Cheukting/mathqa huggingface dataset:
Question (general): the mean of 40 observations was 36 . it was found later that an observation 34 was wrongly taken as 20 . the corrected new mean is
Options: a ) 76.55 , b ) 36.35 , c ) 46.15 , d ) 16.05 , e ) 20
Rationale: "explanation : correct sum = ( 36 * 40 + 34 - 20 ) = 1454 correct mean = = 1454 / 40 = 36.35 answer : b"
Answer: b
Question (general): a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 40 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1312.5 , c ) 1400 , d ) 1600 , e ) 1625
Rationale: "300 gallons of water increases capacity by 40 % that means 40 % is 300 gallons , so 100 % would be = 300 * 100 / 40 = 750 gallons now 750 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1050 * 100 / 80 = 1312.5 b is the answer"
Answer: b
Question (physics): the speed of a car is 10 m / s . what is the its speed in kmph .
Options: a ) 25 kmph , b ) 30 kmph , c ) 50 kmph , d ) 36 kmph , e ) 37 kmph
Rationale: explanation : m / sec to km / hr conversion : x m / sec = [ x x ( 18 / 5 ) ] km / hr 10 x ( 18 / 5 ) 36 kmph answer : option d
Answer: d
Question (general): total dinning bill of 5 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 32.84 , b ) 22.84 , c ) 30.58 , d ) 24.84 , e ) 30.84
Rationale: "dinner bill of 5 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 5 = $ 30.58 answer : c"
Answer: c
Question (general): at a monthly meeting , 3 / 5 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 6 / 25 , b ) 11 / 50 , c ) 14 / 75 , d ) 23 / 100 , e ) 31 / 150
Rationale: "males who did not arrive on time are 1 / 5 * 3 / 5 = 3 / 25 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 5 = 1 / 15 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 25 + 1 / 15 = 14 / 75 the answer is c ."
Answer: c
Question (physics): the sum of 7 consecutive integers is 980 . how many of them are prime ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the middle number is 140 and the seven numbers are 137 , 138 , 139 , · · · , 143 . now 138 , 140 , and 142 are even , 141 is divisible by 3 , and 143 - by 11 . the remaining numbers 137 and 139 are prime ( it is easy to check that they are not divisible by 23 , 57 and 11 ) . correct answer c
Answer: c
Question (general): if n = 8 ^ 8 – 7 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 7 , e ) 4
Rationale: "8 ^ 8 - 8 = 8 ( 8 ^ 7 - 1 ) = = > 8 ( 2 ^ 21 - 1 ) last digit of 2 ^ 21 is 2 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit . now on multiply this with 7 , we get unit digit as 7 answer : d"
Answer: d
Question (other): how many prime numbers between 1 and 100 are factors of 210 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: factor of 210 = 2 * 3 * 5 * 7 - - - 4 prime numbers b
Answer: b
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 12 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 96 % , d ) 124.2 % , e ) 138 %
Rationale: "0,096 r = x / 100 * 0.1 r answer c"
Answer: c
Question (general): when positive integer x is divided by 7 , the quotient is y and the remainder is 3 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 2 . what is the value of 11 y – x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "( 1 ) x = 7 y + 3 ( 2 ) 2 x = 18 y + 2 ( 2 ) - ( 1 ) : x = 11 y - 1 11 y - x = 1 the answer is d ."
Answer: d
Question (general): n is a positive integer . when n + 1 is divided by 9 , the remainder is 1 . what is the remainder when n is divided by 9 ?
Options: a ) 0 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "n + 1 = 9 a + 1 i . e . n + 1 = 10 , 19 , 28 , 37 , . . . etc . i . e . n = 9 , 18 , 27 , 36 , . . . etc . when n is divided by 9 remainder is always 0 answer : a"
Answer: a
Question (general): how many positive integers less than 23 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 17 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "8 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 } 2 odd multiples of 5 : { 5 , 15 } 9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 8 + 1 + 9 - 1 = 17 . answer : a ."
Answer: a
Question (geometry): we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed ?
Options: a ) 8
b ) 9
c ) 10
d ) 11
e ) 12
Rationale: total no . of cubes = n ^ 3 here n ^ 3 = 125 which makes n = 5 , also minimum no . of cuts required = 3 ( n - 1 ) hence , 3 ( 5 - 1 ) = 12 cuts . answer : e
Answer: e
Question (general): if a : b : : 3 : 7 , then what is ( 5 a + 6 b ) : ( a - 2 b ) ?
Options: a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 11 : 10 , e ) - 1 : 10
Rationale: a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 6 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 6 ] / [ ( 3 / 7 ) - 2 ] = - 57 / 11 answer : b
Answer: b
Question (geometry): a block of wood has dimensions 10 cm x 10 cm x 50 cm . the block is painted red and then cut evenly at the 25 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5.5 % , b ) 8.3 % , c ) 11.6 % , d ) 14.2 % , e ) 17.5 %
Rationale: "the area of each half is 100 + 4 ( 250 ) + 100 = 1200 the area that is not painted is 100 . the fraction that is not painted is 100 / 1200 = 1 / 12 = 8.3 % the answer is b ."
Answer: b
Question (physics): a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 30 percent .
Options: a ) 145 , b ) 90 , c ) 175 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 30 percent 90 min . answer : b
Answer: b
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 5 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 304
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with five 5 - s , 5 x 5 x 4 * 1 * 1 * 4 = 16 . thus there are 320 - 16 = 304 such numbers . answer : e ."
Answer: e
Question (general): two brothers ram and ravi appeared for an exam . the probability of selection of ram is 6 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 3 , c ) 6 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 6 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 6 / 7 x 1 / 5 = 6 / 35 answer : c"
Answer: c
Question (general): a volunteer organization is recruiting new members . in the fall they manage to increase their number by 6 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) - 16.16 % , b ) - 15.15 % , c ) - 14.14 % , d ) - 13.13 % , e ) - 12.12 %
Rationale: "( 100 % + 6 % ) * ( 100 % - 19 % ) = 1.06 * . 81 = 0.8586 . 1 - 0.8586 = 14.14 % lost = - 14.14 % the answer is c the organization has lost 14.14 % of its total volunteers from fall to spring ."
Answer: c
Question (physics): one hour after yolanda started walking from x to y , a distance of 31 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 1 miles per hour and bob â s was 2 miles per hour , how many miles had bob walked when they met ?
Options: a ) 19 , b ) 20 , c ) 22 , d ) 21 , e ) 19.5
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked ( t + 1 ) miles . these distances must sum to 31 miles , so 2 t + ( t + 1 ) = 31 , which may be solved for t as follows 2 t + ( t + 1 ) = 31 2 t + t + 1 = 31 3 t = 30 t = 10 ( hours ) therefore , bob had walked 2 t = 2 ( 10 ) = 20 miles when they met . the best answer is b ."
Answer: b
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5565 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 200 , c ) 288 , d ) 210 , e ) 1999
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5565 [ 4 l - 40 ] = 5565 / 26.50 = 210 4 l = 250 l = 250 / 4 = 62.5 meters . answer : d"
Answer: d
Question (geometry): if the perimeter of δ acd is 9 + 3 √ 3 , what is the perimeter of equilateral triangle δ abc ?
Options: a ) 9
b ) 18 − 3 √ 3
c ) 18
d ) 18 + 3 √ 3
e ) 27
Rationale: the altitude of an equilateral triangle is side * √ 3 / 2 . as perimeter of triangle acd is 9 + 3 √ 3 , ac + cd + ad = ( side + side / 2 + side * √ 3 / 2 ) = 9 + 3 √ 3 or side = 6 . perimeter of equilateral triangle , abc is 3 ( side ) or 18 . answer : ( optionc )
Answer: c
Question (general): if 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 28 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 8 * 7 / 2 = 28 answer : b"
Answer: b
Question (gain): a man ' s basic pay for a 40 hour week is rs . 20 . overtime is paid for at 25 % above the basic rate . in a certain week he worked overtime and his total wage was rs . 25 . he therefore worked for a total of :
Options: a ) 45 hours , b ) 47 hours , c ) 48 hours , d ) 50 hours , e ) none
Rationale: explanation : basic rate per hour = rs . ( 20 / 40 ) = rs . 1 / 2 overtime per hour = 125 % of rs . 1 / 2 = 125 / 100 × 1 / 2 = rs . 5 / 8 suppose he worked x hours overtime . then , 20 + 5 / 8 x = 25 or 5 / 8 x = 5 x = 5 × 8 / 5 = 8 hours so he worked in all for ( 40 + 8 ) hours = 48 hours . correct option : c
Answer: c
Question (physics): a can complete a work in 15 days and b can do the same work in 7 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 5 1 / 2 days , c ) 6 1 / 2 days , d ) 7 1 / 2 days , e ) 10 days
Rationale: "the required answer = ( 15 - 3 ) * 7 / 15 = 84 / 15 = 5 1 / 2 days answer is b"
Answer: b
Question (general): how many positive integers less than 60 have a reminder 01 when divided by 3 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 20
Rationale: "1 also gives the remainder of 1 when divided by 3 . so , there are total of 20 numbers . answer : e ."
Answer: e
Question (physics): it takes six minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video ?
Options: a ) 13.8 , b ) 14.1 , c ) 14.4 , d ) 14.6 , e ) 14.8
Rationale: "the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 6 ) = 1 / 360 of the video per second . the combined rate is 1 / 15 + 1 / 360 = 25 / 360 of the video per second . the time required to load the video is 360 / 25 = 14.4 seconds . the answer is c ."
Answer: c
Question (gain): a computer store offers employees a 10 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1200 dollars and marked up the price 10 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 10 % off retail price ) as opposed to the final retail price .
Options: a ) 122 , b ) 132 , c ) 142 , d ) 152 , e ) 162
Rationale: "cost price = 1200 profit = 10 % = 10 % of 1200 = 120 selling price = cp + profit sp = 1320 a discount of 10 % to employees means 10 % off on 1320 so 10 % of 1320 = 132 ans b"
Answer: b
Question (general): for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 12 , then v =
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: ( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 12 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 27 the answer is e .
Answer: e
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions .
Options: a ) 287 m , b ) 704 m , c ) 168 m , d ) 278 m , e ) 107 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : b"
Answer: b
Question (gain): 20 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.2 * 0.6 = 0.12 of the class are female science majors . then 0.28 of the class are male science majors . 0.4 x = 0.28 x = 0.7 = 70 % the answer is d .
Answer: d
Question (general): a grocer has a sale of rs . 8435 , rs . 8927 , rs . 8855 , rs . 9230 and rs . 8562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 8500 ?
Options: a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 6991
Rationale: "explanation : total sale for 5 months = rs . ( 8435 + 8927 + 8855 + 9230 + 8562 ) = rs . 44009 . required sale = rs . [ ( 8500 x 6 ) â € “ 44009 ] = rs . ( 51000 â € “ 44009 ) = rs . 6991 . answer e"
Answer: e
Question (physics): two stations a and b are 110 km apart on a straight line . one train starts from a at 5 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 5 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 8 a . m . answer : c"
Answer: c
Question (physics): a circular ground whose diameter is 40 metres , has a garden of area 1100 m ^ 2 around it . what is the wide of the path of the garden ?
Options: a ) 8.07 , b ) 7.07 , c ) 6.07 , d ) 7.0 , e ) 8.5
Rationale: "req . area = ï € [ ( 20 ) 2 â € “ ( r ) 2 ] = 22 â  „ 7 ã — ( 400 - r ^ 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] ie ) 22 / 7 ( 400 - r ^ 2 ) = 1100 , ie ) r ^ 2 = 50 , r = 7.07 m answer b"
Answer: b
Question (physics): in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 4 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 36 machines take 4 hours to fill 4 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 4 = 6 ans b"
Answer: b
Question (gain): a man gains 20 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 140 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 120 / 100 ) x = 6 x / 5 new s . p . = 2 ( 6 x / 5 ) = 12 x / 5 profit = 12 x / 5 - x = 7 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 7 x / 5 ) * ( 1 / x ) * 100 = 140 % option b"
Answer: b
Question (gain): if the cost price is 90 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 90 profit = $ 10 profit % = 10 / 90 * 100 = 25 / 6 = 11 % approximately answer is b"
Answer: b
Question (general): marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 200 , and the total cost is $ 40,000 , what is the value of n ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 80 , e ) 150
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 40,000 = $ 10,000 + n * $ 200 - - > n = 150 . answer : e ."
Answer: e
Question (general): 7 does not occur in 1000 . so we have to count the number of times it appears between 1 and 999 . any number between 1 and 999 can be expressed in the form of xyz where 0 < x , y , z < 9 .
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 470
Rationale: 1 . the numbers in which 7 occurs only once . e . g 7 , 17 , 78 , 217 , 743 etc this means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits ( i . e 0 to 9 with the exception of 7 ) you have 1 * 9 * 9 = 81 such numbers . however , 7 could appear as the first or the second or the third digit . therefore , there will be 3 * 81 = 243 numbers ( 1 - digit , 2 - digits and 3 - digits ) in which 7 will appear only once . in each of these numbers , 7 is written once . therefore , 243 times . 2 . the numbers in which 7 will appear twice . e . g 772 or 377 or 747 or 77 in these numbers , one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7 ) . there will be 9 such numbers . however , this digit which is not 7 can appear in the first or second or the third place . so there are 3 * 9 = 27 such numbers . in each of these 27 numbers , the digit 7 is written twice . therefore , 7 is written 54 times . 3 . the number in which 7 appears thrice - 777 - 1 number . 7 is written thrice in it . therefore , the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300 option b
Answer: b
Question (physics): a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 16 km ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 7
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 16 t = 16 / 2 = 8 answer : c"
Answer: c
Question (general): in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 5 5 / 9 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: profit in 1982 = 15.6 - 12 = 3.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 3.6 ) / 3.6 * 100 % = 5 5 / 9 % answer b
Answer: b
Question (physics): peter can cover a certain distance in 1 hr . 24 min . by covering two - third of the distance at 4 kmph and the rest at 5 kmph . find the total distance .
Options: a ) 4 km , b ) 5 km , c ) 6 km , d ) 7 km , e ) 8 km
Rationale: time = distance / speed let total distance travelled be x in 84 / 60 hrs 2 / 3 rd of x travelled in 4 km / hr 1 / 3 rd of distance travelled in 5 km / hr 2 x / ( 3 * 4 ) + x / ( 3 * 5 ) = 84 / 60 x = 6 km answer : c
Answer: c
Question (geometry): if the area of a circle decreases by 20 % , then the radius of a circle decreases by
Options: a ) 20 %
b ) 18 %
c ) 36 %
d ) 11 %
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 − 20 ) % = ( 100 − 10 √ 80 ) % = 100 - 89 = 11 % answer d
Answer: d
Question (general): if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) by 18 only , e ) none of these
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . correct option : b"
Answer: b
Question (physics): two trains 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 11.52 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 10.2 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 180 = 320 m . required time = 320 * 9 / 250 = 11.52 sec . answer : a"
Answer: a
Question (general): the average of first seven multiples of 8 is :
Options: a ) 9 , b ) 16 , c ) 15 , d ) 32 , e ) 10
Rationale: "explanation : ( 8 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 8 x 28 / 7 = 32 answer : d"
Answer: d
Question (probability): a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability j that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability j is 2 / 3 . d"
Answer: d
Question (geometry): the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 54 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 54 2 l ^ 2 / 3 = 54 l ^ 2 = 81 l = 9 cm the answer is d ."
Answer: d
Question (geometry): carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 3 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 43 , c ) 42 , d ) 40 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 3 w = 120 = > w = 40 answer d"
Answer: d
Question (general): dacid obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 98 , b ) 78 , c ) 76 , d ) 87 , e ) 75
Rationale: "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : e"
Answer: e
Question (general): 16 ltr of water is added with 24 ltr of a solution containing 90 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 48 % , b ) 52 % , c ) 54 % , d ) 60 % , e ) 70 %
Rationale: "we have a 24 litre solution containing 90 % of alcohol in the water . = > quantity of alcohol in the solution = 24 ã — 90 / 100 now 16 litre of water is added to the solution . = > total quantity of the new solution = 24 + 16 = 40 percentage of alcohol in the new solution = 24 ã — 90 / 100 40 ã — 100 = 24 ã — 9010040 ã — 100 = 24 ã — 2.25 / 100 = 54 % c"
Answer: c