
Answer: d
Question (general): a student got twice as many sums wrong as he got right . if he attempted 54 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 54 3 x = 54 x = 18 . answer : c"
Answer: c
Question (general): the instructions state that deepthi needs 4 / 17 square yards of one type of material and 3 / 10 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 9 / 30 square yards left that she did not use . what is the total amount of square yards of material deepthi used ?
Options: a ) 1 / 12 , b ) 4 / 17 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: total bought = 4 / 17 + 3 / 10 left part 9 / 30 - - - > 3 / 10 so used part 4 / 17 + 3 / 10 - 3 / 10 = 4 / 17 answer : b
Answer: b
Question (general): a certain city with a population of 108,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 9,000 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 108 k x = 9,000 answer : c"
Answer: c
Question (gain): company p had 15 percent more employees in december than it had in january . if company p had 470 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 408 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 470 j = 470 / 1.15 j = 47,000 / 115 = 408 thus b is the correct answer ."
Answer: b
Question (physics): a , b and c can do a piece of work in 5 days , 10 days and 15 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 , c ) 2 8 / 11 , d ) 67 , e ) 9
Rationale: "1 / 5 + 1 / 10 + 1 / 15 = 11 / 30 = > 30 / 11 = > 2 8 / 11 days answer : c"
Answer: c
Question (probability): two unbiased coins are tossed . find the probability of getting at most one head ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 5 , d ) 2 / 3 , e ) 1 / 4
Rationale: "s = { hh , ht , th , tt } e = event of getting at most one head e = { tt , ht , th } p ( e ) = 3 / 4 answer is b"
Answer: b
Question (gain): find the annual income derived by investing $ 6800 in 60 % stock at 136 .
Options: a ) 550 , b ) 3000 , c ) 250 , d ) 300 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 60 . by investing $ 6800 , income obtained = $ [ ( 60 / 136 ) * 6800 ] = $ 3000 . answer b ."
Answer: b
Question (general): when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum w of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . w = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616"
Answer: b
Question (general): jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 81 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 81 * 3 = 243 jerry wants the average to be = 83 hence total score on 4 tests should be = 83 * 4 = 332 score required on the fourth test = 332 - 243 = 89 option b"
Answer: b
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 390 sq . feet , how many feet of fencing will be required ?
Options: a ) 34
b ) 59
c ) 68
d ) 88
e ) 92
Rationale: given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 390 breadth = 19.5 feet area to be fenced = 2 b + l = 2 ( 19.5 ) + 20 = 59 feet answer : b
Answer: b
Question (general): in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 60 % , e ) 27 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 2000 : 8000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : a"
Answer: a
Question (geometry): what is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square ?
Options: a ) 2
b ) 3
c ) 5
d ) 7
e ) 11
Rationale: 1008 = 2 ^ 4 x 3 ^ 2 x 7 . therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7 . answer d .
Answer: d
Question (other): how many factors of 660 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 15
Rationale: when factorized , 660 has 5 prime factors . of these prime factors 4 are odd and 1 is even . hence total number of odd factors is 2 * 2 * 2 * 2 ( 16 ) , which includes 1 . the total number of odd factors greater than 1 are 15 . ( option e )
Answer: e
Question (general): a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 300 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: given that p is smallest integer greater than 300 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 d
Answer: d
Question (physics): a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . if 60 cubic centimeters of the solution were poured into an empty container , how many grams of sucrose would be in the container ?
Options: a ) 4.00
b ) 6.00
c ) 5.50
d ) 6.50
e ) 6.75
Rationale: we are given that a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of sucrose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of sucrose would be in the container when we have 60 cubic centimeters of solution , we can set up a proportion . we can say : “ 10 grams of sucrose is to 100 cubic centimeters of solution as x grams of sucrose is to 60 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 10 / 100 = x / 60 when we cross multiply we obtain : ( 10 ) ( 60 ) = 100 x 600 = 100 x 6.00 = x there are 6.00 grams of sucrose in the solution in the container . the answer is b .
Answer: b
Question (geometry): a crate measures 6 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 6 for the surface 8 * 12 face . volume = 216 pi answer c"
Answer: c
Question (physics): a man can row downstream at 20 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 13 , 3 , b ) 12 , 6 , c ) 16 , 4 , d ) 14 , 4 , e ) none of these
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 32 = > x = 16 , y = 4 . answer : option c"
Answer: c
Question (physics): a and b go around a circular track of length 1200 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 240 sec , b ) 165 sec , c ) 186 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1200 / ( 36 * 5 / 18 ) , 1200 / ( 54 * 5 / 18 ) } = lcm ( 120 , 80 ) = 240 sec . answer : a"
Answer: a
Question (general): if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 24 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 24 ) / 10 = ( 54 - 24 ) / 10 = 3 answer : option e"
Answer: e
Question (general): tom read a book containing 560 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 19 , b ) 18 , c ) 9.12 , d ) 20 , e ) none
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 560 ( we want to find the days , sop = 560 / d ) 2 ) ( p + 16 ) ( d - 5 ) = 560 = > pd - 5 p + 16 d - 80 = 560 as the 1 ) stated u can put 1 ) into 2 ) = > 560 - 5 p + 16 d - 80 = 560 = > 16 d - 5 p = 80 put the bold one into it = > 16 d - 5 ( 560 / d ) = 80 the we get the final equation 16 d ^ 2 - 2800 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 175 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 9.12 days ans : c"
Answer: c
Question (physics): john bought 9.25 m of cloth for $ 407 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 44 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 407 cost per metre = 407 ÷ 9.25 the cost of the cloth per metre = $ 44 answers : d"
Answer: d
Question (geometry): how many pieces can a square pizza be cut into by making 6 linear cuts ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "1 cut makes 2 pieces a second cut can make 4 pieces by cutting through both pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a sixth cut can make 22 pieces by cutting through 6 of the pieces c"
Answer: c
Question (geometry): on the xy - plane , each point on circle c has coordinates such that x 0 and y 0 . if the center of circle c is the point ( 3 ; 9 ) , what is the maximum possible area of c ?
Options: a ) 6 , b ) 9 , c ) 24 , d ) 32 , e ) 64
Rationale: i think that theintentof this question is that the circle will have no co - ordinates that fit the following 2 forms : ( 0 , y ) or ( x , 0 ) . in real basic terms , this circle will neither touch ( nor cross ) the x - axis nor will it touch ( nor cross ) the y - axis . with a center at ( 3,8 ) , the longest possible radius would almost touch the x - axis , so the radius would be a little less than 3 . if the radius was 3 exactly , then the area would be 9 pi , which is approximately 28.26 since the circle ca n ' t touch the x - axis , the area has to be less than approximately 28.26 as it ' s written , none of the answers is clearly the correct one . c
Answer: c
Question (general): if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 30 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 48 % , d ) 34 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.30 = 12 gallons of grape juice . 40 × 0.70 = 28 gallons of other components . if we add 10 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we will have a total of 50 gallons of the mixture . so 24 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 24 / 50 = 48 / 100 = 48 % . the correct answer is choice ( c )"
Answer: c
Question (other): in a school 10 % of the boys are same in number as 1 / 5 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 1 : 2 , d ) 3 : 7 , e ) 2 : 5
Rationale: 10 % of b = 1 / 5 g 10 b / 100 = g / 5 b = g / 2 b / g = 1 / 2 b : g = 1 : 2 answer is c
Answer: c
Question (geometry): in a certain parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle ?
Options: a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 40 ) = 180 - - > x = 70 . answer : a ."
Answer: a
Question (geometry): a farmer built a fence around his square plot . he used 27 fence poles on each side of the square . how many poles did he need altogether ?
Options: a ) 100
b ) 104
c ) 108
d ) 112
e ) none of these
Rationale: one side = 2 corners ( 1 nd 1 each ) plus 25 . . . 1 25 1 25 25 1 25 1 der 4 ans = 25 * 4 + 4 = 104 answer : b
Answer: b
Question (general): if one positive integer is greater than another positive integer by 4 , and the difference of their cubes is 208 , what is their sum ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 the two numbers are 2 and 6 . the answer is a ."
Answer: a
Question (general): if s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } , how much less is the mean of the numbers in s than the median of the numbers in s ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "mean = ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 4 median = 4 difference = 4 - 4 = 0 option a"
Answer: a
Question (general): 45 x ? = 40 % of 900
Options: a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) 8
Rationale: "answer let 45 x a = ( 40 x 900 ) / 100 ∴ a = ( 40 x 9 ) / 45 = 8 correct option : e"
Answer: e
Question (gain): ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 18 , d ) 77 , e ) 65
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 64900 profit ( % ) = ( 64900 - 55000 ) / 55000 * 100 = 18 % answer : c"
Answer: c
Question (physics): a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 8 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 2.6 , b ) 5.6 , c ) 6.3 , d ) 8 , e ) 10
Rationale: let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 8 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 2.6 m / s a
Answer: a
Question (other): of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 3 / 5 of the students are female , what is ratio of male to female students on honor roll ?
Options: a ) 5 / 9 , b ) 8 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 30 given 3 / 5 of the students are females = 18 then males = 2 / 5 = 12 5 / 6 of the females are on honor roll = 15 males on the honor roll = 2 / 3 = 8 ratio of m : f students on honor roll = 8 / 15 b"
Answer: b
Question (physics): if in a race of 90 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 18 m
Rationale: explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 90 * 5 ) / 25 = 18 m hence , a beats b by 18 m . answer e
Answer: e
Question (general): the sum of all two digit numbers divisible by 9 is
Options: a ) 910 , b ) 585 , c ) 785 , d ) 685 , e ) 885
Rationale: required numbers are 18,27 . . . . . 99 this is an a . p . in which a = 18 , d = 9 and l = 99 . let the number of terms in it be n . then t = 99 so a + ( n - 1 ) d = 99 . 18 + ( n - 1 ) * 9 = 99 , 18 + 9 n - 9 = 99 9 + 9 n = 99 9 n = 99 - 9 n = 90 / 9 then n = 10 . required sum = n / 2 ( a + l ) = 10 / 2 ( 18 + 99 ) = 585 answer is b .
Answer: b
Question (general): find the least number must be subtracted from 899830 so that remaining no . is divisible by 16 ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 9
Rationale: "on dividing 899830 by 16 we get the remainder 6 , so 6 should be subtracted d"
Answer: d
Question (physics): at 3 : 40 , the hour hand and the minute hand of a clock form an angle of :
Options: a ) 130 , b ) 125 , c ) 140 , d ) 154 , e ) 145
Rationale: angle traced by hour hand in 12 hrs . = 360 â ° . abgle traced it in 11 / 3 hrs = ( 360 / 12 * 11 / 3 ) = 110 angle traced by min hand in 60 min = 360 angle traced by it in 40 min = ( 360 / 60 * 40 ) = 240 req ( 240 - 110 ) = 130 d
Answer: a
Question (physics): express 60 mps in kmph ?
Options: a ) 200 , b ) 182 , c ) 216 , d ) 127 , e ) 400
Rationale: "60 * 18 / 5 = 216 kmph answer : c"
Answer: c