Cheukting/mathqa huggingface dataset:
Question (geometry): the area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm . what is the perimeter of the square ?
Options: a ) 802 , b ) 800 , c ) 829 , d ) 389 , e ) 245
Rationale: "area of the square = s * s = 5 ( 125 * 64 ) = > s = 25 * 8 = 200 cm perimeter of the square = 4 * 200 = 800 cm . answer : b"
Answer: b
Question (general): when positive integer x is divided by 10 , the quotient is y and the remainder is 3 . when 2 x is divided by 7 , the quotient is 3 y and the remainder is 1 . what is the value of 11 y – x ?
Options: a ) 2 , b ) - 2 , c ) 3 , d ) - 3 , e ) 4
Rationale: "( 1 ) x = 10 y + 3 ( 2 ) 2 x = 21 y + 1 ( 2 ) - ( 1 ) : x = 11 y - 2 11 y - x = 2 the answer is a ."
Answer: a
Question (general): at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 160.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 39 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 160.5 subtracting the first equation from the second gives us b + 3 s = 40.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 39 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d"
Answer: d
Question (general): if 300 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 75 , b ) 74 , c ) 79 , d ) 77 , e ) 72
Rationale: "the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 300 factorial will have 74 as - 300 / 5 = 60 60 / 5 = 12 12 / 5 = 2 so answer will be ( d ) 74"
Answer: d
Question (general): 15.06 * 0.0001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 6 digits should be there . option b"
Answer: b
Question (general): addison high school ’ s senior class has 200 boys and 160 girls . if 60 % of the boys and 75 % of the girls attended college , what percentage of the total class that did not attend college ?
Options: a ) 33.33 , b ) 60 , c ) 80 , d ) 66.67 , e ) 64
Rationale: "number of boys attending the college : 0.60 * 200 = 120 number of girls attending the college : 0.75 * 160 = 120 total attending = 120 + 120 = 240 total people = 200 + 160 = 360 % of people attending = 240 / 360 = 66.67 % . d is the correct answer"
Answer: d
Question (other): find the fraction which has the same ratio to 1 / 13 that 5 / 34 has to 7 / 48 .
Options: a ) 110 / 1547 , b ) 120 / 1547 , c ) 140 / 1547 , d ) 160 / 1547 , e ) 220 / 1547
Rationale: p : 1 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 1 / 13 * 5 / 34 p * 7 / 48 = 5 / 442 p = 240 / 3094 = > p = 120 / 1547 answer : b
Answer: b
Question (general): two numbers are such that the square of one is 224 less than 8 times the square of the other . if the numbers be in the ratio of 3 : 4 , the numbers are
Options: a ) 6 , 8 , b ) 9 , 12 , c ) 12 , 16 , d ) 16 , 20 , e ) none
Rationale: solution let the numbers be 3 x and 4 x . then , ( 4 x ) 2 = 8 x ( 3 x ) 2 - 224 ‹ = › 16 x 2 = 72 x 2 - 224 ‹ = › 56 x 2 = 224 . ‹ = › x 2 = 4 . ‹ = › x = 2 . so , the numbers are 6 and 8 . answer a
Answer: a
Question (gain): a and b invests rs . 3500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 21 : 5 , b ) 21 : 16 , c ) 21 : 2 , d ) 9 : 9 , e ) 21 : 11
Rationale: "( 3.5 * 6 + 7 * 6 ) : ( 4 * 12 ) 63 : 48 = > 21 : 16 answer : b"
Answer: b
Question (physics): a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ?
Options: a ) 5 / 6 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 5
Rationale: "the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 10 / 30 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is c ."
Answer: c
Question (physics): tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 4 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 7 / 15 , b ) 9 / 20 , c ) 11 / 25 , d ) 13 / 27 , e ) 15 / 31
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 3 / 4 ) = 4 / 9 hours peter worked for 13 / 9 hours so he painted 13 / 9 * 1 / 3 = 13 / 27 of the room . the answer is d ."
Answer: d
Question (physics): the distance from city a to city b is 30 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 88 , c ) 120 , d ) 152 , e ) 154
Rationale: "the time it takes bob to drive to city b is 30 / 40 = 0.75 hours . alice needs to take less than 0.25 hours for the trip . alice needs to exceed a constant speed of 30 / 0.25 = 120 miles per hour . the answer is c ."
Answer: c
Question (general): if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 83 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 83 0.18 x = 243 x = 1350 then the amount invested at 8 % is $ 2000 - $ 1350 = $ 650 the answer is b ."
Answer: b
Question (general): line q has the equation 5 y – 3 x = 90 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 58 , b ) 61 , c ) 64 , d ) 67 , e ) 70
Rationale: 5 y - 3 x = 90 and so y = 3 x / 5 + 18 when x = 0 , then y = 18 . when y = 0 , then x = - 30 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 30 , 0 ) , 0 = - 5 ( - 30 ) / 3 + c the y - intercept is c = - 50 . thus the perpendicular line s can have y - intercepts from - 49 up to 17 . the number of possible lines is 49 + 17 + 1 = 67 the answer is d .
Answer: d
Question (general): the ratio of expenditure and savings is 3 : 2 . if the income increases by 15 % and the savings increases by 6 % , then by how much percent should his expenditure increases ?
Options: a ) 22 , b ) 21 , c ) 88 , d ) 76 , e ) 29
Rationale: answer : b ) 21
Answer: b
Question (gain): in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 160 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 400 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 160 ( 40 * 4 = 160 ) 100 % - - - - - > 400 ( 100 * 4 = 400 ) answer : option b"
Answer: b
Question (physics): the sum of three consecutive even numbers is 48 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 64
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 48 6 p = 48 = > p = 8 . the middle number is : 8 p = 64 . answer : e"
Answer: e
Question (general): there are 8 stores in town that had a total of 24 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 9 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "9 people visited 2 stores each for 18 visits . to maximize the number of stores that one person visited , let ' s assume that 2 people visited 1 store each . the number of remaining visits is 24 - 18 - 2 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Question (physics): if a train , travelling at a speed of 80 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 110.111 m , b ) 121.111 m , c ) 111.11 m , d ) 141.111 m , e ) 181.111 m
Rationale: "d = 80 * 5 / 18 * 5 = 111.11 m answer : c"
Answer: c
Question (general): in how many ways can the integer 120 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "120 = ( 2 ^ 3 ) * 3 * 5 since 120 is not a perfect square , no of ways = 5 answer c"
Answer: c
Question (general): a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 4 : 5 : 2 , respectively , by weight . if 44 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 4 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 4 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 4 x + 5 x + 2 x = 44 11 x = 44 x = 4 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 2 ) ( 4 ) = 8 pounds of apples = ( 4 ) ( 4 ) = 16 thus we know that there are 16 – 8 = 8 more pounds of apples than grapes . answer is c ."
Answer: c
Question (general): if an integer n is to be selected at random from 1 to 99 , inclusive , what is probability n ( n + 1 ) will be divisible by 3 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 3 , either n or n + 1 has to be a multiple of 3 . thus n must be of the form 3 k or 3 k - 1 , but not 3 k + 1 . the probability is 2 / 3 . the answer is d ."
Answer: d
Question (gain): a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3267 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 10 , c ) 28 , d ) 24 , e ) 35
Rationale: "explanation : 2420 - - - 847 100 - - - ? = > 35 % answer : option e"
Answer: e
Question (general): workers in a factory store products inside two different sized boxes . the bigger of the boxes can store 50 products while the smaller box can store 40 products . if a fresh batch of products numbering 212 in total were to be stored , what is the least number of products that will not be boxed ?
Options: a ) 23 , b ) 11 , c ) 2 , d ) 10 , e ) 12
Rationale: total products to be stored 212 the big box can store 50 small box can store 40 storing 212 products in big box 212 / 50 = 4 r 12 least number of toys that will be left unboxed = 12 answer : e
Answer: e
Question (general): a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes william can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Question (general): in a hostel , the number of students decreased by 5 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 12.3 % , c ) 25 % , d ) 40 % , e ) 9.4 %
Rationale: cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 5 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.95 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.95 * 1.2 ) = > f ( new ) = 0.877 f therefore the new cost of food must be 87.7 % of the old cost , or the cost of food must decrease by 12.28 % ( optionb )
Answer: b
Question (physics): at 15 : 00 there were 21 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d
Answer: d
Question (physics): a boy wants to make cuboids of dimension 5 m , 6 m and 7 m from small cubes of . 03 m 3 . later he realized he can make same cuboids by making it hollow . then it takes some cubes less . what is the number of the cubes to be removed ?
Options: a ) 1000
b ) 2000
c ) 3000
d ) 4000
e ) 5000
Rationale: volume of the small cube = 0.03 m ^ 3 so side of this cube = cubic root of 0.03 m ^ 3 = . 312 m so after removing the outermost layer the dimensions for the inner cuboid will be ( 5 - 2 * 0.312 ) , ( 6 - 2 * 0.312 ) , ( 7 - 2 * 0.312 ) so total volume will be ( 4.376 ) * ( 5.376 ) * ( 6.376 ) = 150 m ^ 3 so no of cubes will be 150 / 0.03 = 5000 so we can remove 5000 inner cubes answer : e
Answer: e
Question (gain): if a speaks the truth 70 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.42 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 70 / 100 = 0.7 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.7 × 0.6 = 0.42 answer : d"
Answer: d
Question (geometry): find the curved surface area , if the radius of a cone is 21 m and slant height is 15 m ?
Options: a ) 660
b ) 770
c ) 880
d ) 900
e ) 990
Rationale: cone curved surface area = ï € rl 22 / 7 ã — 21 ã — 15 = 66 ã — 15 = 990 m ( power 2 ) answer is e .
Answer: e
Question (general): of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 130 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 650 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 130 geese survived the first year : 1 / 5 * ( total ) = 130 - - > ( total ) = 650 . answer : d ."
Answer: d
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 22 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 190 , c ) 276 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 22 sec . let the length of the train be x meters . then , ( x + 250 ) / 22 = 20 x = 190 m . answer : b"
Answer: b
Question (general): john was thrice as old as tom 6 years ago . john will be 9 / 7 times as old as tom in 6 years . how old is tom today ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 9 / 7 * ( t + 6 ) 7 j + 42 = 9 t + 54 7 ( 3 t - 12 ) + 42 = 9 t + 54 12 t = 96 t = 8 the answer is b ."
Answer: b
Question (general): how many integers from 0 to 48 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 46 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 46 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 45 or , n - 1 = 15 or , n = 16 b"
Answer: b
Question (other): what is the prime factors ’ number of 36 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 2 * 3 ^ 2 prime factors ’ number will be 2 + 2 = 4 . hence , answer is c ."
Answer: c
Question (physics): how much time will a train of length 250 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 55 , b ) 99 , c ) 88 , d ) 76 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 250 + 300 = 550 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 550 / 10 = 55 sec . answer : a"
Answer: a
Question (general): for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 20 , then v =
Options: a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) 48
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 20 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 45 the answer is d ."
Answer: d
Question (general): ( 4300231 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764613 , d ) 1675123 , e ) none of them
Rationale: "let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c"
Answer: c
Question (general): the difference of 2 digit no . & the no . obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 13
Rationale: let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b
Answer: b
Question (general): the average of 5 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 12.5 , b ) 26.2 , c ) 6.5 , d ) 7.5 , e ) 12
Rationale: "5 * 15 + 36 – 26 = 75 / 10 = 7.5 answer : d"
Answer: d
Question (geometry): the length of a rectangle is reduced by 10 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 10 % , b ) 11.1 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 10 * 100 ) / ( 100 - 10 ) = 11.1 % b"
Answer: b
Question (gain): rs 3500 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 2800 , c ) s 1800 , d ) s 1500 , e ) s 1550
Rationale: "explanation : average rate = ( 144 / 3500 ) * 100 = 4.11 ratio = 8.85 : 11.14 so , first part = ( 8.85 / 20 ) * 3500 = rs 1550 . answer : e"
Answer: e
Question (physics): a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 4 sec , d ) 2 sec , e ) 9 sec
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 110 * 3 / 55 = 6 sec . answer : b"
Answer: b
Question (general): what is the sum of all 4 digit integers formed using the digits 2 , 3 , 4 and 5 ( repetition is allowed )
Options: a ) 444440 , b ) 610000 , c ) 666640 , d ) 995456 , e ) 880000
Rationale: n = 4 * 4 * 4 * 4 = 256 < x > = ( 5555 + 2222 ) / 2 = 3888.5 sum = number of integers x average value n * < x > = 256 * 3888.5 = 711040 answer = d
Answer: d
Question (physics): length of a rectangular plot is 10 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 55 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m a"
Answer: a
Question (geometry): what is the diagonal of a square field whose perimeter is 24 m ?
Options: a ) 8 m
b ) 2 m
c ) 7 m
d ) 10 m
e ) 6 √ 2 m
Rationale: sol : let the side of the square be x meters . therefore , 4 x = 24 x = 6 diagonal of the square is = √ 2 * ( 6 ) ^ 2 = 6 √ 2 answer : e
Answer: e
Question (physics): due to construction , the speed limit along an 5 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 3.12 , b ) 8 , c ) 10 , d ) 15 , e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 55 = 5 * 12 / 11 = 5.45 new time in minutes to cross 5 miles stretch = 5 * 60 / 35 = 5 * 12 / 7 = 8.57 time difference = 3.12 ans : a"
Answer: a
Question (general): the average age of an adult class is 40 years . 2 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was the original strength of class ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 2 , e ) 22
Rationale: "let original strength = y then , 40 y + 2 x 32 = ( y + 2 ) x 36 â ‡ ’ 40 y + 64 = 36 y + 72 â ‡ ’ 4 y = 8 â ˆ ´ y = 2 d"
Answer: d
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 9 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 4 : 3 , c ) 4 : 4 , d ) 4 : 9 , e ) 3 : 4
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 9 : √ 16 = 3 : 4 answer : e"
Answer: e