Cheukting/mathqa huggingface dataset:
Question (general): how many numbers from 10 to 50 are exactly divisible by 3
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 19
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits b )"
Answer: b
Question (gain): at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "explanation : let rate will be r % 1200 ( 1 + r / 100 ) 2 = 134832 / 100 ( 1 + r / 100 ) 2 = 134832 / 120000 ( 1 + r / 100 ) 2 = 11236 / 10000 ( 1 + r / 100 ) = 106 / 100 = > r = 6 % option d"
Answer: d
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ?
Options: a ) 70 , b ) 105 , c ) 178 , d ) 177 , e ) 169
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 18 35 - - - ? = > 70 answer : a"
Answer: a
Question (gain): andrew purchased 7 kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 908 , c ) 930 , d ) 1075 , e ) 1080
Rationale: "cost of 7 kg grapes = 68 × 7 = 476 . cost of 9 kg of mangoes = 48 × 9 = 432 . total cost he has to pay = 476 + 432 = 908 b"
Answer: b
Question (general): two numbers a and b are such that the sum of 5 % of a and 3 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 7 : 3 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 5 % of a + 3 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 3 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 3 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 9 b = 12 a + 16 b ⇒ 3 a = 7 b ⇒ ab = 7 / 3 ⇒ a : b = 7 : 3 answer : option c"
Answer: c
Question (gain): radha bought a watch for rs . 144 and got a percentage of profit equal to the cost price of the watch . what is the cost price of the watch ?
Options: a ) rs . 72 , b ) rs . 78 , c ) rs . 80 , d ) rs . 90 , e ) rs . 92
Rationale: sp = 144 cp = x profit % = x c . p . = ( 100 / ( 100 + gain % ) ) * s . p . x = ( 100 / 100 + x ) * 144 x ^ 2 + 100 x = 14400 x ^ 2 + 180 x - 80 x - 14400 = 0 ( x + 180 ) ( x - 80 ) = 0 x = - 180 x = 80 answer : d
Answer: d
Question (general): a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 3 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 36 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 3 = 1 / 3 ( b + 3 ) - - - - > 3 a - 9 = b + 3 scenario 2 b - 3 = 1 / 2 ( a + 3 ) - - - - - > 2 b - 6 = a + 3 from scenario 1 , b = 3 a - 12 substitute b with this information in stmt 2 2 ( 3 a - 12 ) - 9 = a + 3 - - - - - - > 6 a - 24 - 9 = a + 3 - - - - - - > 6 a - a = 33 + 3 - - - > 5 a = 36 a = 36 / 5 , answer choice a"
Answer: a
Question (other): 27 is a perfect cube . when x is perfect cube which is added to the prime factor of 27 , the result is not a prime number . what is the square root of x ?
Options: a ) 2
b ) 4
c ) 6
d ) 8
e ) 10
Rationale: 27 is 3 * 3 * 3 2 * 2 = 4 , 3 + 4 = 7 4 * 4 = 16 , 3 + 16 = 17 6 * 6 = 36 , 3 + 36 = 39 8 * 8 = 64 , 3 + 64 = 67 10 * 10 = 100 , 3 + 100 = 103 here c is the only addition that is not a prime number . so the answer is c
Answer: c
Question (general): | x + 3 | – | 4 - x | = | 8 + x | how many k solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Question (general): the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 55 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 55 has the form 4 k + 3 , so the units digit of 93 ^ 55 is 7 . the units digit of powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a
Question (physics): a train traveling at 36 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 120 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 36 kmph * 12 seconds convert 36 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 36 kmph = 5 / 18 ∗ 36 = 10 m / sec therefore , length of the platform = 10 m / s * 12 sec = 120 meters . choice a"
Answer: a
Question (general): when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.05 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 280 , d ) 112 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.05 = 14 / j 0.05 * j = 14 j = 14 / 0.05 = 1400 / 5 = 280 so j = 280 , answer = c ."
Answer: c
Question (general): what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 8 ?
Options: a ) 61,600 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 8 seeing the options after dividing an finding the reminder of 2 my answer was a"
Answer: a
Question (physics): an engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 53 , c ) c . 55 , d ) d . 68 , e ) e . 60
Rationale: "35 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 35 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 87.5 that is approximately 88 thus , more men needed to finish the task = 88 - 35 = 53 hence answer is b"
Answer: b
Question (general): what least number should be subtracted from 1,439 so that the remainder when divided by 5 , 11 , and 13 will leave in each case the same remainder 3 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the lcm of 5 , 11 , and 13 is 715 . the next multiple is 2 * 715 = 1,430 . 1,430 + { remainder } = 1,430 + 3 = 1,433 , which is 6 less than 1,439 . answer : e ."
Answer: e
Question (gain): a and b invests rs . 5000 and rs . 6000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 2 : 3 , b ) 82 : 31 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 5000 * 4 ) + ( 2500 * 8 ) : ( 6000 * 6 ) + ( 4000 * 6 ) 40000 : 60000 2 : 3 answer : a"
Answer: a
Question (gain): how long will a boy take to run round a square field of side 20 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 24 sec , e ) 39 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 20 * 4 = 80 m time taken = 80 * 3 / 10 = 24 sec answer is d"
Answer: d
Question (general): ( 4300731 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1765113 , d ) 1675123 , e ) none of them
Rationale: "let 4300731 - x = 2535618 then x = 4300731 - 2535618 = 1765113 answer is c"
Answer: c
Question (general): what two - digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 4 = 10 x + y = x ^ 2 y ^ 2 - 11 thus 2 xy + 4 = x ^ 2 + y ^ 2 - 11 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 26 or 98 thus the answer is c"
Answer: c
Question (geometry): if a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius , then surface area of each ball ( in sq . cm ) is ?
Options: a ) 100 π
b ) 101 / π
c ) 99 π / 12
d ) 54 / 13 π
e ) 22 / 10 π
Rationale: explanation : 4 / 3 π x 10 x 10 x 10 = 8 x 4 / 3 π rxrxr r = 5 4 π x 5 x 5 = 100 π answer is a
Answer: a
Question (general): what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1115 , 1120 , and 1 , 1252140 , 2345 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54
Rationale: add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e
Answer: e
Question (general): the price of a certain painting increased by 20 % during the first year and decreased by 25 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 90 % , c ) 120 % , d ) 85 % , e ) 95 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.25 = 120 * 0.75 = 90 hence required answer = ( 90 / 100 ) * 100 % = 90 % answer is b ."
Answer: b
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 13 years and that of the other 9 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15
Rationale: explanation : age of the 15 th student = [ 15 * 15 - ( 13 * 5 + 16 * 9 ) ] = 16 years . answer : b
Answer: b
Question (general): if 64 ( 2 ^ x ) = 1 then x =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) - 6 , e ) 5
Rationale: "2 ^ x = 1 / 64 2 ^ x = 1 / 2 ^ 6 2 ^ x = 2 ^ - 6 x = - 6 d"
Answer: d
Question (general): if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 13.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 160 , b ) $ 289 , c ) $ 334 , d ) $ 274 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 13 = 16 * 13 = 208 $ total charge = 126 + 208 = 334 $ answer c"
Answer: c
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 18 km / hr . what is the length of the platform ?
Options: a ) 80 , b ) 240 , c ) 288 , d ) 277 , e ) 221
Rationale: "speed = 18 * 5 / 18 = 5 m / sec . length of the train = 5 * 20 = 100 m . let the length of the platform be x m . then , ( x + 100 ) / 36 = 5 = > x = 80 m . answer : a"
Answer: a
Question (physics): if the lcm and hcf of 12 and another number is 60 and 3 respectively . find the other number ?
Options: a ) 17 , b ) 12 , c ) 15 , d ) 13 , e ) 11
Rationale: "hcf x lcm = product of numbers 3 x 60 = 12 x the other number other number = ( 3 x 60 ) / 12 other number = 15 answer : c"
Answer: c
Question (geometry): the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 828 , c ) c ) 25 , d ) d ) 34 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : option c"
Answer: c
Question (gain): a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 280 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.2
Rationale: price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 280 / 45 = $ 6.2 answer : e .
Answer: e
Question (physics): a train covers a distance of 12 km in 10 minutes . if it takes 6 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 6 ) m = 120 m answer : option b"
Answer: b
Question (general): if x / 2 = y / 4 = z / 6 , then find the value of ( x + y + z ) / z
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) none of these
Rationale: explanation : x / 2 = y / 4 = z / 6 = k , then x = 2 k , y = 4 k and z = 6 k . now , ( x + y + z ) / z = ( 2 k + 4 k + 6 k ) / 6 k = 12 k / 6 k = 2 answer : option e
Answer: e
Question (general): country x taxes each of its citizens an amount equal to 15 percent of the first $ 40000 of income , plus 20 percent of all income in excess of $ 40000 . if a citizen of country x is taxed a total of $ 8000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b .
Answer: b
Question (other): the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 1 / 8 is given by ?
Options: a ) 1 / 49 , b ) 1 / 42 , c ) 1 / 09 , d ) 1 / 77 , e ) 1 / 12
Rationale: "2 / 3 * 6 / 7 * 1 / 3 * 1 / 8 = 1 / 42 answer : b"
Answer: b
Question (other): if w is the set of all the integers between 39 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 40
Rationale: "multiples of 2 from 39 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 38 = [ 99 / 2 ] - [ 38 / 2 ] = 49 - 19 = 30 multiples of 3 from 39 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 38 = [ 99 / 3 ] - [ 38 / 3 ] = 33 - 13 = 20 multiples of 2 and 3 bothi . e . 6 from 39 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 38 = [ 99 / 6 ] - [ 38 / 6 ] = 16 - 6 = 10 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 30 + 20 - 10 = 40 answer option e"
Answer: e
Question (general): the number 500 can be written as the sum of the squares of 2 different positive integers . what is the difference of these 2 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 18 , e ) 13
Rationale: "22 ^ 2 + 4 ^ 2 = 500 - - > 22 - 4 = 18 . d"
Answer: d
Question (gain): the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 15 percent , what was the annual interest rate last year ?
Options: a ) 14.04 % , b ) 15.04 % , c ) 13.64 % , d ) 12.04 % , e ) 10.04 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.1 i ( last year ) = 1.1 i ( last year ) 15 = 1.1 x i ( last year ) i ( last year ) = 15 / 1.1 = 150 / 11 = 13.64 % answer : c"
Answer: c
Question (gain): a sum of money at simple interest amounts to rs . 845 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 728
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 845 - 117 ) = rs . 728 . answer : option e"
Answer: e
Question (gain): find number which is 70 % less than 80 .
Options: a ) 18 , b ) 22 , c ) 24 , d ) 26 , e ) 98
Rationale: "explanation : 70 % less is 30 % of the given number therefore , 30 % of 80 is 24 . answer : c"
Answer: c
Question (general): the sum of 3 consecutive odd numbers is 20 more than the first of these numbers . what is the middle number ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 10
Rationale: solution let the numbers be x , x + 2 , x + 4 then x , ( x + 2 ) + ( x + 4 ) = x + 20 ‹ = › 2 x = 14 ‹ = › x = 7 . therefore middle number = x + 2 = 9 . answer c
Answer: c
Question (general): the sum of ages of 4 children born 4 years different each is 48 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 x = 6 x + 12 = 6 + 12 = 18 answer : e"
Answer: e
Question (gain): a tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 9.33 % , d ) 10.67 % , e ) 11.7 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 2,500 = 7,500 gallons and sodium chloride is 700 gallons ( 7 % of initial solution of 10,000 gallons ) then sodium chloride is 700 / 7,500 * 100 = ~ 9.33 % of the remaining solution of 7,500 gallons . answer : c ."
Answer: c
Question (physics): the speed of a boat in still water is 18 kmph . what is the speed of the stream if the boat can cover 48 km downstream or 32 km upstream in the same time ?
Options: a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "x = the speed of the stream ( 18 + x ) / ( 18 - x ) = 2 / 1 18 + x = 36 - 2 x 3 x = 18 x = 6 km / hour if the speed of the stream is 6 km / hour , then the ' downstream ' speed of the boat is 18 + 6 = 24 km / hour and the ' upstream ' speed of the boat is 18 - 6 = 12 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 24 = 48 km downstream and 2 x 12 = 24 km / hour upstream . answer : c"
Answer: c
Question (physics): a train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train ?
Options: a ) 322 , b ) 324 , c ) 326 , d ) 328 , e ) 330
Rationale: "length = speed * time speed = l / t s = 2000 / 25 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 324 kmph answer : b"
Answer: b
Question (general): a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 32 % of the original number . what percent of the red candies remain ?
Options: a ) 27.5 % , b ) 33.3 % , c ) 35.5 % , d ) 42.5 % , e ) 47.5 %
Rationale: "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.6 x red + yellow = 0.85 x red = 0.425 x , since red = yellow . the answer is d ."
Answer: d
Question (general): the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 61 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.65 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 61 ) = 1173 kgs actual average weight is 1177 / 20 = 58.65 kgs b"
Answer: b
Question (physics): n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n
Options: a ) 11
b ) 12
c ) 13
d ) 14
e ) 15
Rationale: each of 2 present in the party = > no . of pairs possible = nc 2 possible adjacent pairs = n total required combinations = nc 2 - n time taken by each combination to sing a song = 2 min total time taken = 2 ( nc 2 - n ) = 28 on solving the above equation , we get n = 14 answer : d
Answer: d
Question (general): in the floor of a particular kitchen owned by an abstract artist , each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left . if there are 9 rows in all and a total of 405 tiles in the floor , how many tiles does the leftmost row contain ?
Options: a ) 53 , b ) 56 , c ) 60 , d ) 64 , e ) 68
Rationale: this question can be solved in a variety of ways : with algebra , by testing the answers and by using a great number property shortcut involving consecutive integers . we ' re given a few facts to work with : 1 ) there are 9 rows of tiles . 2 ) when going from ' left to right ' , each row contains two fewer tiles than the one next to it . 3 ) there are a total of 405 tiles we ' re asked how many tiles the left - most most row holds ( meaning the one with the most tiles ) . to start , 405 is divisible by 9 , so we can figure out the average number of tiles per row . that is 405 / 9 = 45 . since we ' re dealing with a set of 9 consecutive integers that differ by 2 each , we know that the ' 5 th row ' will have 45 tiles ( the average ) . then we just have to ' add 2 s ' until we get to the first row . . . 45 + 2 + 2 + 2 + 2 = 53 . final answer : a
Answer: a
Question (general): each of 3 charities in novel grove estates has 8 persons serving on its board of directors . if exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors , then how many distinct persons serve on one or more boards of directors ? a . b . c . d . e .
Options: a ) 8 , b ) 13 , c ) 16 , d ) 24 , e ) 27
Rationale: each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b
Answer: b
Question (general): a mixture of 20 kg of spirit and water contains 10 % water . how much water must be added to this mixture to raise the percentage of water to 25 %
Options: a ) 4 kg , b ) 5 kg , c ) 8 kg , d ) 30 kg , e ) 35 kg
Rationale: exp . water in the given mixture = 10 * 20 / 100 = 2 kg , and spirit = ( 20 - 2 ) = 18 kg let x kg of water added , then , x + 2 / 20 + x * 100 = = 25 4 x + 8 = 20 + x , or x = 4 kg answer : a
Answer: a