euclaise/mathqa_programs huggingface dataset:
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 12000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 403200 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 12000 * 112 / 100 = rs . 13440 b ' s monthly income = 2 parts - - - - > rs . 13440 a ' s monthly income = 5 parts = 5 / 2 * 13440 = rs . 33600 a ' s annual income = rs . 33600 * 12 = rs . 403200 answer : b"
Answer: b
Python program:
a = 12 / 100
b = 1 + a 
c = 12000 * b
d = 5 / 2
e = c * d
f = e * 12
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) 50 , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 42.5 ) / ( 100 â ˆ ’ 5 ) = 150 hence , required % profit = 150 â € “ 100 = 50 % answer d"
Answer: d
Python program:
a = 100 + 42 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: pants , shorts and shirts in a dresser are in the ratio of 7 : 7 : 10 . if there are 14 pants , the number of shirts in the dresser is :
Options: a ) 14 , b ) 7 , c ) 20 , d ) 70 , e ) 35
Rationale: explanation : let pants = 7 x , shorts = 7 x & shirts = 10 x . now , 7 x = 14 hence x = 2 . number of apples = 10 x = 20 . answer : c
Answer: c
Python program:
a = 14 * 10
b = a / 7
Problem: if x / ( 11 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: "x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c"
Answer: c
Python program:
a = 11 * 2
b = a * 2
Problem: list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median r of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals
Options: a ) 5 , b ) 7 , c ) 8 , d ) r = 9 , e ) 10
Rationale: mode of list ii = 3 median r of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d )
Answer: d
Python program:
a = 6 + 4 
b = a / 2
c = b + 3 
d = c * 2
e = d - 7
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 194
Rationale: "by the question , the equation would be 150 p - 84 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 194 . answer e for me ."
Answer: e
Python program:
a = 4 * 4
b = a * 1000
c = 4 * 100
d = b + c 
e = 80 + 4 
f = e * 150
g = d + f 
h = g / 150
Problem: at a special sale , 9 tickets can be purchased for the price of 6 tickets . if 9 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 9 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 9 tickets cost 900 9 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 300 , % of 9 tickets = ( 300 / 900 ) * 100 = 33.3 % answer : b"
Answer: b
Python program:
a = 9 * 9
b = 6 * 9
c = a - b
d = c * 100
e = 9 * 9
f = d / e
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.35 * 8 = 0.2 ( x + 8 ) - - > x = 12 . answer : b ."
Answer: b
Python program:
a = 35 - 20
b = a * 8
c = b / 10
Problem: a students was asked to find the arithmetic mean of the numbers 3 , 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x . he found the mean to be 12 . what should be the number in place of x ?
Options: a ) 3 , b ) 7 , c ) 17 , d ) 31 , e ) 38
Rationale: adding all the numbers we get 137 + x given - ( 137 + x ) / 12 = 12 137 + x = 12 * 12 x = 144 - 137 x = 7 answer : b
Answer: b
Python program:
a = 12 * 12
b = 3 + 11 
c = b + 7 
d = c + 9 
e = d + 15 
f = e + 13 
g = f + 8 
h = g + 19 
i = h + 17 
j = i + 21 
k = j + 14 
l = a - k
Problem: harkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1190 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 10 kg grapes = 70 × 10 = 700 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 700 + 490 = 1190 a"
Answer: a
Python program:
a = 10 * 70
b = 9 * 55
c = a + b
Problem: a chemical supply company has 60 liters of a 40 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 40 % hno 3 solution means hno 3 = 24 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 24 + x = 50 % of ( 60 + x ) or x = 12 . hence , a"
Answer: a
Python program:
a = 60 / 2
b = 60 * 40
c = b / 100
d = a - c
e = d * 2
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 36 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 24 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) solve the equation . 262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) 9 , 462.6 + 3 , 104.35 x = 50 , 380.2 + 1 , 399.45 x 9 , 462.6 + 1 , 704.9 x = 50 , 380.2 1 , 704.9 x = 40 , 917.6 x = 24 answer is b ."
Answer: b
Python program:
a = 36 * 1399
b = 36 * 262
c = a - b
d = 3104 - 35
e = c / d
Problem: a man spends 35 % of his income on food , 25 % on children education and 80 % of the remaining on house rent . what percent of his income he is left with ?
Options: a ) 1 % , b ) 8 % , c ) 12 % , d ) 5 % , e ) 4 %
Rationale: let the total income be x then , income left = ( 100 - 80 ) % of x - [ 100 - ( 35 + 25 ) ] % of x = 20 % of 40 % of x = 8 % of x answer is b
Answer: b
Python program:
a = 100 - 35
b = a - 25
c = 100 - 80
d = b * c
e = d / 100
Problem: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 261 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 408 , b ) 475 , c ) 550 , d ) 625 , e ) 700
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 261 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 561 a + b + c = 51 per hour so for eight hrs = 51 * 8 = 408 = answer = a"
Answer: a
Python program:
a = 600 / 11
b = a * 8
Problem: a container contains 20 liters of milk , from this container 2 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 ) 14.58 liters , b ) 20.16 liters , c ) 22.45 liters , d ) 26.95 liters , e ) 31.45 liters
Rationale: "amount of milk left after 3 operations = 20 ( 1 - 2 / 20 ) ^ 3 = 20 * 9 / 10 * 9 / 10 * 9 / 10 = 14.58 liters answer is a"
Answer: a
Python program:
a = 20 - 2
b = a - 2
c = b - 2
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "given that the area of the square = 2025 sq . units = > side of square = √ 2025 = 45 units the radius of the circle = side of the square = 45 units length of the rectangle = 2 / 5 * 45 = 18 units given that breadth = 10 units area of the rectangle = lb = 18 * 10 = 180 sq . units answer : option e"
Answer: e
Python program:
a = math.sqrt(2025)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: a train of length 250 m crosses a bridge of length 150 m in 25 seconds . what is the speed of train ?
Options: a ) 57.6 , b ) 27 , c ) 25 , d ) 22 , e ) 72
Rationale: sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 25 x speed speed = 400 / 25 = 16 m / s = 57.6 km / h answer = a
Answer: a
Python program:
a = 250 + 150 
b = a / 25
c = const_3_6 * b
Problem: indu gave bindu rs . 500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 0.2 , b ) 1.2 , c ) 3 , d ) 4 , e ) 0.8
Rationale: "500 = d ( 100 / 4 ) 2 d = 0.8 answer : e"
Answer: e
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 500 * c
e = d - 500
f = 4 / 100
g = 500 * f
h = g * 2
i = e - h
Problem: the product of the squares of two positive integers is 9 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : b - 1 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 9 [ square root both sides ] xy = 3 3 = 1 x 3 , 3 x 1 cancel the repeats this leaves us with exactly 1 options . hence , b"
Answer: b
Python program:
a = 2 + 3 
b = a - 2
Problem: with both inlets open , a water tank will be filled with water in 52 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 10,500 , c ) 11,750 , d ) 17,500 , e ) 19,500
Rationale: "the work done by inlet a and b together in 1 min = 1 / 52 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 52 ) - ( 1 / 120 ) = 1 / 92 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 92 ) - ( 1 / 120 ) = 50 cubic meter = 19,500 cubic meter answer : option e"
Answer: e
Python program:
a = const_60 / 52
b = 1/(2)
c = a - b
d = c / const_60
e = const_60 * 2
f = 1/(e)
g = d - f
h = 50 / g
i = h / 1000
Problem: if each edge of a cube is increased by 50 % , find the percentage increase in its surface area
Options: a ) 125 %
b ) 129 %
c ) 185 %
d ) 725 %
e ) 145 %
Rationale: let the edge = a cm so increase by 50 % = = total surface area of original cube = tsa of new cube = = = increase in area = = increase % = = 125 % answer : a
Answer: a
Python program:
a = 3 / 2
b = a ** 2
c = 3 * 2
d = b * c
e = 3 * 2
f = d - e
g = 3 * 2
h = f / g
i = h * 100
Problem: 12 : 8 seconds : : ? : 4 minutes
Options: a ) 10 , b ) 15 , c ) 6 , d ) 8 , e ) 7
Rationale: "12 * 4 = 8 * x x = 6 answer : c"
Answer: c
Python program:
a = 12 / 8
b = 4 * a
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 4 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 2700 , c ) 18 , d ) 18000 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 40 * 50 ) therefore , number of stones = ( 3600 * 1500 / 40 * 50 ) = 2700 answer : b"
Answer: b
Python program:
a = 36 * 15
b = 4 * 5
c = b / 100
d = a / c
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent r ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . r = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c"
Answer: c
Python program:
a = 100 - 80
b = a - 10
c = 10 / b
d = c * 100
Problem: the cost to park a car in a certain parking garage is $ 15.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 3.03
Rationale: total cost of parking for 9 hours = 15 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 15 + 7 * 1.75 = 27.25 thus the average parking price = 27.25 / 9 = 3.03 $ e is the correct answer .
Answer: e
Python program:
a = 9 - 2
b = 1 * 75
c = 15 + b 
d = c / 9
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 2 ) / ( 10 - 4 ) = 2 / 6 = 1 / 3 so they should be mixed in the ratio 1 : 3 answer - e"
Answer: e
Python program:
a = 4 - 2
b = 10 - 4
c = a / b
Problem: a trader sells 75 meters of cloth for rs . 4950 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 51 , b ) 88 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 4950 / 75 = rs . 66 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 66 - rs . 15 = rs . 51 answer : a"
Answer: a
Python program:
a = 4950 / 75
b = a - 15
Problem: 587 x 999 = ?
Options: a ) 586413 , b ) 587523 , c ) 614823 , d ) 615173 , e ) none of them
Rationale: "= 587 x 999 = 587 x ( 1000 - 1 ) = 587 x 1000 - 587 - 1 = 587000 - 587 = 586413 answer is a"
Answer: a
Python program:
a = 587 / 999
b = a * 100
Problem: the contents of a certain box consist of 14 apples and 12 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 12 oranges , so to get to 6 oranges , we should remove 12 - 6 = 6 oranges . answer b"
Answer: b
Python program:
a = 14 + 12 
b = 70 / 100
c = 14 / b
d = a - c
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 110 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 = 110 + p c + m = 110 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 110 / 2 = 55 . answer : a"
Answer: a
Python program:
a = 110 / 2
Problem: the diagonal of a square is 4 ? 2 cm . what will be the diameter of another square if their area is double that of the first square ?
Options: a ) 8 cm
b ) 9 cm
c ) 10 cm
d ) 11 cm
e ) 12 cm
Rationale: d 1 = 4 ? 2 = > area = 1 / 2 d 12 = 1 / 2 * ( 4 ? 2 ) 2 = 16 cm 2 area of new square = ( 2 * 16 ) cm 2 = 32 cm 2 therefore 1 / 2 * d 22 = 32 = > d 22 = 64 = > d 2 = 8 cm answer a
Answer: a
Python program:
a = 4 * 2
b = math.sqrt(square_area)
Problem: the sale price sarees listed for rs . 400 after successive discount is 10 % and 5 % is ?
Options: a ) 166 , b ) 178 , c ) 342 , d ) 199 , e ) 112
Rationale: "400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 answer : c"
Answer: c
Python program:
a = 400 * 10
b = a / 100
c = 400 - b
d = 400 * 10
e = d / 100
f = 400 - e
g = f * 5
h = g / 100
i = c - h
Problem: a volume of 10936 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812
b ) 8231
c ) 2734
d ) 4222
e ) 4254
Rationale: a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10936 l can be kept in ( 10936 / 4 ) hemispheres ans . 2734 answer : c
Answer: c
Python program:
a = 10936 / 4
Problem: the average age of 31 students in a group is 16 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 31 , b ) 36 , c ) 48 , d ) 45 , e ) 57
Rationale: "age of the teacher = ( 32 * 17 - 31 * 16 ) = 48 years . answer : c"
Answer: c
Python program:
a = 31 + 1
Problem: venki takes a trip and drives 5 hours from town x to town z at a rate of 80 miles per hour . on her way back , venki drives 45 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take venki to drive from town z to town y ?
Options: a ) 1.01 , b ) 4.44 , c ) 11.5 , d ) 1.75 , e ) 2.14
Rationale: distance from x to z = 5 hr * 80 mph = 400 miles hence distance from y to z = 1 / 2 * 400 = 200 time = 200 / 45 = 4.44 hrs imo : b
Answer: b
Python program:
a = 5 * 80
b = a / 2
c = b / 45
Problem: if a rectangle have length 16 cm and diagonal 20 cm . calculate its area .
Options: a ) 185
b ) 132
c ) 165
d ) 192
e ) 212
Rationale: breadth = √ 20 ^ 2 - 16 ^ 2 = √ 144 = 12 cm area = 16 * 12 = 192 sq . cm answer d
Answer: d
Python program:
a = 20 ** 2
b = 16 ** 2
c = a - b
d = math.sqrt(c)
e = d * 16
Problem: a qualified worker digs a well in 5 hours . he invites 2 apprentices , both capable of working 3 / 5 as fast and 2 trainees both working 1 / 5 as fast as he . if the 5 - person team digs the same well , how much time does the team need to finish the job ?
Options: a ) 1 : 42 , b ) 1 : 34 , c ) 1 : 44 , d ) 1 : 54 , e ) 2 : 14
Rationale: and answer is correct as you have calculated : 100 / 59 hrs that is 1.71 hrs - 1 hr and 42 minutes , so 1 : 42 , hence , a .
Answer: a
Python program:
a = 12 / 100
b = 1 / 5
c = 1 / 5
d = b * c
e = d * 2
f = 1 / 5
g = 1 / 5
h = f * g
i = e + h 
j = 1 / 5
k = i + j 
l = a + k 
m = 1 + l 
n = m / const_60
Problem: find the cost of fencing around a circular field of diameter 28 m at the rate of rs . 1.50 a meter ?
Options: a ) rs . 150
b ) rs . 132
c ) rs . 100
d ) rs . 125
e ) rs . 225
Rationale: 2 * 22 / 7 * 14 = 88 88 * 1 1 / 2 = rs . 132 answer : b
Answer: b
Python program:
a = 28 / 2
b = circumface * (
Problem: truck x is 14 miles ahead of truck y , which is traveling the same direction along the same route as truck x . if truck x is traveling at an average speed of 57 miles per hour and truck y is traveling at an average speed of 63 miles per hour , how long will it take truck y to overtake and drive 4 miles ahead of truck x ?
Options: a ) 5 hours , b ) 3 hours 20 minutes , c ) 3 hours , d ) 2 hours 45 minutes , e ) 8 hours
Rationale: "relative speed = 63 - 57 = 6 miles per hour dist required = 14 + 4 = 18 miles time taken to overtake = 18 / 6 = 3 hours . c is the answer ."
Answer: c
Python program:
a = 14 + 4 
b = 63 - 57
c = a / b
Problem: a and b ’ s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) rs . 500 , b ) rs . 750 , c ) rs . 1250 , d ) rs . 1500 , e ) rs . 1520
Rationale: "explanation : ( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 a = 1500 answer is d"
Answer: d
Python program:
a = 2 + 3 
b = 4 * a
c = 2 * b
d = c * 100
e = 85 / 100
f = 1 - e
g = d * f
h = 95 / 100
i = 1 - h
j = 85 / 100
k = 1 - j
l = i + k 
m = g / l
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 80 vehicles were involved in accidents . if 4 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 1600 , b ) 3200 , c ) 800 , d ) 400 , e ) 200
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 80 accidents as 4 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 4,000 million rather than 4 billion . creating a proportion we have : 100 / 80 = 4,000 / x cross multiplying gives us : 100 x = 4,000 * 80 x = 40 * 80 = 3200 answer : b"
Answer: b
Python program:
a = 4 * 10
b = 80 * a
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 20 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 20 . . 4 x + 12 = 20 . . x = 2 . . ans = x + 4 = 2 + 4 = 6 answer b
Answer: b
Python program:
a = 2 * 4
b = 4 + a 
c = 20 - b
d = c / 4
e = d + 4
Problem: log root ( 8 ) / log 8 is equal to
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: = > log ( 8 ) ^ 1 / 2 / log 8 = 1 / 2 log 8 / log 8 = 1 / 2 answer a
Answer: a
Python program:
a = 8 / 4
b = 1 / a
Problem: one - third less than 40 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 48
Rationale: "lots of ways to tackle this . 40 % of 180 = 72 1 / 3 of 72 = 24 so , 1 / 3 less than 72 is equal to 72 - 24 = 48 answer : e"
Answer: e
Python program:
a = 40 / 100
b = a * 180
c = 1 / 3
d = 40 / 100
e = d * 180
f = c * e
g = b - f
Problem: alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 4,600 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,100 , c ) 1,700 , d ) 2,550 , e ) 2,300
Rationale: "assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 4600 therefore x = 3400 / 4 = 850 price of 28 inch + 30 inch = 1050 + 1250 = 2300 option e"
Answer: e
Python program:
a = 200 + 3600 
b = 1 + 2 
c = b + 3 
d = c * 200
e = a - d
f = e / 4
g = f + 200 
h = 200 + 3600 
i = 1 + 2 
j = i + 3 
k = j * 200
l = h - k
m = l / 4
n = m + 200 
o = n + 200 
p = g + o 
q = 2 * 10
r = q - 1
s = p / r
Problem: a can finish a piece of work in 4 days . b can do it in 12 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "2 / 4 + ( 2 + x ) / 12 = 1 = > x = 4 days answer : a"
Answer: a
Python program:
a = 1 / 4
b = a * 2
c = 1 / 12
d = c * 2
e = b + d 
f = 1 - e
g = 1 / 12
h = f / g