euclaise/mathqa_programs huggingface dataset:
Problem: a starts business with rs . 35,000 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 22378 , b ) 279889 , c ) 2788 , d ) 9000 , e ) 2882
Rationale: "explanation : ratio in which profit is to be divided = 2 : 3 assume that b ' s contribution to the capital = b ⇒ 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 / 7 b = 2 / 3 ⇒ b = ( 3500 × 12 × 3 ) / ( 2 × 7 ) = 500 × 6 × 3 = 9000 answer : d"
Answer: d
Python program:
a = 35 * 0
b = a * 3
c = 12 - 5
d = c * 2
e = b / d
Problem: a person want to give his money of $ 600 to his 3 children a , b , c in the ratio 1 : 2 : 3 . what is the b + c share ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 150 , d ) $ 450 , e ) $ 500
Rationale: "b ' s share = 600 * 2 / 6 = $ 200 c ' s share = 600 * 3 / 6 = $ 300 b + c = $ 500 answer is e"
Answer: e
Python program:
a = 1 + 3 
b = a + 3 
c = 3 / b
d = c * 600
Problem: if the area of a square with sides of length 7 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 13 , e ) 18
Rationale: "let length of rectangle = l 7 ^ 2 = l * 4 = > l = 49 / 4 = 13 answer d"
Answer: d
Python program:
a = 7 ** 2
b = a / 4
Problem: the tax on a commodity is diminished by 30 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 70 * 115 = 8050 10000 - - - - - - - 1950 100 - - - - - - - ? = 20 % answer : a"
Answer: a
Python program:
a = 100 + 15 
b = 100 - 30
c = a * b
d = c / 100
e = 100 - d
Problem: two trains 137 meters and 163 meters in length are running towards each other on parallel lines , one at the rate of 42 kmph and another at 48 kmpb . in what time will they be clear of each other from the moment they meet
Options: a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 16 sec
Rationale: explanation : relative speed of the trains = ( 42 + 48 ) kmph = 90 kmph = ( 90 × 5 / 18 ) m / sec = 25 m / sec . time taken by the trains to ‘ pass each other = time taken to cover ( 137 + 163 ) m at 25 m / sec = ( 300 / 25 ) sec = 12 sec answer : option c
Answer: c
Python program:
a = 137 + 163 
b = 48 + 42 
c = b * 1000
d = c / 3600
e = a / d
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 17 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 17 0 = a + d - 16 a + d = 16 a = d ( as they are twin brothers ) a = d = 8 e is the answer"
Answer: e
Python program:
a = 17 - 1
b = a / 2
Problem: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30 % of the original number . what percent of the red candies remain ?
Options: a ) 22.5 % , b ) 31.5 % , c ) 37.5 % , d ) 42.5 % , e ) 46.5 %
Rationale: "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.5 x red + yellow = 0.75 x red = 0.375 x , since red = yellow . the answer is c ."
Answer: c
Python program:
a = 2 + 3 
b = 100 / a
c = b / 2
d = 2 + 3 
e = 100 / d
f = e / 2
g = f / 2
h = c + g 
i = 30 - h
j = i / 2
k = 2 + 3 
l = 100 / k
m = j / l
n = m * 100
Problem: mixture a is 10 percent alcohol , and mixture b is 40 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 20 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 1.6 , b ) 1.7 , c ) 1.8 , d ) 1.9 , e ) 2.0
Rationale: "( 40 - 20 ) / ( 20 - 15 ) = qa / qb 20 / 10 = qa / qb 2 / 1 = qa / qb qa = ( 2 / 5 ) * 4 = 8 / 5 = 1.6 approx answer : a"
Answer: a
Python program:
a = 10 * 40
b = a / 40
c = b / 2
Problem: rs . 100 amounts to rs . 320 in 4 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?
Options: a ) 246 , b ) 650 , c ) 110 , d ) 240 , e ) 360
Rationale: "( 100 * 4 * 3 ) / 100 = 12 100 + 12 = 112 answer : c"
Answer: c
Python program:
a = 3 / 100
b = 1 + a 
c = b ** 4
d = c * 100
Problem: a family has two children . find the probability that both the children are girls given that at least one of them is a girl ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 3 / 7 , d ) 2 / 7 , e ) 3 / 7
Rationale: let b stand for boy and g for girl . the sample space of the experiment is s = { ( g , g ) , ( g , b ) , ( b , g ) , ( b , b ) } let e and f denote the following events : e : ‘ both the children are girls ’ f : ‘ at least one of the child is a girl ’ then e = { ( g , g ) } and f = { ( g , g ) , ( g , b ) , ( b , g ) } now e n f = { ( g , g ) } thus p ( f ) = 3 / 4 and p ( e n f ) = 1 / 4 therefore p ( e | f ) = p ( e ∩ f ) / p ( f ) = ( 1 / 4 ) / ( 3 / 4 ) = 1 / 3 b )
Answer: b
Python program:
a = 3 * const_0_25
b = const_0_25 / a
Problem: two good train each 650 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 ) 12.4 sec , b ) 24.3 sec , c ) 62.4 sec , d ) 60.1 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 650 + 650 ) m = 1300 m . required time = ( 1300 x 6 / 125 ) sec = 62.4 sec . answer c"
Answer: c
Python program:
a = 45 + 30 
b = a * const_0_2778
c = 1/(b)
d = 650 * c
e = d * 2
Problem: 1 , 3,5 , 7,9 , . . 50 find term of sequnce for this ?
Options: a ) 1235 , b ) 1540 , c ) 1650 , d ) 2000 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 e"
Answer: e
Python program:
a = negate - (
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 130 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 130 + p c + m = 130 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 130 / 2 = 65 . answer : b"
Answer: b
Python program:
a = 130 / 2
Problem: the tax on a commodity is diminished by 10 % and its consumption increased by 20 % . the effect on revenue is ?
Options: a ) 2 % decrease , b ) 8 % increase , c ) 9 % decrease , d ) 3 % decrease , e ) 2 % decrease
Rationale: "100 * 100 = 10000 90 * 120 = 10800 - - - - - - - - - - - 10000 - - - - - - - - - - - 800 100 - - - - - - - - - - - ? = > 8 % increase answer : b"
Answer: b
Python program:
a = 20 / 100
b = 1 + a 
c = 10 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: 4 , 12 , 48 , 240 , 1440 , ( . . . )
Options: a ) 7620 , b ) 6200 , c ) 10020 , d ) 10080 , e ) 11000
Rationale: "go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7 4 x 3 = 12 ; 12 x 4 = 48 . . . . . 1440 x 7 = 10080 answer is d ."
Answer: d
Python program:
a = negate - (
Problem: a salesman gets commission on total sales at 9 % . if the sale is exceeded rs . 10000 he gets an additional commission as bonus of 3 % on the excess of sales over rs . 10000 . if he gets total commission of rs . 1380 , then the bonus he received is :
Options: a ) 22 , b ) 120 , c ) 388 , d ) 377 , e ) 272
Rationale: explanation : commission up to 10000 = \ inline 10000 \ times \ frac { 9 } { 100 } = 900 again after 10000 , commission : bonus 9 : 3 \ inline \ rightarrow 3 x : x \ therefore bonus = \ inline ( 1380 - 900 ) \ times \ frac { 1 } { 4 } = rs . 120 answer : b ) rs . 120
Answer: b
Python program:
a = 9 * 10000
b = a / 100
c = 1380 - b
d = 1 / 4
e = c * d
Problem: a work can be finished in 20 days by 10 women . the same work can be finished in fifteen days by 20 men . the ratio between the capacity of a man and a woman is
Options: a ) 1 : 3 , b ) 4 : 3 , c ) 2 : 3 , d ) 2 : 1 , e ) 2 : 4
Rationale: "work done by 10 women in 1 day = 1 / 20 work done by 1 woman in 1 day = 1 / ( 10 × 20 ) work done by 20 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 × 20 ) ratio of the capacity of a man and woman = 1 / ( 15 × 20 ) : 1 / ( 10 × 20 ) = 1 / 15 : 1 / 10 = 1 / 3 : 1 / 2 = 2 : 3 option c"
Answer: c
Python program:
a = 20 + 2 
b = a * 10
c = 1 / b
d = 20 * 10
e = 1 / d
f = c / e
Problem: the length of a train and that of a platform are equal . if with a speed of 216 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 1752 , b ) 1799 , c ) 1719 , d ) 1750 , e ) 1800
Rationale: "speed = [ 216 * 5 / 18 ] m / sec = 60 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 60 ã ¨ x = 60 * 60 / 2 = 1800 answer : e"
Answer: e
Python program:
a = 216 * 1000
b = const_60 / 1
c = a / b
d = c / 2
Problem: if it takes a machine 4 ⁄ 5 minute to produce one item , how many items will it produce in 2 hours ?
Options: a ) 1 ⁄ 3 , b ) 150 , c ) 80 , d ) 120 , e ) 180
Rationale: 1 item takes 4 / 5 min so it takes 120 min to produce x 4 x / 5 = 120 the x = 150 answer : b
Answer: b
Python program:
a = 2 * const_60
b = 4 / 5
c = a / b
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 120 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 32
Rationale: "we have : l = 20 ft and lb = 120 sq . ft . so , b = 6 ft . length of fencing = ( l + 2 b ) = ( 20 + 12 ) ft = 32 ft . answer : e"
Answer: e
Python program:
a = 120 / 20
b = a * 2
c = b + 20
Problem: what is the units digit of 31 ! + 50 ! + 2 ! + 3 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 2 + 6 = 8 the units digit is 8 . the answer is e ."
Answer: e
Python program:
a = 4 + 3 
b = a + 2
Problem: what is the smallest positive integer x such that 520 - x is the cube of a positive integer
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "given 520 - x is a perfect cube so we will take 512 = 8 * 8 * 8 520 - x = 512 x = 520 - 512 = 8 correct option is c"
Answer: c
Python program:
a = 3 + 4
Problem: if equation | x / 2 | + | y / 2 | = 2 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 32 , c ) 100 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 4 | + | y / 4 | = 1 , so these are lines in four quadrants with x and y intercept as 14 , so it is a rhombus with diagonals of 8 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 8 * 8 = 32 . answer b .
Answer: b
Python program:
a = 2 * 2
b = a ** 2
c = 2 * 2
d = c ** 2
e = b + d
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 25 cm .
Options: a ) 700 cm 2 , b ) 600 cm 2 , c ) 500 cm 2 , d ) 400 cm 2 , e ) 100 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 25 x 32 ) cm 2 = 400 cm 2 answer : option d"
Answer: d
Python program:
a = 1 / 2
b = a * 25
c = 20 * 20
d = c * 4
e = 25 * 25
f = d - e
g = math.sqrt(f)
h = b * g
i = h + 25
Problem: what is the smallest integer k for which 64 ^ k > 4 ^ 22 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "64 ^ k > 4 ^ 22 4 ^ ( 3 k ) > 4 ^ 22 3 k > 22 k = 8 the answer is e ."
Answer: e
Python program:
a = 22 / 3
b = math.floor(a)
c = b + 1
Problem: the number 0.8 is how much greater than 1 / 8 ?
Options: a ) ½ , b ) 27 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: let x be the difference then . 8 - 1 / 8 = x 8 / 10 - 1 / 8 = x x = 27 / 40 ans b
Answer: b
Python program:
a = 1 / 8
b = 0 - 8
Problem: if the radius of a circle is decreased by 50 % , find the percentage decrease
Options: a ) 22 , b ) 099 , c ) 75 , d ) 26 , e ) 18
Rationale: "let original radius = r . new radius = = original area = and new area = decrease in area = = 75 % answer : c"
Answer: c
Python program:
a = 100 / 100
b = 100 / 100
c = 50 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
Problem: guadalupe owns 2 rectangular tracts of land . one is 300 m by 500 m and the other is 250 m by 630 m . the combined area of these 2 tracts is how many square meters ?
Options: a ) 3,360
b ) 307,500
c ) 621,500
d ) 704,000
e ) 2 , 816,000
Rationale: one is 300 m by 500 m and the other is 250 m by 630 m : ( 300 * 500 ) + ( 250 * 630 ) = 150000 + 157500 307500 answer : b
Answer: b
Python program:
a = rectangle_area + (
Problem: the difference between the place values of 9 and 4 in the number 927435 is
Options: a ) 899600 , b ) 856200 , c ) 875200 , d ) 896200 , e ) none
Rationale: sol . = ( place value of 9 ) – ( place value of 4 ) = ( 900000 - 400 ) = 899600 answer a
Answer: a
Python program:
a = 10 * 9
b = a - 9
Problem: a certain hobby shop sold model cars for $ 5.00 each and model trains for $ 8.00 each . if a customer purchased both cars and trains from the store for a total of $ 31.00 , what total number of cars and trains did the customer purchase ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: we can take numbers , as price of car 5 , 8 for train and 31 total for ease . now we can determine quickly that total number should range between 31 / 8 < = n < = 31 / 5 , so ans should be between 3 and 7 . now solving the expression 5 a + 8 b = 31 decreasing 31 in multiple of 5 and checking divisibility of that number by 8 . this way we get 3 cars , 2 trains we get $ 31.00 total 3 * 5 + 2 * 8 = 31 hence total number is 3 + 2 = 5 ans c
Answer: c
Python program:
a = 5 * 3
b = 31 - a
c = b / 8
d = 5 * 3
e = d / 5
f = c + e
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 180,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 6 a * 1 + a * 5 ) / 6 = 11 a / 6 = 55000 answer is c . $ 55,000"
Answer: c
Python program:
a = 3 * 3
b = a * 10
c = 100 * 10
d = b * c
e = 3 * 10
f = 100 * 10
g = e * f
h = d + g 
i = 75 + 15 
j = h / i
Problem: john and david work at a hospital with 10 other workers . for an internal review , 2 of the 10 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?
Options: a ) 1 / 45 , b ) 1 / 35 , c ) 1 / 25 , d ) 1 / 15 , e ) 1 / 10
Rationale: "probability that john and david will both be chosen out of 8 workers = ( 2 / 10 ) * ( 1 / 9 ) = 1 / 45 answer a"
Answer: a
Python program:
a = 10 - 1
b = 1 / a
c = 1 / 10
d = b * c
e = 2 * d
Problem: in a two - digit , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) none
Rationale: let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 . sum of digits = x + ( x + 2 ) = 2 x + 2 . ( 11 x + 2 ) ( 2 x + 2 ) = 144 22 x 2 + 26 x - 140 = 0 11 x 2 + 13 x - 70 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 . hence , required number = 11 x + 2 = 24 . option a
Answer: a
Python program:
a = 10 * 2
b = a + 4
Problem: mrs . evans gave a test to her freshmen economics class , which has 30 students enrolled and 25 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?
Options: a ) 30 , b ) 28 , c ) 26 , d ) 22 , e ) 19
Rationale: total number of enrolled students = 30 number of students who did not take test = 5 hence , number of students who took test = 30 - 5 = 25 number of students who answered q 2 correctly = 22 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : d
Answer: d
Python program:
a = 25 + 22 
b = a + 5 
c = b - 30
Problem: what is the smallest number which when diminished by 12 , is divisible 8 , 12 , 22 and 24 ?
Options: a ) 276 , b ) 295 , c ) 230 , d ) 225 , e ) 245
Rationale: "required number = ( lcm of 8 , 12 , 22 and 24 ) + 12 = 264 + 12 = 276 answer : option a"
Answer: a
Python program:
a = math.lcm(8, 12)
b = math.lcm(22, 24)
c = math.lcm(a, b)
d = c + 12
Problem: k is a 3 digit number such that the the ratio of the number to the sum of its digits is least . what is the difference between the hundreds and tens digit ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: explanation : this is only possible only when the hundreds digit has the least value and tens and units has the highest value . so we could get the highest possible sum but possible lowest number . so by this logic this number could only be 199 . so the difference is 8 . note : remember a number given as abc i . e abc = ax 100 + bx 10 + c . so 123 = 1 x 100 + 2 x 10 + 3 . answer : b
Answer: b
Python program:
a = 3 + 4 
b = a + 1
Problem: ♠ n denotes the number obtained when n is rounded to the nearest tenth . for example ♠ 4.31 = 4.3 ♠ 2.423 - ♠ 3.421 =
Options: a ) 1.05 , b ) 1.04 , c ) - 0.8 , d ) - 1.0 , e ) - 0.1
Rationale: ♠ 2.423 - ♠ 3.421 2.4 - 3.2 = - 0.8 answer : c
Answer: c
Python program:
a = 2 - 423
Problem: if 1 tic equals 5 tacs and 2 tacs equal 8 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 20 / 1 , c ) 5 / 6 , d ) 3 / 10 , e ) 1 / 15
Rationale: "tic = 5 * tac and 2 * tac = 8 * toc ; 2 * tic = 10 * tac and 10 * tac = 40 * toc - - > 2 * tic = 40 * toc - - > tic / toc = 40 / 2 = 20 / 1 . answer : b ."
Answer: b
Python program:
a = 8 / 1
b = 5 / 1
c = a + b
Problem: one hour after yolanda started walking from x to y , a distance of 65 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 5 miles per hour and bob â s was 7 miles per hour , how many miles had bob walked when they met ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
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 5 ( t + 1 ) miles . these distances must sum to 65 miles , so 7 t + 5 ( t + 1 ) = 65 , which may be solved for t as follows 7 t + 5 ( t + 1 ) = 65 7 t + 5 t + 5 = 65 12 t = 60 t = 5 ( hours ) therefore , bob had walked 7 t = 7 ( 5 ) = 35 miles when they met . the best answer is e ."
Answer: e
Python program:
a = 65 - 5
b = 5 + 7 
c = a / b
d = c * 7
Problem: if 30 % of 100 is greater than 50 % of a number by 10 , then the number is ?
Options: a ) 40 , b ) 30 , c ) 60 , d ) 80 , e ) 50
Rationale: "let the number be x 30 % of 100 - 50 % of x = 10 50 / 100 x = ( 30 / 100 * 100 ) - 10 x / 2 = 20 x = 40 answer is a"
Answer: a
Python program:
a = 30 / 100
b = a * 100
c = b - 10
d = 50 / 100
e = c / d
Problem: there were 35 students in a hostel . due to the admission of 7 new students , he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . what was the original expenditure of the mess ?
Options: a ) 125 , b ) 321 , c ) 561 , d ) 852 , e ) 420
Rationale: "let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42 ; 7 x = 84 ; x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . . ans : e"
Answer: e
Python program:
a = 42 + 42 
b = 42 - 35
c = a / b
d = c * 35
e = 42 + 42 
f = 42 - 35
g = e / f
h = 42 - g
i = 42 + 42 
j = 42 - 35
k = i / j
l = h - k
m = l + 2 
n = d - m
Problem: at a speed of 40 miles per hour , a certain car uses 1 gallon of gasoline every 40 miles . if the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 5 / 12 , c ) 7 / 12 , d ) 2 / 3 , e ) 25 / 36
Rationale: "gas used = ( 5 hours ) * ( 40 miles / hour ) * ( 1 gallon / 40 miles ) = 5 gallons portion used = ( 5 ) / 12 = 5 / 12 ans b"
Answer: b
Python program:
a = 40 * 5
b = a / 40
c = b / 12
Problem: niharika covers a distance in 30 min , if she drives at a speed of 60 km / h on an average . find the speed at which she must drive at to reduce the time of the journey by 30 % .
Options: a ) 84.71 kmph . , b ) 85.74 kmph . , c ) 83.71 kmph . , d ) 85.71 kmph . , e ) 84.71 kmph .
Rationale: given speed = 60 kmph . it means niharika covered 60 km in 60 min ( 1 hour ) . so , in 30 min he will cover 30 km . 30 % time reduced = 30 - 30 % of 30 = 21 min . thus , niharika needs to cover 30 km in 21 min ( 0.35 hour ) . speed * time = distance . speed * 0.35 = 30 speed = 85.71 kmph . answer : option d
Answer: d
Python program:
a = 100 - 10
b = a - 4
Problem: rahul ' s housing colony have one tap , working alone at its maximum constant rate , can fill a certain tank in 230 seconds . a second tap , working alone at its maximum constant rate , can fill the same tank in 234 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the tank is closest to
Options: a ) 116 seconds , b ) 150 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 230 secs tap 2 : 234 secs considering the average of these 2 taps : 232 secs . so 1 tap can fill the tank in 232 secs , so 2 taps can fill the tank in 232 / 2 = 116 secs . closest answer is a .
Answer: a
Python program:
a = 230 + 234 
b = 230 / a
c = b * 230
Problem: a certain junior class has 1,000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 10,000 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "total number of ways of choosing one student from each group is = 600 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 600 * 1000 ) = 1 / 10,000 b"
Answer: b
Python program:
a = 1 / 3
Problem: what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 2 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) none of the above , e ) 5
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 2 , which yields remainder of 0 upon division by 2 . answer : d"
Answer: d
Python program:
a = 8 ** 1
b = 8 ** 1
c = a - b
d = c / 8