regisss/math_qa huggingface dataset:
Problem: approximately how many cubic feet of water are needed to fill a circular swimming pool that is 70 feet across and 9 feet deep ?
Options: a ) 4000
b ) 10000
c ) 20000
d ) 35000
e ) 45000
Rationale: answer should be d . v = \ pir ^ 2 h = \ pi * 35 ^ 2 * 9 = approximately 35000
Answer: d
Problem: an empty wooden vessel weighs 14 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 6 / 13 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5
Rationale: "an empty wooden vessel weighs 14 % of its total weight when filled with paint : vessel = 0.14 ( vessel + paint ) ; 14 v = v + p ( so the weight of completely filled vessel is 14 v ) p = 13 v ( so the weight of the paint when the vessels is completely filled is 13 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 14 v ; p ' = 6 v ( so the weight of the paint when the vessels is partially filled is 6 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 6 v / 13 v = 6 / 13 . answer : a ."
Answer: a
Problem: 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 61 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 61 answer : c"
Answer: c
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 12 and 1.2 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 9.6 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "mean = 12 two standard deviations is 1.2 + 1.2 = 2.4 there could be two calues for this . mean + two standard deviations = 14.4 mean - two standard deviations = 9.6 answer choice has 9.6 and so a is the answer ."
Answer: a
Problem: for what value of â € œ k â €  will the equation ( 2 kx 2 + 4 kx + 2 ) = 0 have equal roots ?
Options: a ) 1 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 4 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 1 answer : a"
Answer: a
Problem: a is the average ( arithmetic mean ) of the first 7 positive multiples of 7 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 4 , b ) 12 , c ) 14 , d ) 21 , e ) 28
Rationale: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 28 , which also equals b . b is the second positive multiple of n , thus n = 28 / 2 = 14 . the answer is c ."
Answer: c
Problem: find the highest common factor of 36 and 84 ?
Options: a ) 4 , b ) 6 , c ) 12 , d ) 18 , e ) none of these
Rationale: 36 = 2 ^ 2 * 3 ^ 2 ; 84 = 2 ^ 2 * 3 * 7 h . c . f = 2 ^ 2 * 3 = 12 . correct option : c
Answer: c
Problem: the area of a base of a cone is 30 cm 2 . if the height of the cone is 6 cm , find its volume ?
Options: a ) 87
b ) 16
c ) 17
d ) 60
e ) 18
Rationale: π r 2 = 30 h = 6 1 / 3 * 30 * 6 = 60 answer : d
Answer: d
Problem: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 3 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 12 : 7 , b ) 15 : 11 , c ) 25 : 16 , d ) 30 : 23 , e ) 32 : 25
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 3 y and y . 2 ( 3 x + 2 x ) = 2 ( 3 y + y ) 5 x = 4 y ( 5 / 4 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 3 y * y = 6 x ^ 2 : 3 y ^ 2 = 6 x ^ 2 : 3 * ( 25 / 16 ) * x ^ 2 = 96 : 75 = 32 : 25 the answer is e ."
Answer: e
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 8 ?
Options: a ) 5 , b ) 9 , c ) 16 , d ) 20 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 8 ? 9 ^ 8 = ( 3 ^ 2 ) ^ 8 = 3 ^ 16 c . 16"
Answer: c
Problem: find the average of all the numbers between 11 and 36 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 15 + 20 + 25 + 30 + 35 ) / 5 = 125 / 5 = 25 answer c"
Answer: c
Problem: a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 a receives :
Options: a ) rs . 11900 , b ) rs . 8400 , c ) rs . 14700 , d ) rs . 13600 , e ) rs . 14600
Rationale: "let c = x . then b = x + 5000 and a + x + 5000 + 4000 = x + 9000 therefore , x + x + 5000 + x + 9000 = 50000 û x = 12000 . therefore , a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 therefore , a ’ s share = rs ( 35000 * 21 / 50 ) = rs . 14700 answer : c"
Answer: c
Problem: one hour before john started walking from p to q , a distance of 28 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 18 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 28 - 3 = 25 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 25 miles so it will take them 25 / 5 = 5 hours to meet . in 5 hrs , ann would have covered 5 hrs * 3 miles per hour = 15 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 15 = 18 miles . answer ( e )"
Answer: e
Problem: roses can be purchased individually for $ 4.50 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 318 , d ) 324 , e ) 325
Rationale: buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 4.5 = ~ 6 roses for that amount . total = 312 + 6 = 318 . answer : c .
Answer: c
Problem: the population of a town is 10000 . it increases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 12100 , b ) 14400 , c ) 14500 , d ) 14600 , e ) 14700
Rationale: "formula : 10000 × 110 / 100 × 110 / 100 = 12100 answer : a"
Answer: a
Problem: set a contains all the even numbers between 8 and 50 inclusive . set b contains all the even numbers between 108 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2200 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 8 , 10 , 12 . . . 50 set b contains 108 , 110 , 112 . . . 150 number of terms in each set = 22 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 22 = 2200 answer a"
Answer: a
Problem: john makes $ 45 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
Options: a ) 16 % , b ) 46.66 % , c ) 44.44 % , d ) 36.98 % , e ) 17 %
Rationale: "increase = ( 20 / 45 ) * 100 = ( 4 / 9 ) * 100 = 44.44 % . c"
Answer: c
Problem: pipe a can fill a tank in 12 hours . due to a leak at the bottom it takes 20 hours to fill the tank . in what time the leak alone can empty the full tank ?
Options: a ) 18 hours , b ) 23 hours , c ) 28 hours , d ) 30 hours , e ) 40 hours
Rationale: "let leak can empty the full tank in x hours . 1 / 12 - 1 / x = 1 / 20 = > 1 / 12 – 1 / 20 = 1 / x 1 / x = 5 - 3 / 60 = 1 / 30 x = 30 hours answer : d"
Answer: d
Problem: find 30 % of 240
Options: a ) 72 , b ) 94 , c ) 86 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 30 % of 240 30 / 100 × 240 = 72 answer : a"
Answer: a
Problem: 11 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 88 m , c ) 14 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 11 ⇔ = [ 11 * 20 * 20 * 7 / 22 ] = 1400 cm = 14 m . answer c"
Answer: c
Problem: the length of a rectangle is one - fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 350 sq . units
b ) 250 sq . units
c ) 300 sq . units
d ) 200 sq . units
e ) 100 sq . units
Rationale: given that the area of the square = 6400 sq . units = > side of square = √ 6400 = 80 units the radius of the circle = side of the square = 35 units length of the rectangle = 1 / 4 * 80 = 20 units given that breadth = 10 units area of the rectangle = lb = 20 * 10 = 200 sq . units answer : d
Answer: d
Problem: what sum of money will produce rs . 70 as simple interest in 4 years at 2 1 / 2 percent ?
Options: a ) 337 , b ) 500 , c ) 700 , d ) 288 , e ) 211
Rationale: "70 = ( p * 4 * 5 / 2 ) / 100 p = 700 answer : c"
Answer: c
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 16 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 16 incorrect ( division by zero ) a . 2 / 1 = 2 / 2 + 2 / 17 incorrect a . 2 / 2 = 2 / 3 + 2 / 18 incorrect a . 2 / 3 = 2 / 4 + 2 / 19 incorrect a . 2 / 4 = 2 / 5 + 2 / 20 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Problem: the area of a square is equal to five times the area of a rectangle of dimensions 50 cm * 10 cm . what is the perimeter of the square ?
Options: a ) 289 cm , b ) 200 cm , c ) 829 cm , d ) 288 cm , e ) 289 cm
Rationale: "area of the square = s * s = 5 ( 50 * 10 ) = > s = 50 = 50 cm perimeter of the square = 4 * 50 = 200 cm . answer : b"
Answer: b
Problem: a truck covers a distance of 360 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 360 / 8 = 45 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 45 + 18 ) = 63 kmph distance travelled by car = 360 + 81 = 441 km time taken by car = distance / speed = 441 / 63 = 8 hours . answer – d"
Answer: d
Problem: the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 3.6 miles in the fifth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 31 , b ) 35 , c ) 39 , d ) 43 , e ) 47
Rationale: ( 3.6 miles / 8 minutes ) * 60 minutes / hour = 27 mph let x be the original speed . x - 4 ( 3 ) = 27 x = 39 mph the answer is c .
Answer: c
Problem: a took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m / min and b took the same time to cross the same field along its sides walking at the rate of 68 m / min . the area of the field is ?
Options: a ) 33
b ) 60
c ) 88
d ) 27
e ) 26
Rationale: explanation : length of the diagonal = 52 * ( 15 / 60 ) = 13 m sum of length and breadth = 68 * ( 15 / 60 ) = 17 m \ inline { \ color { black } \ sqrt { l ^ { 2 } + b ^ { 2 } } = 13 \ ; or \ ; l + b = 17 } area = lb = 1 / 2 [ ( 2 lb ) ] = 1 / 2 [ ( l + b ) ² - ( l ² + b ² ) ] = 1 / 2 [ 17 ² - 169 ] = 1 / 2 * 120 = 60 sq meter answer : b ) 60
Answer: b
Problem: a geometric shape is obtained by combining a square of side 8 cm and a semicircle of diameter 8 cm . what is the perimeter of the shape obtained ?
Options: a ) 28.32
b ) 36.57
c ) 44.57
d ) 48.93
e ) 54.24
Rationale: circumference of the semicircle = ï € xd / 2 = ( 22 / 7 ) x 4 = 12.57 perimeter of the square plot = 3 x 8 = 24 perimeter of the shape = 36.57 cm answer : b
Answer: b
Problem: the simple interest on a certain sum of money for 2 years at 10 % per annum is half the compound interest on $ 100 for 2 years at 5 % per annum . the sum placed on simple interest is ?
Options: a ) $ 602.5 , b ) $ 625.8 , c ) $ 710.6 , d ) $ 745 , e ) $ 790.3
Rationale: "c . i . = 100 * ( 1 + 5 / 100 ) ^ 2 - 100 = 100 * 21 / 20 * 21 / 20 - 100 = $ 120.5 sum = 120.5 * 100 / 2 * 10 = $ 602.5 answer is a"
Answer: a
Problem: redo ’ s manufacturing costs for sets of horseshoes include a $ 10,500 initial outlay , and $ 15 per set . they can sell the sets $ 40 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?
Options: a ) $ 2100 , b ) $ 2000 , c ) $ 2050 , d ) $ 2070 , e ) $ 2500
Rationale: "total manufacturing cost = 10500 + 500 * 15 = 18000 total selling cost = 500 * 40 = 20000 profit = 20000 - 18000 = 2000 answer : b"
Answer: b
Problem: find the highest value of ' a ' so that 365 a 16 is divisible by 8 .
Options: a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1
Rationale: explanation : given , number is divisible by 8 only if ' a 16 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b
Answer: b
Problem: if 15 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 240 , c ) 287 , d ) 450 , e ) 281
Rationale: explanation : let the required no of hectares be x . then men - - - hectares - - - days 15 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 15 * 30 / 24 * 80 x = 240 answer : b
Answer: b
Problem: in a office work is distribute between p persons . if 1 / 8 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14.28 % , c ) 15.28 % , d ) 16.28 % , e ) 17.28 %
Rationale: "let total % of work is 100 % total person = p 1 / 8 person are absent of total person . so absent person is 1 / 8 p ie p / 8 . left person is , p - p / 8 = 7 p / 8 . p person do the work 100 % 1 person do the work 100 * p % 7 p / 8 person do the work ( 100 * p * 8 ) / 7 p % = 114.28 % work increased for each person is = ( 114.28 - 100 ) % = 14.28 % answer : b"
Answer: b
Problem: if a * b * c = 65 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 65 / 65 = > a / d = 1 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 1000 = > f / c = 1 / 4 a / d * f / c = 1 * 1 / 4 = 1 / 4 answer : b"
Answer: b
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 20 % . what is the selling price of the cycle ?
Options: a ) rs . 1090 , b ) rs . 1160 , c ) rs . 1120 , d ) rs . 1202 , e ) none
Rationale: "solution s . p = 80 % of rs . 1400 = rs . ( 80 / 100 × 1400 ) rs . 1120 . answer c"
Answer: c
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 8.6 % , e ) 8.4 %
Rationale: the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.12 * 15 + 0.08 * 35 = 4.6 kg , so the percentage is 4.6 / 50 * 100 = 9.2 % . answer : c .
Answer: c
Problem: in may mrs lee ' s earnings were 90 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 92 , b ) 35 , c ) 64 , d ) 46 , e ) 355
Rationale: "lets say the family income is 100 in may , lee earned 90 family income is 10 in june , lee earned 20 % more than may , so it is ( 90 + 20 * 90 / 100 = 108 ) family income is same 10 in june lee ' s income percent is 108 * 100 / 118 ~ 92 ans is a"
Answer: a
Problem: ? % of 360 = 165.6
Options: a ) 277 , b ) 36 , c ) 64 , d ) 72 , e ) 46
Rationale: "? % of 360 = 165.6 or , ? = 165.6 × 100 / 360 = 46 answer e"
Answer: e
Problem: find the simple interest on $ 6000 at 15 % per annum for 9 months ?
Options: a ) $ 492 , b ) $ 512 , c ) $ 675 , d ) $ 745 , e ) $ 1020
Rationale: "p = $ 6000 r = 15 % t = 9 / 12 years = 3 / 4 years s . i . = p * r * t / 100 = 6000 * 15 * 3 / 400 = $ 675 answer is c"
Answer: c
Problem: how many integers between 324,805 and 458,705 have tens digit 1 and units digit 3 ?
Options: a ) 1,349 , b ) 1,353 , c ) 10,040 , d ) 1,354 , e ) 10,400
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,805 and 458,705 is 458,705 - 324,805 = 134,900 - one number per each hundred gives 134,900 / 100 = 1,349 numbers . answer : a ."
Answer: a
Problem: a container contains 40 liters of milk , from this container 4 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?
Options: a ) 25.5 liters , b ) 29.16 liters , c ) 30.98 liters , d ) 42.15 liters , e ) 48.32 liters
Rationale: "amount of milk left after 3 operations = 40 ( 1 - 4 / 40 ) ^ 3 = 40 * 9 / 10 * 9 / 10 * 9 / 10 = 29.16 liters answer is b"
Answer: b
Problem: solve the quickfire maths brain teaser â ˆ š 25 % = ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 19 % , e ) 29 %
Rationale: "â ˆ š 25 % = > â ˆ š 25 / â ˆ š 100 = > 5 / 10 = > 50 / 100 = > 50 % c"
Answer: c
Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 3 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 24
Rationale: let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 3 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 3 ) = 8 x . the fraction of sensors which have been upgraded is x / ( x + 8 x ) = x / 9 x = 1 / 9 the answer is d .
Answer: d
Problem: tom drives from town a to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between a and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point a to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b
Answer: b
Problem: the average ( arithmetic mean ) of 22 , 33 , and 53 is 8 less than the average of 30 , 56 , and x . what is x ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the average of 22 , 33 , and 53 is 108 / 3 = 36 . the average of 30 , 56 and x is 44 . then 30 + 56 + x = 132 . x = 46 . the answer is c ."
Answer: c
Problem: how many 3 - digit numbers are completely divisible 6 ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300
Rationale: "3 - digit number divisible by 6 are : 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then tn = 996 . a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 number of terms = 150 . b )"
Answer: b
Problem: 1 , 6 , 16 , 31 , 51 , ( . . . . )
Options: a ) 61 , b ) 66 , c ) 76 , d ) 86 , e ) 83
Rationale: "explanation : the pattern is 5 , 10 , 15 , 20 , 25 , etc hence 25 = 66 answer : b"
Answer: b
Problem: in a public show 60 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 240
Rationale: "75 % of 600 = 60 / 100 × 600 = 360 therefore , the number of vacant seats = 600 - 360 = 240 . answer : e"
Answer: e
Problem: what is the decimal equivalent of ( 1 / 10 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.01
Rationale: "( 1 / 10 ) ² = ( 1 / 10 ) ( 1 / 10 ) = 1 / 100 approach # 1 : use long division to divide 100 into 1 to get 1 / 100 = 0.01 e"
Answer: e
Problem: for a bake sale , simon baked 2 n more pies than theresa . theresa baked half as many pies as roger , who baked 1313 n pies . no other pies were baked for the sale . what fraction of the total pies for sale did roger bake ?
Options: a ) 1 / 16 , b ) 1 / 8 , c ) 3 / 16 , d ) 3 / 8 , e ) 13 / 16
Rationale: s : simon t : theresa r : roger let theresa baked a . as per question , we have s = a + 2 n r = 2 a = n / 3 or a = n / 6 now , total = a + ( a + 2 n ) + 2 a = 8 n / 3 fraction , ( n / 3 ) / ( 8 n / 3 ) = 1 / 8 answer : b
Answer: b
Problem: sarah is driving to the airport . after driving at 50 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 100 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 140 , b ) 175 , c ) 200 , d ) 245 , e ) 280
Rationale: "after driving at 50 miles per hourfor one hour , this distance left to cover is d - 50 . say this distance is x miles . now , we know that the difference in time between covering this distance at 50 miles per hour and 100 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 50 - x / 100 = 3 / 2 - - > 2 x / 100 - x / 100 = 3 / 2 - - > x / 100 = 3 / 2 - - > x = 150 total distance = x + 50 = 200 miles . answer : c ."
Answer: c
Problem: two trains a and b are 225 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 15 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 225 + 150 = 375 m . time taken = 375 / 25 = 15 s . correct answer b ."
Answer: b
Problem: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 10,000 , b ) 11,025 , c ) 14,400 , d ) 12,696 , e ) can not be determined
Rationale: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 199 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 199 ( x + y ) ( x - y ) = 199 199 is a prime number and thus it will be ( 100 + 99 ) * ( 100 - 99 ) . thus x = 100 and y = 99 x ^ 2 = 100 ^ 2 = 10,000 the answer is a ."
Answer: a
Problem: if x , y , and z are positive integers and x = 4 y = 7 z , then the least possible value of x - y - z is
Options: a ) 33 , b ) 17 , c ) 49 , d ) 16 , e ) 23
Rationale: x - y - z = x - x / 4 - x / 7 = ( 28 - 7 - 4 ) x / 28 = 17 x / 28 17 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - b
Answer: b
Problem: one hour after yolanda started walking from x to y , a distance of 80 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 8 miles per hour and bob â s was 9 miles per hour , how many miles had bob walked when they met ?
Options: a ) 38.07 , b ) 40 , c ) 42 , d ) 39 , e ) 40.07
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 8 ( t + 1 ) miles . these distances must sum to 80 miles , so 9 t + 8 ( t + 1 ) = 80 , which may be solved for t as follows 9 t + 8 ( t + 1 ) = 80 9 t + 8 t + 8 = 80 17 t = 72 t = 4.23 ( hours ) therefore , bob had walked 9 t = 9 ( 4.23 ) = 38.07 miles when they met . the best answer is a ."
Answer: a
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 5 km / hr . find the time taken by the boat to go 68 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 3 hours 48 minutes , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 5 ) km / hr = 18 km / hr . time taken to travel 68 km downstream = ( 68 / 18 ) hrs = 3 hrs 48 minutes . answer c"
Answer: c
Problem: the speed of a train is 94 kmph . what is the distance covered by it in 12 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 88 kmph , d ) 19 kmph , e ) 12 kmph
Rationale: "94 * 12 / 60 = 18.8 kmph answer : d"
Answer: d
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 180 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 22.5 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 180 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 180 units is ' 9 times ' 20 , we need ' 9 times ' more time . ( 2.5 hours ) ( 9 times ) = 22.5 hours final answer : [ reveal ] spoiler : c"
Answer: c
Problem: a worker ' s daily wage is increased by 50 % and the new wage is $ 51 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 28 , b ) $ 32 , c ) $ 34 , d ) $ 35 , e ) $ 40
Rationale: "let x be the daily wage before the increase . 1.5 x = $ 51 x = $ 34 the answer is c ."
Answer: c
Problem: in an election , candidate douglas won 60 percent of the total vote in counties x and y . he won 72 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 18 % , b ) 30 % , c ) 36 % , d ) 48 % , e ) 54 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 72 % voted means 72 * 200 = 144 votes combined for xy has 300 voters and voted 60 % so total votes = 180 balance votes = 180 - 144 = 36 as y has 100 voters so 36 votes means 36 % of votes required ans c"
Answer: c
Problem: a ferry can transport 50 tons of vehicles . automobiles range in weight from 1600 to 3200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 41 , c ) 48 , d ) 62 , e ) 86
Rationale: to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d
Answer: d
Problem: how much time does a train 150 metres long running at 54 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 10 s
Rationale: "explanation : 54 km / hr = 54 * 5 / 18 = 15 m / s speed = distance / time ; v = d / t 15 = 150 / t t = 10 s answer : e"
Answer: e
Problem: the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 104
Rationale: "explanation : cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : e"
Answer: e
Problem: by selling 12 pencils for a rupee a man loses 12 % . how many for a rupee should he sell in order to gain 18 % ?
Options: a ) 12 , b ) 9 , c ) 10 , d ) 89 , e ) 81
Rationale: "88 % - - - 12 112 % - - - ? 88 / 112 * 12 = 9 answer : a"
Answer: a
Problem: ages of two persons differ by 4 years . if 3 years ago , the elder one was 3 times as old the younger one , find their present age
Options: a ) 5,9 , b ) 14,18 , c ) 16,20 , d ) 18,22 , e ) 19,23
Rationale: "explanation : let the age of the younger person be x , then the elder person ' s age is ( x + 4 ) = > 3 ( x - 3 ) = ( x + 4 - 3 ) [ 3 years before ] = > 3 x - 9 = x + 1 = > x = 5 . so the elder person ' s age is x + 4 = 9 answer : option a"
Answer: a
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 23 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 280 , e ) 312
Rationale: "so 12.2 * 23 = 280 . . imo option d is correct answer . ."
Answer: d
Problem: if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 21 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "b 30 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 21 women = 15 women + 21 women = 36 women 20 women can do the work in 54 days . so , 36 women can do it in ( 20 * 54 ) / 36 = 30 days ."
Answer: b
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 70 to incur a loss 20 % ?
Options: a ) 45 , b ) 35 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 70 * ( 100 % + 20 % ) = $ 84 number of articles to be sold for $ 84 to incur a 20 % loss : $ 84 / $ 2.40 = 35 thus , solution b is correct ."
Answer: b
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 60 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "60 % is 20 % - points below 80 % and 5 % - points above 55 % . so the ratio of solution p to solution q is 1 : 4 . mixture p is 1 / 5 = 20 % of the volume of mixture pq . the answer is a ."
Answer: a
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 11 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 11 c + 3 . the minimum is 3 when c = 0 . the maximum is 47 when c = 4 . there are 5 such numbers . the answer is a ."
Answer: a
Problem: find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number .
Options: a ) 3 , b ) 5 , c ) 7 , d ) 12 , e ) 15
Rationale: "sol . let the number be x . then , x + 17 = 60 / x ⇔ x 2 + 17 x - 60 = 0 ⇔ ( x + 20 ) ( x - 3 ) = 0 ⇔ x = 3 . answer a"
Answer: a
Problem: the largest five digit number which is a perfect cube , is :
Options: a ) 85184
b ) 91125
c ) 97336
d ) 96806
e ) 99999
Rationale: explanation : 46 * 46 * 46 = 97336 answer : c
Answer: c
Problem: in one hour , a boat goes 15 km / hr along the stream and 11 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 15 + 11 ) kmph = 13 kmph . answer : option b"
Answer: b
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 80 as remainder . find the no . is ?
Options: a ) 220880 , b ) 145778 , c ) 220081 , d ) 220080 , e ) 220030
Rationale: ( 555 + 445 ) * 2 * 110 + 80 = 220000 + 80 = 220080 d
Answer: d
Problem: the sum of two number is 120 and their difference is 30 . find the numbers .
Options: a ) 9525 , b ) 5565 , c ) 7545 , d ) 6555 , e ) 8535
Rationale: let the two number be x and y . x + y = 120 . . . . . . . ( 1 ) x - y = 30 . . . . . . . . . ( 2 ) = > 2 x = 150 = > x = 75 . x - y = 30 = > y = 45 . the two numbers are 7545 ans : c
Answer: c
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 10 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 50 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 45 , c ) 52.63 , d ) 40 , e ) 35
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.1 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.1 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 50 = > x = 52.63 c"
Answer: c
Problem: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 30 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 120 , d ) 23 : 4 , e ) 23 : 120
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 30 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.30 = $ 36 cost = 36 / 1.3 = 360 / 12 = $ 27.69 if he wants a 30 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 27.69 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 27.69 / 33 = 120 / 143 of a liter . if milk is 120 / 143 of the liter , then water is 23 / 143 of the liter , and the ratio of water to milk is 23 : 120 . answer choice ( e )"
Answer: e
Problem: a train 110 m long is running at 50 kmph . in how much time will it pass a platform 210 m long ?
Options: a ) 14.15 seconds , b ) 15.24 seconds , c ) 16.28 seconds , d ) 13.30 seconds , e ) 10.24 seconds
Rationale: distance travelled = 110 + 210 m = 320 m speed = 50 * 5 / 8 = 125 / 4 m time = 320 * 4 / 125 = 10.24 seconds answer : e .
Answer: e
Problem: a man buys an article for $ 100 . and sells it for $ 115 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 115 gain = $ 15 gain % = 15 / 100 * 100 = 25 % answer is b"
Answer: b
Problem: there was a cycle race going on . 1 / 5 th of the those in front of a person and 5 / 6 th of those behind him gives the total number of participants . how many people took part in the race ?
Options: a ) 31 , b ) 39 , c ) 30 , d ) 33 , e ) 34
Rationale: explanation : let total participants be ( x + 1 ) then = > ( 1 / 5 ) * x + ( 5 / 6 ) * x = x + 1 = > 31 x / 30 = x + 1 = > x = 30 so total participants ( x + 1 ) = 31 hence ( a ) is the correct answer . answer : a
Answer: a
Problem: at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 2 years ?
Options: a ) 4 % , b ) 7.14 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 2 xr ) / 100 r = 7.14 % answer : option b"
Answer: b
Problem: what is the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder ?
Options: a ) 1108 , b ) 1683 , c ) 2007 , d ) 3363 , e ) 1436
Rationale: "lcm of 5 , 6 , 7 and 8 = 840 hence the number can be written in the form ( 840 k + 3 ) which is divisible by 9 . if k = 1 , number = ( 840 × 1 ) + 3 = 843 which is not divisible by 9 . if k = 2 , number = ( 840 × 2 ) + 3 = 1683 which is divisible by 9 . hence 1683 is the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder . answer : b"
Answer: b
Problem: what is the difference between the largest number and the least number written with the digits 7 , 3 , 1 , 4 ?
Options: a ) 6084 , b ) 6184 , c ) 5084 , d ) 6048 , e ) 6049
Rationale: "1347 7431 - - - - - - - - - - - - 6084 answer : a"
Answer: a
Problem: if a light flashes every 30 seconds , how many times will it flash in 1 / 2 of an hour ?
Options: a ) 30 , b ) 42 , c ) 61 , d ) 59 , e ) 45
Rationale: "there are 60 minutes in an hour . in 1 / 2 of an hour there are ( 60 * 1 / 2 ) minutes = 30 minutes . in 1 / 2 of an hour there are ( 60 * 30 ) seconds = 1800 seconds . light flashed for every 30 seconds . in 1800 seconds 1800 / 30 = 60 times . the count start after the first flash , the light will flashes 61 times in 1 / 2 of an hour . answer : c"
Answer: c
Problem: what is the smallest positive integer k such that the product of 720 x k is a perfect square ?
Options: a ) 5 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 720 = 3 ^ 2 * 4 ^ 2 * 5 , so if k = 5 then 720 k = ( 3 * 4 * 5 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Problem: the ratio of two numbers is 2 : 3 and their h . c . f . is 6 . their l . c . m . is
Options: a ) 48 , b ) 22 , c ) 36 , d ) 27 , e ) 67
Rationale: explanation : let the numbers be 2 x and 3 x . then , their h . c . f . = x . so , x = 6 . so , the numbers 12 and 18 l . c . m . of 12 and 18 = 36 option c
Answer: c
Problem: the speed at which a girl can row a boat in still water is 90 kmph . if she rows downstream , where the speed of current is 18 kmph , what time will he take to cover 330 metres ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5 / 18 = 30 m / s hence time taken to cover 330 m = 330 / 30 = 11 seconds . answer : a"
Answer: a
Problem: one hour after matthew started waking from q to y , a distance of 45 km , johnny started walking along the same road from y to q . matthew ' s walking rate was 3 km per hour and johnny ' s was 4 km per hour , how many km had johnny walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 19.5
Rationale: just an alternative method . . . after the first hour the distance q is 42 km ( 45 - 3 ) . now the problem can be treated as if bothof them started at the same time . since the speeds are in the ratio 3 : 4 , the distances will also be in the same ratio . splitting 42 in that ratio we get 18 : 24 . so answer is 24 . hence a .
Answer: a
Problem: if 2 / w + 2 / x = 2 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 2 / w + 2 / x = 2 / ywx = y find : ( w + x ) / 2 = ? 2 ( 1 / w + 1 / x ) = 2 ( 1 / y ) - divide both sides by 2 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Problem: a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 810 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 84 , e ) none
Rationale: "explanation we have : l = 30 ft and lb = 810 sq . ft . so , b = 27 ft . length of fencing = ( l + 2 b ) = ( 30 + 54 ) ft = 84 ft . answer d"
Answer: d
Problem: the food in a camp lasts for 40 men for 45 days . if fifteen more men join , how many days will the food last ?
Options: a ) 80 days , b ) 33 days , c ) 35 days , d ) 16 days , e ) 15 days
Rationale: one man can consume the same food in 40 * 45 = 1800 days . 15 more men join , the total number of men = 55 the number of days the food will last = 1800 / 55 = 33 days . answer : b
Answer: b
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 3 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 4 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 4 * 3 = 12 miles . so , the distance between him and walt was 48 - 12 = 36 miles when walt left his house . now , their combined rate to cover this distance was 3 + 6 = 9 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 36 / 9 = 4 hours . total time that lionel was walking is 4 + 4 = 8 hours , which means that he covered in that time interval distance = rate * time = 3 * 8 = 24 miles . answer : d ."
Answer: d
Problem: a certain car can travel 72 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 117 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 72 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 72 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : c ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 72 x 3.9 x 3.8 / 5.7 x 1.6 = 117 c"
Answer: c
Problem: find the probability that a leap year selected at random will have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: "there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 sundays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 sundays we should have either { sat , sun } or { sun , mon } case . the probability of that is 2 / 7 . answer : e ."
Answer: e
Problem: a tank is 25 m long , 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 75 paise per sq . m , is :
Options: a ) rs . 456 , b ) rs . 458 , c ) rs . 558 , d ) rs . 568 , e ) none of these
Rationale: explanation : area to be plastered = [ 2 ( l + b ) x h ] + ( l x b ) = { [ 2 ( 25 + 12 ) x 6 ] + ( 25 x 12 ) } m 2 = ( 444 + 300 ) m 2 = 744 m 2 . cost of plastering = rs . 744 x 75 / 100 = rs . 558 answer : c
Answer: c
Problem: if p is the product of the integers from 1 to 38 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "38 ! has 3 , 6 , 9 , . . . . 30 , 33 , 36 as factors , which are 12 multiples of 3 . we need to add 5 more to these 12 because of 9 , 18 , 27 , and 36 . the greatest integer of k is 17 . the answer is c ."
Answer: c
Problem: find the average increase rate , if increase in the population in the first year is 30 % and that in the second year is 40 % .
Options: a ) 41 , b ) 56 , c ) 40 , d ) 38 , e ) 39
Rationale: solution : let 100 be the original population . 1 st year ' s population increased = 30 % so , population after first year = ( 100 + 30 % of 100 ) = 130 . population in second year increases by 40 % , then population = ( 130 + 40 % of 130 ) = 182 . the final population become 182 which was originally at 100 . it means there is 82 % increment in the population in 2 years so , average increment = 82 / 2 = 41 % . mind calculation method : increase in population is given by , 100 = = 30 % ↑ = = > 130 = = 40 % ↑ = = > 182 . hence , average increase = 82 / 2 = 41 % answer : option a
Answer: a
Problem: rs . 6000 is lent out in two parts . one part is lent at 4 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 7 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 4 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 4 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 2500 amount lent at 10 % = 3500 required ratio = 5 : 7 answer : b"
Answer: b
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 800 per sq . metre .
Options: a ) $ 12500 , b ) $ 13500 , c ) $ 16500 , d ) $ 14500 , e ) $ 18500
Rationale: "c $ 16500 area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = $ 16500"
Answer: c
Problem: ? % of 360 = 115.2
Options: a ) 277 , b ) 36 , c ) 64 , d ) 32 , e ) none of these
Rationale: ? % of 360 = 115.2 or , ? = 115.2 × 100 / 360 = 32 answer d
Answer: d
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 2 min early . find his usual time to reach the school ?
Options: a ) 14 , b ) 28 , c ) 99 , d ) 77 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 2 - - - - - - - - - ? 14 m answer : a"
Answer: a
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 11
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 11 we get the remainder 4 , so 4 should be subtracted answer : option b"
Answer: b
Problem: 4 milkmen rented a pasture . a grazed 24 cows for 3 months , b 10 cows for 5 months , c 35 cows for 4 months and d 21 cows for 3 months . if a ’ s share of rent is rs . 720 , find the total rent of the field .
Options: a ) rs . 3250 , b ) rs . 3350 , c ) rs . 3450 , d ) rs . 3550 , e ) rs . 3650
Rationale: ratio of shares of a , b , c , d = ( 24 * 3 ) : ( 10 * 5 ) : ( 35 * 4 ) : ( 21 * 3 ) = 72 : 50 : 140 : 63 let total rent be rs . x . then , a ’ s share = rs . 72 x / 325 . therefore , 72 x / 325 = 720 = > x = 720 * 325 / 72 = 3250 . hence , total rent of the field is rs . 3250 . answer : a
Answer: a
Problem: 500 , 250 , 750 , 375 . . .
Options: a ) 875 , b ) 1050 , c ) 950 , d ) 1125 , e ) 925
Rationale: "500 / 2 = 250 x 3 = 750 / 2 = 375 x 3 = 1125 answer is d"
Answer: d
Problem: at present , the ratio between the ages of shekhar and shobha is 4 : 3 . after 6 years , shekhar ' s age will be 26 years . find out the age of shobha at present ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 20
Rationale: after 6 years , shekhar ' s age will be 26 years therefore , present age of shekhar = 26 − 6 = 20 let present age of shobha = x then , 20 x = 43 x = 20 × 34 = 15 answer is d .
Answer: d