euclaise/mathqa_programs huggingface dataset:
Problem: the price of 80 apples is equal to that of 120 oranges . the price of 60 apples and 75 oranges together is rs . 1320 . the total price of 25 apples and 40 oranges is
Options: a ) 620 , b ) 610 , c ) 630 , d ) 625 , e ) 635
Rationale: "let the price of one apple = a and price of one orange = b the price of 80 apples is equal to that of 120 oranges 80 a = 120 b = > 2 a = 3 b ⇒ b = 2 a / 3 - - - - - ( equation 1 ) price of 60 apples and 75 oranges together is rs . 1320 = > 60 a + 75 b = 1320 = > 4 a + 5 b = 88 ⇒ 4 a + 5 ( 2 a ) / 3 = 88 ( ∵ substituted the value of b from equation 1 ) = > 12 a + 10 a = 88 × 3 = > 6 a + 5 a = 44 × 3 = > 11 a = 44 × 3 = > a = 4 × 3 = 12 b = 2 a / 3 = ( 2 × 12 ) / 3 = 8 total price of 25 apples and 40 oranges = 25 a + 40 b = ( 25 × 12 ) + ( 40 × 8 ) = 300 + 320 = 620 answer is a ."
Answer: a
Python program:
a = 80 / 120
b = 75 * a
c = 60 + b 
d = 1320 / c
e = d * 25
f = 80 / 120
g = 75 * f
h = 60 + g 
i = 1320 / h
j = 80 / 120
k = i * j
l = k * 40
m = e + l
Problem: two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ration 8 : 5 ?
Options: a ) 4 : 3 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 9 , e ) none
Rationale: let the c . p . of spirit be re . 1 litre . spirit in 1 litre mix . of a = 5 / 7 litre , c . p . of 1 litre mix . in a = re . 5 / 7 spirit in 1 litre mix . of b = 7 / 13 litre , c . p . of 1 litre mix . in b = re . 7 / 13 spirit in 1 litre mix . of c = 8 / 13 litre , mean price = re . 8 / 13 . by the rule of alligation , we have : required ratio = 1 / 13 : 9 / 91 = 7 : 9 . answer d
Answer: d
Python program:
a = 2 + 7 
b = 7 / a
Problem: a scale 7 ft . 6 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 18 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 7 * 12 ) + 6 = 90 inches length of each of the 5 parts = 90 / 5 = 18 inches answer : d"
Answer: d
Python program:
a = 7 * 12
b = a + 6 
c = b / 5
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 18
b ) 6
c ) 27
d ) 48
e ) 36
Rationale: volume of cube = lbh = 3 new cube l , b , h are increases of 3 l , 2 b , 2 h new volume of cube = 3 l * 2 b * 2 h = 12 lbh = 12 * 3 = 36 answer : e
Answer: e
Python program:
a = 2 * 2
b = a * 3
c = b * 3
Problem: having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 2.25 , b ) $ 2.75 , c ) $ 3.00 , d ) $ 3.50 , e ) $ 3.75
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 60 cents ( 4 / 15 ) x = 60 x = $ 2.25 the answer is a ."
Answer: a
Python program:
a = 3 * 5
b = a * 0
c = b / 4
Problem: there are 14 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 91 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 14 c 2 = 14 * 13 / 2 = 91 so option a is correct"
Answer: a
Python program:
a = 14 - 1
b = 14 * a
c = b / 2
Problem: a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 60 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "60 % is 20 % - points above 40 % and 20 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 1 : 1 . so the team played a total of 30 + 30 = 60 games . the answer is b ."
Answer: b
Python program:
a = 40 / 100
b = 30 * a
c = 80 / 100
d = 60 / 100
e = c - d
f = b / e
Problem: cereal a is 11 % 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 : 5 , b ) 1 : 3 , c ) 2 : 7 , d ) 3 : 4 , e ) 1 : 5
Rationale: "2 % is 2 % - points below 4 % and 11 % is 7 % - points above 4 % . the ratio of a : b should be 2 : 7 . the answer is c ."
Answer: c
Python program:
a = 4 - 2
b = 11 - 4
c = a / b
Problem: 10 years ago a was half of b in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Options: a ) 30 , b ) 35 , c ) 37 , d ) 41 , e ) 43
Rationale: explanation : let a ' s age 10 years ago = x years . then , b ' s age 10 years ago = 2 x years . ( x + 10 ) / ( 2 x + lo ) = 3 / 4 = > x = 5 . so , the total of their present ages = ( x + 10 + 2 x + 10 ) = ( 3 x + 20 ) = 35 years . answer : option b
Answer: b
Python program:
a = 10 / 2
b = 10 - a
c = 4 / 2
d = 3 - c
e = b / d
f = 3 * e
g = 10 / 2
h = 10 - g
i = 4 / 2
j = 3 - i
k = h / j
l = 4 * k
m = f + l
Problem: a rectangular tiled patio is composed of 126 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 126 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5
b ) 6
c ) 9
d ) 13
e ) 28
Rationale: suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 126 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 126 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 126 ( 2 r - 4 ) * r = 126 2 r ^ 2 - 4 r - 126 = 0 r can not be negative so r = 9 and c = 14 so , answer will be c
Answer: c
Python program:
a = negate + ( 
b = 4 ** 2
c = 126 * 2
d = 4 * c
e = b + d 
f = math.sqrt(e)
g = a / f
h = 126 / g
Problem: in a class of 39 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 39 - 29 = 10 play neither answer is c"
Answer: c
Python program:
a = 26 + 20 
b = a - 17
c = 39 - b
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 18 * 12 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 12 is 6 . hence 18 * 12 = 6 . hence ( ( 12 * 16 ) * ( 18 * 12 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Python program:
a = 18 / 3
b = a / 3
Problem: if 24 men take 15 days to to complete a job , in how many days can 18 men finish that work ?
Options: a ) 20 , b ) 19 , c ) 18 , d ) 17 , e ) 16
Rationale: ans . 20 days
Answer: a
Python program:
a = 24 * 15
b = a / 18
Problem: the circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long . what is the distance travelled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 1200 ft , b ) 800 ft , c ) 900 ft , d ) 1000 ft , e ) 1500 ft
Rationale: "total distance - x x / 40 - x / 48 = 5 x = 1200 ft answer a"
Answer: a
Python program:
a = 10 / 2
b = 40 * a
c = b / 3
d = 10 / 2
e = c + d 
f = 40 * e
Problem: a train requires 10 seconds to pass a pole while it requires 30 seconds to cross a stationary train which is 600 mtrs long . find the speed of the train .
Options: a ) 110 kmph , b ) 120 kmph , c ) 108 kmph , d ) 100 kmph , e ) 98 kmph
Rationale: "in 10 s the train crosses the pole and in 30 sec the train crosses one more stationary train in 20 sec the train travels a distance of 600 mtrs speed = 600 / 20 = 30 m / s = 30 ( 3600 / 1000 ) = 30 * 18 / 5 = 108 kmph answer : c"
Answer: c
Python program:
a = 30 - 10
b = 600 / a
c = b * const_3_6
Problem: the average of runs of a cricket player of 10 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 76 , b ) 80 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 x 10 = 360 . now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 x 11 = 440 runs made in the 11 th inning = 440 - 360 = 80 answer : b"
Answer: b
Python program:
a = 10 + 1 
b = 4 + 36 
c = a * b
d = 10 * 36
e = c - d
Problem: john had a stock of 800 books in his bookshop . he sold 62 on monday , 62 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 78 % , b ) 66 % , c ) 62 % , d ) 64 % , e ) 60 %
Rationale: "let n be the total number of books sold . hence n = 62 + 62 + 60 + 48 + 40 = 272 let m be the books not sold m = 800 - n = 1400 - 272 = 528 percentage books not sold / total number of books = 528 / 800 = 0.66 = 66 % correct answer b"
Answer: b
Python program:
a = 62 + 62 
b = 60 + 48 
c = a + b 
d = c + 40 
e = 800 - d
f = e / 800
g = f * 100
Problem: a certain city with a population of 180,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 15,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 180 k x = 15,000 answer : d"
Answer: d
Python program:
a = 4 * 2
b = a * 100
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 100 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 c"
Answer: c
Python program:
a = 3 + 3
Problem: circular gears l and r start to rotate at the same time at the same rate . gear l makes 20 complete revolutions per minute and gear r makes 40 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 6 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 12 , e ) e ) 15
Rationale: gear l - - 20 rotations per 60 seconds - - 2 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 4 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 2 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 2 units . required net difference should be 6 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : a
Answer: a
Python program:
a = 40 / const_60
b = 20 / const_60
c = a - b
d = 6 / c
e = d / 3
Problem: two pipes a and b can fill a tank in 4 and 12 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 , b ) 3 , c ) 6 , d ) 9 , e ) 10
Rationale: "part filled by a in 1 min . = 14 part filled by b in 1 min . = 1 / 12 part filled by ( a + b ) in 1 min . = 1 / 4 + 1 / 12 = 1 / 3 . both the pipes can fill the tank in 3 minutes . answer : b"
Answer: b
Python program:
a = 4 * 100
b = 1 / 4
c = 1 / 12
d = b + c 
e = d * 2
f = 1 - e
g = f * 4
h = g * const_60
i = a + h
Problem: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1206 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1206 or 9 x = 1206 or x = 134 . required number = 134 . answer : c"
Answer: c
Python program:
a = 43 - 34
b = 1206 / a
Problem: a company pays 18.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 18 , d ) 37 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 18.5 * 50 ) / 100 = rs . 9.25 rs . 25 is income on an investment of rs . 100 rs . 9.25 is income on an investment of rs . ( 9.25 * 100 ) / 25 = rs . 37 answer : d"
Answer: d
Python program:
a = 18 * 5
b = a / 100
c = b * 100
d = c / 25
Problem: 1000 men have provisions for 20 days . if 650 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.5 , c ) 12.6 , d ) 12.2 , e ) 12.1
Rationale: "1000 * 20 = 1650 * x x = 12.1 answer : e"
Answer: e
Python program:
a = 20 * 1000
b = 1000 + 650 
c = a / b
Problem: david ' s bank ' s saving amount is decreased 10 % due to loan payment and current balance is rs . 90000 . find the actual balance before deduction ?
Options: a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 100000
Rationale: 10 % decreased 90 % balance = 90000 100 % = 90000 / 90 * 100 = 100000 answer : e
Answer: e
Python program:
a = 90000 * 100
b = 100 - 10
c = a / b
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2200 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 5500 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 2200 … ( i ) and 4 x – 2 y = 2200 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2200 - > x = 1100 p 1 ’ s income = rs 5 * 1100 = rs . 5500 answer : d"
Answer: d
Python program:
a = 2200 / 2
b = a * 3
c = b - 2200
d = c * 5
Problem: 3 math classes : x , y , and z , take an algebra test . the average score in class x is 83 . the average score in class y is 76 . the average score in class z is 85 . the average score of all students in classes x and y together is 79 . the average score of all students in classes y and z together is 81 . what is the average score for all the 3 classes , taken together ?
Options: a ) 81 , b ) 81.5 , c ) 82 , d ) 84.5 , e ) none of these
Rationale: explanation : let the number of students in classes x , y and z be a , b and c respectively . then total of x = 83 a total of y = 76 b total of z = 85 c and , ( 83 a + 76 b ) / ( a + b ) = 79 . i . e 4 a = 3 b . also , ( 76 b + 85 c ) / ( b + c ) = 81 . i . e 4 c = 5 b . hence , b = ( 4 / 3 ) a , c = ( 5 / 4 ) b = ( 5 / 4 ) x ( 4 / 3 ) a = ( 5 / 3 ) a . average of x , y and z = ( 83 a + 76 b + 85 c ) / ( a + b + c ) . = > 83 a + 76 ∗ ( 4 / 3 ) a + 85 ∗ ( 5 / 3 ) a / a + ( 4 / 3 ) a + ( 5 / 3 ) a . = > 978 / 12 = > 81.5 answer : b
Answer: b
Python program:
a = 79 - 76
b = 83 * a
c = 81 - 76
d = 85 * c
e = 83 - 79
f = 76 * e
g = d + f 
h = b + g 
i = 81 - 76
j = 83 - 79
k = 79 - 76
l = j + k 
m = i + l 
n = h / m
Problem: a can finish a piece of work in 4 days . b can do it in 14 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "2 / 4 + ( 2 + x ) / 14 = 1 = > x = 5 days answer : b"
Answer: b
Python program:
a = 1 / 4
b = a * 2
c = 1 / 14
d = c * 2
e = b + d 
f = 1 - e
g = 1 / 14
h = f / g
Problem: the population of a town increased from 1 , 34,000 to 2 , 32,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 7.3 % , c ) 7.6 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 232500 - 134000 ) = 98500 . increase % = ( 98500 / 134000 x 100 ) % = 73 % . required average = ( 73 / 10 ) % = 7.3 % . answer : option b"
Answer: b
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 2 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: if r is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of r ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: answer is c . numbers in format of 3 ^ k in the series from 1 to 30 inclusive r are : 3 * 1 , 3 * 2 , 3 * 3 , 3 * 4 , 3 * 5 , 3 * 3 * 2 , 3 * 7 , 3 * 8 , 3 * 3 * 3 , 3 * 10 . total number of 3 = 13 . so k = 14 .
Answer: c
Python program:
a = 30 / 2
b = a - 1
Problem: rs . 460 was divided among 41 boys and girls such that each boy rs . 12 and each girl got rs . 8 . what is the number of boys ?
Options: a ) 33 , b ) 30 , c ) 36 , d ) 28 , e ) 26
Rationale: explanation : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - assume that the number of boys = b and number of girls is g number of boys + number of girls = 41 = > b + g = 41 - - - - - - - - - - - - ( equation 1 ) given that each boy got rs . 12 and each girl got rs . 8 and total amount = rs . 460 = > 12 b + 8 g = 460 - - - - - - - - ( equation 2 ) now we need solve equation 1 and equation 2 to get b and g ( equation 1 ) × 8 = > 8 b + 8 g = 8 × 41 = 328 − − − − − − − − ( equation 3 ) ( equation 2 ) - ( equation 3 ) = 4 b = 460 - 328 = 132 = > b = 1324 = 33 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - given that amount received by a boy = rs . 12 and amount received by a girl = rs . 8 total amount = 460 given that number of boys + number of girls = 41 hence mean amount = 460 / 41 by the rule of alligation , we have amount received by a boy amount received by a girl 12 8 mean amount 460 / 41 460 / 41 - 8 = 132 / 41 12 - 460 / 41 = 32 / 41 number of boys : number of girls = 132 / 41 : 32 / 41 = 132 : 32 = 66 : 16 = 33 : 8 given that number of boys + number of girls = 41 hence number of boys = 41 × 3341 = 33 answer : option a
Answer: a
Python program:
a = 8 * 41
b = 460 - a
c = b / 4
Problem: a shopkeeper sells 200 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 55 , e ) 95
Rationale: sp per metre = 18000 / 200 = rs . 90 loss per metre = rs . 5 cp per metre = 90 + 5 = rs . 95 . answer : e
Answer: e
Python program:
a = 18000 / 200
b = a + 5
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 .
Options: a ) 29 , b ) 27 , c ) 28 , d ) 24 , e ) 21
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is a ."
Answer: a
Python program:
a = 2 * 11
b = a + 5 
c = b + 2
Problem: a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . if 45 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 3.0 , b ) 5.0 , c ) 5.5 , d ) 6.5 , e ) 6.75
Rationale: "construct an equation : 15 / 100 = x / 45 - > x = 6.75 answer : e ."
Answer: e
Python program:
a = 15 / 100
b = 45 * a
Problem: two trains of equal lengths take 5 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 12 , c ) 7.5 , d ) 99 , e ) 21
Rationale: "speed of the first train = 120 / 5 = 24 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 24 + 8 = 32 m / sec . required time = ( 120 + 120 ) / 32 = 7.5 sec . answer : c"
Answer: c
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: machine a and machine b are each used to manufacture 880 sprockets . it takes machine a 10 hours longer to produce 880 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 6 , b ) 6.6 , c ) 8.8 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 880 qt = 800 for a : ( t + 10 ) ( q ) = 880 qt + 10 q = 880 800 + 10 q = 880 q = 8 so a can produce 8 / hour . then b can produce = 8 ( 1.1 ) = 8.8 / hour . c"
Answer: c
Python program:
a = 10 * 880
b = 100 + 10 
c = b / 100
d = a * c
e = 100 + 10 
f = e / 100
g = 880 * f
h = g - 880
i = d / h
j = 880 / i
Problem: an empty fuel tank with a capacity of 204 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 66 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 204 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 204 - a gallons of fuel b is 0.16 ( 204 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 204 - a ) = 30 - - > a = 66 . answer : d ."
Answer: d
Python program:
a = 16 / 100
b = 204 * a
c = b - 30
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
Problem: what is the largest 4 digit number exactly divisible by 50 ?
Options: a ) 4676 , b ) 4678 , c ) 9950 , d ) 9504 , e ) 9936
Rationale: "largest 4 digit number = 9999 9999 ÷ 50 = 199 , remainder = 49 hence largest 4 digit number exactly divisible by 50 = 9999 - 49 = 9950 answer : c"
Answer: c
Python program:
a = 10 ** 4
b = a / 50
c = math.floor(b)
d = c * 50
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind poe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of poe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . poe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins = d"
Answer: d
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60