euclaise/mathqa_programs huggingface dataset:
Problem: the length of a rectangle is 5 more than the width . what are the dimensions of the rectangle if the perimeter is 34 ?
Options: a ) 11
b ) 12
c ) 13
d ) 14
e ) none
Rationale: pretend width = 1 , then length = 6 ( 1 + 5 ) 2 × 1 + 2 × 7 = 2 + 14 = 16 . notice that 16 is far from a perimeter of 34 try much bigger number . how about if we . . . pretend width = 4 , then length = 9 ( 4 + 5 ) 2 × 4 + 2 × 9 = 6 + 18 = 24 . we are getting closer to a perimeter of 34 pretend width = 5 , then length = 10 ( 5 + 5 ) 2 × 5 + 2 × 10 = 10 + 30 = 30 . pretend width = 7 , then length = 12 ( 7 + 5 ) 2 × 7 + 2 × 12 = 14 + 24 = 38 . this is higher than a perimeter of 34 . so width should be higher than 5 and smaller than 7 . may be a width of 6 will work . pretend width = 6 , then length = 11 ( 6 + 5 ) 2 × 6 + 2 × 11 = 12 + 22 = 34 . use of algebra : let width = x let length = x + 5 p = 2 × l + 2 × w 34 = 2 × ( x + 5 ) + 2 × x 34 = 2 x + 10 + 2 x 34 = 4 x + 10 34 - 10 = 4 x + 10 - 10 24 = 4 x 24 / 4 = 4 x / 4 6 = x therefore , width = 6 and length = x + 5 = 6 + 5 = 11 answer a
Answer: a
Python program:
a = 34 / 2
b = a + 5 
c = b / 2
Problem: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 54 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: four wheeler = 13 * 4 = 52 ( max ) 2 wheel = 1 so no of 4 wheeler = 13 answer : c
Answer: c
Python program:
a = 54 - 2
b = a / 4
Problem: a train passes a train standing in platform in 30 sec and a man standing on the platform in 12 sec . if the speed of the train is 36 km / hr . what is the length of the platform ?
Options: a ) 250 , b ) 200 , c ) 300 , d ) 240 , e ) 180
Rationale: speed = 36 * 5 / 18 = 10 m / sec . length of the train = 10 * 12 = 120 m . let the length of the platform be x m . then , ( x + 120 ) / 30 = 10 = > x = 180 m . answer : e
Answer: e
Python program:
a = 36 * 1000
b = a / 3600
c = 30 * b
d = 36 * 1000
e = d / 3600
f = e * 12
g = c - f
Problem: what is the tenth digit of ( 4 ! * 3 ! + 4 ! * 2 ! ) / 3 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 1 , e ) 0
Rationale: "( 4 ! * 3 ! + 4 ! * 2 ! ) / 2 = 4 ! ( 3 ! + 2 ! ) / 2 = 24 ( 6 + 2 ) / 2 = 96 units digit of the above product will be equal to 9 answer c"
Answer: c
Python program:
a = math.factorial(4)
b = math.factorial(4)
c = a * b
d = math.factorial(4)
e = math.factorial(2)
f = d * e
g = c - f
h = g / 4
i = 100 * 10
j = h / i
k = math.floor(j)
Problem: bullock likes to keep a spare tyre in his car every time . on a certain day , he travels 1 , 60,000 km and just to make the most of all the tyres , he changes the tyres between his journey such that each tyre runs the same distance . what is the distance traveled by each tyre ?
Options: a ) 70,000 , b ) 60,000 , c ) 128,000 , d ) 90,000 , e ) 10,000
Rationale: the distance traveled by each tyre : 4 / 5 * 1 , 60 , 000 km = 128,000 km . c
Answer: c
Python program:
a = 1 * const_60
Problem: evaluate : 60 - 9 ÷ 3 × 6 =
Options: a ) 52 , b ) 18 , c ) 42 , d ) 102 , e ) 36
Rationale: "according to order of operations , 9 ÷ 3 × 6 ( division and multiplication ) is done first from left to right 9 ÷ 3 × 6 = 3 × 6 = 18 hence 60 - 9 ÷ 3 × 6 = 60 - 18 = 42 correct answer c ) 42"
Answer: c
Python program:
a = 9 * 3
b = a * 6
c = 60 - b
Problem: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 20 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 20 ) / 100 × 16 = 19.2 answer d"
Answer: d
Python program:
a = 80 * 15
b = 20 * 20
c = a + b 
d = 80 + 20 
e = c / d
f = e * 20
g = f / 100
h = 80 * 15
i = 20 * 20
j = h + i 
k = 80 + 20 
l = j / k
m = g + l
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number w ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = w answer : b"
Answer: b
Python program:
a = 12 / 5
b = 1 + a 
c = 25 / 100
d = 1 - c
e = b - d
f = 30 / e
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 12 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9
Rationale: "answer is a . x / x + 36 = 1 / 5 x = 9 12 - 9 = 3"
Answer: a
Python program:
a = 20 / 100
b = a * 20
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
Python program:
a = 14 / 2
b = a - 1
c = 14 - 1
d = b / c
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
Python program:
a = 43 * 23
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
Python program:
a = 2 * 1
b = 12 - 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
Python program:
a = 2 + 2 
b = 2 ** a
c = 4 ** 2
d = b / c
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
Python program:
a = 7 * 4
b = a / 2
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
Python program:
a = math.gcd(36, 84)
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
Python program:
a = 30 * 6
b = a / 3
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
Python program:
a = rectangle_area / (
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
Python program:
a = 9 - 8
b = a * 8
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
Python program:
a = 11 + 4 
b = 36 - 4
c = a + b 
d = c / 2
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
Python program:
a = 10 * 5000
b = a - 5000
c = 4000 + 5000 
d = b - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 10 * 5000
i = g / h
j = 3 + 4 
k = j * 5000
l = i * k
m = l / 1000
n = math.floor(m)
o = n - 1
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
Python program:
a = 3 + 2 
b = 28 / a
c = b * 2
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
Python program:
a = 680 / 50
b = math.floor(a)
c = 12 * 2
d = b * c
e = 680 / 50
f = math.floor(e)
g = f * 50
h = 680 - g
i = h / 4
j = math.floor(i)
k = d + j
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
Python program:
a = 10000 * 10
b = a / 100
c = b * 2
d = 10000 + c
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
Python program:
a = 108 - 8
b = 50 - 8
c = b / 2
d = c + 1 
e = a * d
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
Python program:
a = 75 - 45
b = a / 45
c = b * 100
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
Python program:
a = 20 * 12
b = 20 - 12
c = a / b
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
Python program:
a = 30 / 240
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
Python program:
a = 1 / 2
b = a ** 2
c = b * math.pi
d = 11 / c
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
Python program:
a = 1 / 2
b = 2 + a 
c = 4 * b
d = c / 100
e = 70 / d
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
Python program:
a = 2 + 2 
b = a + 1 
c = 16 / 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
Python program:
a = 360 + 14 
b = 360 / 8
c = b + 18 
d = a / c
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
Python program:
a = 8 / const_60
b = 3 / 6
c = b + 3 
d = c + 3 
e = d + 3 
f = e + 3
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
Python program:
a = 4 * 2
b = 68 - a
c = 15 / b
d = 68 * c
e = d ** 2
f = 4 * 2
g = 68 - f
h = 15 / g
i = h * 52
j = i ** 2
k = e - j
l = k / 2
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
Python program:
a = square_perimeter - (
b = a + 8
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
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 100 * c
e = d - 100
f = e / 2
g = 10 / 100
h = 2 * g
i = f / h
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
Python program:
a = 15 * 2
b = 40 - a
c = b * 500
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
Python program:
a = math.lcm(100, 8)
b = math.gcd(100, 8)
c = a * b
d = c / 100
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
Python program:
a = 36 * 30
b = 15 * 24
c = b / 80
d = a / c
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
Python program:
a = 100 * 8
b = 8 - 1
c = a / b
d = c - 100
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
Python program:
a = 65 * 250
b = 1000 * 65
c = a / 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
Python program:
a = 100 - 20
b = a * 1400
c = b / 100
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
Python program:
a = 12 * 15
b = a / 100
c = 8 * 35
d = c / 100
e = b + d 
f = 15 + 35 
g = e / f
h = g * 100
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
Python program:
a = 100 + 20 
b = 100 + 20 
c = b + 100 
d = a / c
e = d * 100
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
Python program:
a = 165 * 6
b = a / 360
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
Python program:
a = 15 / 100
b = 6000 * a
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
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 458 - 705
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
Python program:
a = 40 - 4
b = a - 4
c = b - 4
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
Python program:
a = 1 + 25 
b = 100 / a