Cheukting/mathqa huggingface dataset:
Question (general): in a class of 38 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15
Rationale: "total # of students = 38 avg # of books per student = 2 total # of books = 38 * 2 = 76 # of student borrowed at least 3 books = 38 - 2 - 12 - 10 = 14 # of books borrowed by above 14 students = 76 - ( 12 * 1 ) + ( 10 * 2 ) = 44 considering that 13 out of above 14 students borrowed only 3 books , # of books borrowed = 13 * 3 = 39 so maximum # of books borrowed by any single student = 44 - 39 = 5 option b"
Answer: b
Question (general): in a hostel there were 100 students . to accommodate 25 more students the average is decreased by some rupees . but total expenditure increased by rs . 500 . if the total expenditure of the hostel now 8500 , find decrease of average budget ?
Options: a ) 20 , b ) 15 , c ) 12 , d ) 18 , e ) 24
Rationale: "let average is x 100 x + 500 = 8500 x = 80 let decrease = y 125 ( 80 – y ) = 8500 y = 12 answer : c"
Answer: c
Question (physics): 8 men , working 7 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 7 * 18 = 1008 12 × 12 × ( x ) = 1008 x = 7 the answer is b ."
Answer: b
Question (general): of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 6048 , b ) 3648 , c ) 7248 , d ) 1448 , e ) 2168
Rationale: "of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; # of permutations of 3 digits in ppqr - 4 ! / 2 ! total : 9 * 8 * 7 * 4 ! / 2 ! = 6048 . answer : a ."
Answer: a
Question (general): ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ?
Options: a ) 420 , b ) 260 , c ) 200 , d ) 300 , e ) 400
Rationale: explanation : ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 × 5 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 ) 0.75 × ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) × ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 × ( 12 ) 1 = 25 × 12 = 300 answer : option d
Answer: d
Question (physics): a computer factory produces 4200 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 , b ) 3.125 . , c ) 4.5 , d ) 5.225 , e ) 6.25
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 4200 / ( 28 * 24 * 2 ) = 3.125 answer b"
Answer: b
Question (general): a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is 12 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 and 6 , d ) 4 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = 4 i . e x ^ 2 + 4 x - 12 = 0 is the quadratic equation which needs to be solved . ( x - 2 ) ( x + 6 ) = 0 hence x = 2 , x = - 6 imo c"
Answer: c
Question (gain): a bowl of fruit contains 14 apples and 20 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 14 number of oranges = 20 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 20 - x ) = 34 - x 14 / ( 34 - x ) = 7 / 10 = > 20 = 34 - x = > x = 14 answer c"
Answer: c
Question (geometry): the area of a square field is 1225 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?
Options: a ) 7 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 1225 km 2 . then , each side of field = √ 1225 = 35 km distance covered by the horse = perimeter of square field = 35 × 4 = 140 km ∴ time taken by horse = distances / peed = 140 / 20 = 7 h answer a
Answer: a
Question (physics): xavier starts from p towards q at a speed of 50 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 52 km , then how much time does he take to cover the distance ?
Options: a ) 40 , b ) 60 , c ) 48 , d ) 70 , e ) 80
Rationale: first 12 min = 50 * 12 / 60 = 10 km 2 nd 12 min = 60 * 12 / 60 = 12 km 3 rd 12 min = 70 * 12 / 60 = 14 km 4 th 12 min = 80 * 12 / 60 = 16 km total time 12.4 = 48 min c
Answer: c
Question (gain): a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 5 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 89.0 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 5 % of 400 = 20 therefore , total number of rotten fruits = 90 + 20 = 110 therefore number of fruits in good condition = 1000 - 110 = 890 therefore percentage of fruits in good condition = ( 890 / 1000 × 100 ) % = ( 89000 / 1000 ) % = 89.0 % answer : b"
Answer: b
Question (geometry): if a rectangular room measures 8 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000
b ) 16 , 000,000
c ) 2 , 400,000
d ) 24 , 000,000
e ) 240 , 000,000
Rationale: b . 160 , 000,000 8 * 100 * 5 * 100 * 4 * 100 = 160 , 000,000
Answer: b
Question (physics): on a 20 mile course , pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break , ran the rest of the distance at an average rate of 8 miles per hour . how many minutes did pat take to cover the entire course ?
Options: a ) 75 , b ) 105 , c ) 117 , d ) 150 , e ) 162
Rationale: at an average rate of 30 miles per hour in 12 minute ( 1 / 5 hours ) pat covers ( distance ) = ( time ) * ( rate ) = 1 / 5 * 30 = 6 miles , thus she should cover the remaining distance of 20 - 6 = 14 miles at an average rate of 8 miles per hour . to cover 14 miles at an average rate of 8 miles per hour pat needs ( time ) = ( distance ) / ( rate ) = 14 / 8 = 1.75 hours = 105 minutes . therefore pat needs total of 12 + 105 = 117 minutes to cover the entire course . answer : c .
Answer: c
Question (general): the sum of all the integers k such that – 25 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 47
Rationale: "- 24 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 24 - 23 sum of which is - 47 . hence option d . e"
Answer: e
Question (gain): sonika deposited rs . 14500 which amounted to rs . 12200 after 3 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 13505 , b ) 12004 , c ) 15003 , d ) 14500 , e ) 16400
Rationale: "( 14500 * 3 * 3 ) / 100 = 1305 12200 - - - - - - - - 13505 answer : a"
Answer: a
Question (gain): the sale price sarees listed for rs . 298 after successive discount is 12 % and 15 % is ?
Options: a ) 321 , b ) 223 , c ) 245 , d ) 265 , e ) 162
Rationale: "explanation : 298 * ( 88 / 100 ) * ( 85 / 100 ) = 223 answer : b"
Answer: b
Question (general): 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 170 kg then find the average weight of all the 7 rounds ?
Options: a ) 97.1 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 170 / 7 = 97.1 kgs answer : a"
Answer: a
Question (geometry): if the area of the equilateral triangle above is 0.75 , what is the area of the adjacent square ?
Options: a ) ( √ 3 ) / 2
b ) √ 3
c ) √ 6
d ) 3
e ) 2 √ 3
Rationale: area of equilateral triangle : a ^ 2 * ( square root of 3 ) / 4 = 0.75 hence , area of square = a ^ 2 = 0.75 * 4 / ( square root of 3 ) = 3 / ( square root of 3 ) = square root of 3 answer : b
Answer: b
Question (gain): a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 20 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 45
Rationale: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 20 % of 50 % i . e 10 % . so he completed 50 + 10 = 60 % of total trip a"
Answer: a
Question (geometry): it has been raining at the rate of 5 centimeters per hour . if the rain filled a cylindrical drum with a depth of 15 centimeters , and area 300 square centimeters , how long did it take to fill the drum completely ?
Options: a ) 3 hours
b ) 4 hours 15 minutes
c ) 6 hours
d ) 2 hours 5 minutes
e ) 8 hours
Rationale: answer is : a , 3 hours the volume of the drum is irrelevant and only height matters since rain fell all over the city . thus , it takes only 15 / 5 = 3 hours of rain to fill the drum
Answer: a
Question (general): in digging a pond 28 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1000 , c ) 2866 , d ) 2787 , e ) 1400
Rationale: "28 * 10 * 5 = 1400 answer : e"
Answer: e
Question (physics): suppose you work for a manufacturing plant that pays you $ 12.50 an hour and $ . 16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 800 ( before payroll deductions ) ?
Options: a ) 1800 , b ) 1825 , c ) 1850 , d ) 1855 , e ) 1875
Rationale: "hourly = $ 12.50 / hour totalhours = 40 piecework = $ 0.16 / widget totalpieces = ? ? ? ? total pay = ( hourly * totalhours ) + ( piecework * totalpieces ) so , put it all together : $ 800 = ( $ 12.50 * 40 ) + ( $ 0.16 * total pieces ) totalpieces = ( $ 800 - ( $ 12.50 * 40 ) ) / $ 0.16 = 1875 widgets e . 1875"
Answer: e
Question (geometry): the diameter of a cylindrical tin is 10 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 125 , b ) 155 , c ) 130 , d ) 120 , e ) 100
Rationale: "r = 5 h = 5 π * 5 * 5 * 5 = 125 π cc answer : a"
Answer: a
Question (physics): if 8 spiders make 4 webs in 9 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 10 , b ) 20 , c ) 12 , d ) 16 , e ) 18
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 8 : 1 ( webs ) 1 : 9 } : : x : 4 â ‡ ’ 8 ã — 1 ã — 9 = 1 ã — 4 ã — x â ‡ ’ x = 18 answer : option e"
Answer: e
Question (general): if x ^ 2 + ( 1 / x ^ 2 ) = 9 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 79
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 9 ^ 2 - 2 = 79 . thus , the answer is e ."
Answer: e
Question (general): ( 150 % of 1265 ) ÷ 7 = ?
Options: a ) a ) 125 , b ) b ) 175 , c ) c ) 271 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 150 x 1265 / 100 ) ÷ 7 = 189750 / 700 = 271 answer : option c"
Answer: c
Question (other): two vessels contains equal number of mixtures milk and water in the ratio 7 : 2 and 8 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 1 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 7 / 9 + 8 / 9 ) : ( 2 / 9 + 1 / 9 ) = 15 / 9 : 3 / 9 = 5 : 1 answer is c"
Answer: c
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 12 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 477 , b ) 396 , c ) 279 , d ) 276 , e ) 291
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 12 + 21 = 33 t = 12 d = 33 * 12 = 396 . answer : b"
Answer: b
Question (gain): a part of certain sum of money is invested at 9 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 7 , b ) 4 : 0 , c ) 4 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: "12 : 9 = 4 : 3 answer : c"
Answer: c
Question (general): the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 58 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 2 / 35 , e ) none
Rationale: "answer we have , m x n = 6 x 210 = 1260 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 58 / 1260 = 17 / 620 correct option : e"
Answer: e
Question (other): a 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 3 kg when 30 kg alloy is immersed . this is a loss of ( 3 / 30 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Question (geometry): the diameter of a cylindrical tin is 14 cm and height is 2 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 66 , d ) 77 , e ) 98
Rationale: "r = 7 h = 5 π * 7 * 7 * 5 = 98 π cc answer : e"
Answer: e
Question (gain): a shopkeeper sold an article for rs 2552.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: explanation : gain % = ( 152.36 * 100 / 2400 ) = 6.34 % = 6 % approx option c
Answer: c
Question (gain): the balance of a trader weighs 10 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 25 % , d ) 17 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 90 gms because it weighs 10 % less . say , the cost price is $ 90 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 90 + ( 30 / 100 ) * 90 = $ 117 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 117 , the mark up is simply 17 % . ans : d"
Answer: d
Question (general): hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of 3 hammers and 4 wrenches is one - third that of 10 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 1 / 7
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 3 x + 4 y ) = 1 / 3 * ( 10 x + 5 y ) 3 ( 3 x + 4 y ) = ( 10 x + 5 y ) 9 x + 12 y = 10 x + 5 y 7 y = x y = x / 7 ans - e"
Answer: e
Question (general): if a is an integer greater than 2 but less than 7 and b is an integer greater than 4 but less than 13 , what is the range of a / b ?
Options: a ) 23 / 34 , b ) 57 / 60 , c ) 51 / 67 , d ) 19 / 71 , e ) 75 / 64
Rationale: "the way to approach this problem is 2 < a < 7 and 4 < b < 13 minimum possible value of a is 3 and maximum is 6 minimum possible value of b is 5 and maximum is 12 range = max a / min b - min a / max b ( highest - lowest ) 6 / 5 - 3 / 12 = 57 / 60 hence b"
Answer: b
Question (general): all factors of a positive integer a are multiplied and the product obtained is a ^ 3 . if a is greater than 1 , how many factors does a have ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: answer = d = 6 number . . . . . . . . . . . . . . . . factors . . . . . . . . . . . . . . . . . . . . . . . . product 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 6 . . . . . . . . . . . . . . . . . . . . . . . . . 36 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 , 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 , 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 4 , 6 , 12 . . . . . . . . . . . . . . . . . 12 * 12 * 12 number which we are looking for = 12 answer = d
Answer: d
Question (general): when 5 + 1 = 56 , 6 + 1 = 67 , 7 + 1 = 78 , then 8 + 1 = ?
Options: a ) 85 , b ) 98 , c ) 89 , d ) 105 , e ) 129
Rationale: "5 + 1 = > 5 x 1 = 5 & 5 + 1 = 6 = > 5 & 6 = > 56 6 + 1 = > 6 x 1 = 6 & 6 + 1 = 7 = > 6 & 7 = > 67 7 + 1 = > 7 x 1 = 7 & 7 + 1 = 8 = > 7 & 8 = > 78 then 8 + 1 = > 8 x 1 = 8 & 8 + 1 = 9 = > 8 & 9 = > 89 answer : c"
Answer: c
Question (physics): express 22 mps in kmph ?
Options: a ) 79.2 kmph , b ) 89.2 kmph , c ) 79.6 kmph , d ) 99.2 kmph , e ) 69.2 kmph
Rationale: "22 * 18 / 5 = 79.2 kmph answer : a"
Answer: a
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 58 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 4
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 58 * ( n + 1 ) - - > n = 4 . or as 40 extra units increased the average for n + 1 days by 8 units per day then 40 / ( n + 1 ) = 8 - - > n = 4 . answer : e ."
Answer: e
Question (general): the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 32 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 21.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) solve the equation . 262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) 8 , 411.2 + 3 , 104.35 x = 44 , 782.4 + 1 , 399.45 x 8 , 411.2 + 1 , 704.9 x = 44 , 782.4 1 , 704.9 x = 36 , 371.2 x ≈ 21.3 answer is b ."
Answer: b
Question (general): the sum of the squares of 3 numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :
Options: a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these
Rationale: x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c
Answer: c
Question (physics): two goods trains each 720 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 sec , b ) 88 sec , c ) 48 sec , d ) 18 sec , e ) 72 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 750 + 750 = 1500 m . required time = 1500 * 6 / 125 = 72 sec . answer : e"
Answer: e
Question (general): if w / x = 1 / 6 and w / y = 1 / 5 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 11 / 5 , e ) 9 / 5
Rationale: "w / x = 1 / 6 = > x = 6 w and w / y = 1 / 5 = > y = 5 w ( x + y ) / y = ( 6 w + 5 w ) / 5 w = 11 w / 5 w = 11 / 5 correct option : d"
Answer: d
Question (general): 35 liters of a mixture is created by mixing liquid p and liquid q in the ratio 4 : 3 . how many liters of liquid q must be added to make the ratio 5 : 7 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: let x be the amount of liquid q to be added . ( 3 / 7 ) * 35 + x = ( 7 / 12 ) * ( 35 + x ) 1260 + 84 x = 1715 + 49 x 35 x = 455 x = 13 the answer is d .
Answer: d
Question (other): a jar contains a mixture of ab in the ratio 4 : 1 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 32 , d ) 20 , e ) 25
Rationale: "20 litres of mixture that is replaced will contain 16 litres of a and 4 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 16 ] / [ k - 4 + 20 ] = 2 / 3 = > 12 k - 48 = 2 k - 8 + 40 = > 10 k = 80 solve for k which is k = 8 so initial volume of liquid a = 4 k = 32 litres answer : c"
Answer: c
Question (physics): two trains 140 m and 160 m long run at the speed of 60 kmph and 40 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 40 = 100 kmph * 5 / 18 = 250 / 9 m / s distance covered in crossing each other = 140 + 160 = 300 m required time = 300 * 9 / 250 = 54 / 5 = 10.8 sec answer is c"
Answer: c
Question (general): for a certain exam , a score of 60 was 2 standard deviations below mean and a score of 100 was 3 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "mean - 2 sd = 60 mean + 3 sd = 100 by solving above we get , sd ( absolute value ) = 8 mean = 76 ans . b"
Answer: b
Question (general): the sum of the present age of henry and jill is 48 . what is their present ages if 9 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: "let the age of jill 9 years ago be x , age of henry be 2 x x + 9 + 2 x + 9 = 48 x = 10 present ages will be 19 and 29 answer : d"
Answer: d