euclaise/mathqa_programs huggingface dataset:
Problem: in a garden , 26 trees are planted at equal distances along a yard 800 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 32 , d ) 14 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 800 / 25 = 32 i . e . , distance between two consecutive trees = 32 answer is c ."
Answer: c
Python program:
a = 26 - 1
b = 800 / a
Problem: the average age of a , b and c is 28 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 19 , b ) 26 , c ) 20 , d ) 32 , e ) 21
Rationale: "age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 28 ã — 3 â € “ 29 ã — 2 = 84 â € “ 58 = 26 years b"
Answer: b
Python program:
a = 28 * 3
b = 29 * 2
c = a - b
Problem: evaluate : 986 x 237 + 986 x 863
Options: a ) 986000 , b ) 968000 , c ) 978000 , d ) 987000 , e ) none of them
Rationale: "986 x 137 + 986 x 863 = 986 x ( 137 + 863 ) = 986 x 1000 = 986000 . answer is a ."
Answer: a
Python program:
a = 237 * 986
b = a * 863
c = 986 - b
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 3 kgs more for rs . 700 , what is the reduced price for kg ?
Options: a ) 70 , b ) 50 , c ) 60 , d ) 80 , e ) 65
Rationale: "700 * ( 30 / 100 ) = 210 - - - - 3 ? - - - - 1 = > rs . 70 answer : a"
Answer: a
Python program:
a = 700 * 30
b = a / 100
c = b / 3
Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many f ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: "5 choices for each of the 4 questions , thus total f of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."
Answer: c
Python program:
a = 5 ** 4
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 8 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 17 : 7 , b ) 18 : 8 , c ) 19 : 9 , d ) 19 : 5 , e ) 19 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 8 = 5 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 + 7 / 2 = 17 / 2 = 8.5 litres as 12 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 8.5 : 3.5 = 17 : 7 . answer : a"
Answer: a
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 8 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k 
m = e / l
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 10 candidates . she plans to have one working interview with 3 of the 10 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "there are c 310 = 120 different groups of three possible out of 10 candidates and since each of these groups is interviewed every day then total of 120 days are needed . answer : b"
Answer: b
Python program:
a = math.factorial(10)
b = 10 - 3
c = math.factorial(b)
d = a / c
e = math.factorial(3)
f = d / e
g = f / 2
h = g - 10
i = h - 10
j = i - 10
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 34 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 21 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 34 = > x = 7 so deepak age is = 3 ( 7 ) = 21 answer : d"
Answer: d
Python program:
a = 34 - 6
b = a * 3
c = b / 4
Problem: a retailer bought a machine at a wholesale price of $ 99 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 132 , e ) 160
Rationale: "my solution : wholesale price = 99 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 99 + 1 / 5 ( 99 ) x = 132 ; answer : d"
Answer: d
Python program:
a = 99 * 20
b = a / 100
c = 99 + b 
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
Problem: a store reported total sales of $ 480 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 50 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 480 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 480 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 480 – 320 ) / 320 ] x 100 = 50 % . the answer is c ."
Answer: c
Python program:
a = 480 - 320
b = a / 320
c = b * 100
Problem: a cricket bat is sold for $ 850 , making a profit of $ 215 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 34 % , d ) 36 % , e ) 40 %
Rationale: "215 / ( 850 - 215 ) = 215 / 635 = 43 / 127 = 34 % . answer : c ."
Answer: c
Python program:
a = 850 - 215
b = 215 / a
c = b * 100
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 35 % profit ?
Options: a ) 16.39 , b ) 16.33 , c ) 16.35 , d ) 17.01 , e ) 16.32
Rationale: c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 135 % of rs . 630 = 135 / 100 * 630 = rs . 850.50 . s . p . per kg = 850.50 / 50 = rs . 16.38 = 16.30 . answer : d
Answer: d
Python program:
a = 30 * 11
b = 20 * 14
c = a + b 
d = 30 * 11
e = 20 * 14
f = d + e 
g = f / 100
h = g * 35
i = c + h 
j = 30 + 20 
k = i / j
Problem: how many times are the hands of a clock at right angle in 2 days ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "in 1 day , they are at right angles 44 times . in 2 days , they are at right angles 88 times . answer : option e"
Answer: e
Python program:
a = 12 * 2
b = a * 2
c = 12 * 4
d = c - 4
e = b * d
f = 12 * 2
g = e / f
Problem: a cyclist rides a bicycle 8 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.28 , b ) 8.48 , c ) 8.78 , d ) 8.98 , e ) 9.18
Rationale: "distance = 18 km time = 8 / 10 + 10 / 8 = ( 64 + 100 ) / 80 = 164 / 80 = 41 / 20 hours average speed = ( 18 * 20 ) / 41 = 8.78 km / h the answer is c ."
Answer: c
Python program:
a = 8 + 10 
b = 8 / 10
c = 10 / 8
d = b + c 
e = a / d
Problem: find the value of 72516 x 9999 = m ?
Options: a ) 456578972 , b ) 436567874 , c ) 725087484 , d ) 725117481 , e ) 357889964
Rationale: "72516 x 9999 = 72516 x ( 10000 - 1 ) = 72516 x 10000 - 72516 x 1 = 725160000 - 72516 = 725087484 c"
Answer: c
Python program:
a = 9999 - 4
b = a * 72516
Problem: what is the tens digit of 7 ^ 1001 ?
Options: a ) 0 , b ) 0 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1001 = 4 * 250 + 1 the ten ' s digit will be 1 . answer b"
Answer: b
Python program:
a = 4 + 1 
b = 7 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3872 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3872 × 1 / 11 = rs . 352 . c"
Answer: c
Python program:
a = 3 * 4
b = a - 3
c = 3 * 4
d = b / c
e = 12000 * d
f = 3 * 4
g = f - 4
h = 3 * 4
i = g / h
j = 9000 * i
k = e - j
l = 3 * 4
m = l - 3
n = 3 * 4
o = m / n
p = 12000 * o
q = 18000 + p 
r = 3 * 4
s = r - 4
t = 3 * 4
u = s / t
v = 9000 * u
w = q + v 
x = 3872 / w
y = k * x
Problem: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 5,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 10000 , b ) 10100.5 , c ) 20000 , d ) 15000 , e ) 19000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 5,000 ( 1 + 0.04 / 4 ) ^ 4 - 5,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 5,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 5,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 5,000 ( 1.0201 + 1 ) = 10 , 100.5 hence answer is b ."
Answer: b
Python program:
a = 4 * 100
b = a * 100
c = 4 / 100
d = c / 4
e = 1 + d 
f = e ** 4
g = b * f
h = 4 * 100
i = h * 100
j = g - i
k = 2 / 100
l = k / 2
m = 1 + l 
n = m ** 2
o = n - 1
p = j / o
Problem: what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 82 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 6 + 9 = 15 . the answer is e ."
Answer: e
Python program:
a = 98 - 82
b = 1 + 10 
c = 98 / b
d = a - c
Problem: in a certain alphabet , 20 letters contain a dot and a straight line . 36 letters contain a straight line but do not contain a dot . if that alphabet has 60 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 3 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 20 + 36 = 56 ; next , we find the total # of letters without line : 60 - 56 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 ."
Answer: a
Python program:
a = 20 + 36 
b = 60 - a
Problem: an auction house charges a commission of 25 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 165,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.25 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 165,000 ( 25 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : b ."
Answer: b
Python program:
a = 25 * 10
b = a + 10
Problem: a meal cost $ 35.50 adn there was no tax . if the tip was more than 15 pc but less than 25 pc of the price , then the total amount paid should be :
Options: a ) 41 - 44 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "15 % ( 35.5 ) = 5.325 25 % ( 35.5 ) = 8.875 total amount could have been 35.5 + 5.325 and 35.5 + 8.875 = > could have been between 40.825 and 44.375 = > approximately between 41 and 44 answer is a ."
Answer: a
Python program:
a = 35 * 50
b = a / 100
c = b + 35
Problem: the sum of the even numbers between 1 and n is 95 * 96 , where n is an odd number , then n = ?
Options: a ) 167 , b ) 175 , c ) 183 , d ) 191 , e ) 199
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 95 * 96 then a = 95 and n = 191 . the answer is d ."
Answer: d
Python program:
a = 95 * 2
b = a + 1
Problem: the present ratio of students to teachers at a certain school is 50 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 3 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: we are given that the ratio of students to teacher is 50 to 1 . we can rewrite this using variable multipliers . students : teachers = 50 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 30 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 50 x + 50 25 x + 125 = 50 x + 50 3 = x since x is the present number of teachers , currently there are 3 teachers . answer a .
Answer: a
Python program:
a = 50 + 25 
b = a / 25
Problem: julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if julie ' s savings by the end of the year from these monthly savings were 4 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?
Options: a ) 5 / 3 , b ) 3 / 9 , c ) 3 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: let julie ' s monthly savings = s julie ' s monthly pay = p julie ' s monthly expenditure = p - s julie ' s savings by the end of the year from these monthly savings were four times the amount she spent per month 12 s = 4 * ( p - s ) = > 3 s = p - s = > p = 4 s julie ' s monthly expenditure = p - s = 4 s - s = 3 s fraction of her salary that julie spent each month = 3 s / 4 s = p - s / p = 3 / 4 . answer is e
Answer: e
Python program:
a = 3 / 4
Problem: the function f ( n ) is defined as the product of all the consecutive positive integers between 2 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 3 answer : c"
Answer: c
Python program:
a = 2 ** 2
Problem: calculate the amount that an investor needs to be invest to earn $ 441 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 7 % compounded semi - annually ?
Options: a ) 6209 , b ) 6200 , c ) 6799 , d ) 6199 , e ) 6685
Rationale: the approach is substitution , our interest requirement is $ 441 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields $ 441 in 12 months 6200 yielded $ 441 using the formula a = p ( 1 + r / n ) nt hence answer is b
Answer: b
Python program:
a = 100 * 441
b = a / 7
Problem: how many positive integers less than 6,000 are there in which the sum of the digits equals 5 ?
Options: a ) 65 , b ) 62 , c ) 61 , d ) 56 , e ) 58
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . d"
Answer: d
Python program:
a = 4 + 5 
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the average ( arithmetic mean ) of 8 numbers is 8 . if 4 is added from each of 5 of the numbers , what is the new average ?
Options: a ) 4.5 , b ) 8.9 , c ) 10.5 , d ) 4.5 , e ) 5.6
Rationale: sum of 8 numbers = 8 * 8 = 64 if 4 is added from each of five of the numbers , we added 4 * 5 = 20 from the total sum sum of 8 number after adding 4 from each of five of the numbers = 64 + 20 = 84 new average = 84 / 8 = 10.5 answer c
Answer: c
Python program:
a = 8 * 8
b = 5 * 4
c = a + b 
d = c / 8
Problem: list k consists of 10 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: "answer = a = 5 if least = - 3 , then largest = 6 range = 6 - 1 = 5"
Answer: a
Python program:
a = 10 - 3
b = a - 1
c = b - 1
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "total number of apples = 280 let the cost price be x selling price at 20 % profit = 1.2 x selling price at 30 % profit = 1.3 x profit % = ( ( sp - cp ) / cp ) * 100 profit % = ( ( 2 / 5 ) * 280 * 1.2 x + ( 3 / 5 ) * 280 * 1.3 x - 280 x ) / 280 x * 100 = ( 1 / 5 * ( 2.4 + 3.9 ) - 1 ) * 100 = ( 6.3 - 5 ) * 20 = 26 % answer : c"
Answer: c
Python program:
a = 280 * 40
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = 280 * 60
g = f / 100
h = 100 + 30 
i = h / 100
j = g * i
k = e + j 
l = k - 280
m = l * 100
n = m / 280
Problem: we run a business that rents out canoes and kayaks . a canoe rental costs $ 14 per day , and a kayak rental costs $ 15 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 288 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let x be the number of canoes . then 2 x / 3 is the number of kayaks . 14 x + ( 2 x / 3 ) * 15 = 288 14 x + 10 x = 288 24 x = 288 x = 12 ( canoes ) 2 x / 3 = 8 ( kayaks ) there were 12 - 8 = 4 more canoes rented out . the answer is b .
Answer: b
Python program:
a = 3 - 2
b = 3 * 14
c = 2 * 15
d = b + c 
e = 288 / d
f = a * e
Problem: positive integers from 1 to 45 , inclusive are placed in 5 groups of 9 each . what is the highest possible average of the medians of these 5 groups ?
Options: a ) 25 , b ) 31 , c ) 15 , d ) 26 , e ) 23
Rationale: answer we need to maximize the median in each group in order to maximize the average of all the medians . the highest possible median is 41 as there should be 4 numbers higher than the median in a group of 9 . so , if we have a group that has a , b , c , d , 41 , 42 , 43 , 44 , 45 , the median will be 41 . in this set , it is essential not to expend any more high values on a , b , c , or d as these do not affect the median . the median of a group that comprises 1 , 2 , 3 , 4 , 41 , 42 , 43 , 44 , 45 will be 41 . the next group can be 5 , 6 , 7 , 8 , 36 , 37 , 38 , 39 , 40 . the median will be 36 . extrapolating the findings in the two sets listed above , to maximize medians in all the 5 groups , the medians of the 5 groups will have to be 21 , 26 , 31 , 36 and 41 . the average of the highest possible medians will be the average of these 5 numbers = 31 . answer b
Answer: b
Python program:
a = 45 - 5
b = a - 10
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 40 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 28 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 40 / 100 ) * 300 = 100 + 120 = 220 % comission = ( 220 / 800 ) * 100 = 27.5 ~ 28 % answer is e"
Answer: e
Python program:
a = 20 / 100
b = a * 500
c = 40 / 100
d = 800 - 500
e = c * d
f = b + e 
g = f / 800
h = g * 100
Problem: a salt manufacturing company produced a total of 5000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 180 , b ) 185 , c ) 190 , d ) 195 , e ) 200
Rationale: "total production of salt by the company in that year = 5000 + 5100 + 5200 + . . . . + 6100 = 66600 . average monthly production of salt for that year = 66600 / 365 = 185 answer : b"
Answer: b
Python program:
a = 5000 * 2
b = 12 - 1
c = b * 100
d = a + c 
e = d * 12
f = e / 2
g = 3 * 100
h = 2 * 3
i = h * 10
j = g + i 
k = 2 + 3 
l = j + k 
m = f / l
Problem: the average weight of 9 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 88.5 , e ) 89.5
Rationale: "total increase in weight = 9 × 2.5 = 22.5 if x is the weight of the new person , total increase in weight = x − 65 = > 22.5 = x - 65 = > x = 22.5 + 65 = 87.5 answer : c"
Answer: c
Python program:
a = 9 * 2
b = a + 65
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 5 miles per hour for 3 hours . how many miles in total did she walk ?
Options: a ) 53 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 3 hours - 15 miles total 18 + 20 + 15 = 53 answer : option a ."
Answer: a
Python program:
a = 5 * 4
b = 18 + a 
c = 5 * 3
d = b + c
Problem: a can do a job in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 8 / 15 , c ) 3 / 11 , d ) 5 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 5 days work = 7 / 60 * 5 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is d"
Answer: d
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = 5 * c
e = 1 - d
Problem: how many zeros are the end of 380 ! ?
Options: a ) 90 , b ) 91 , c ) 94 , d ) none , e ) 95
Rationale: 380 ! has 380 / 5 + 380 / 5 ^ 2 + 380 / 5 ^ 3 = 76 + 15 + 3 = 94 trailing zeros ( take only the quotient into account ) . answer : c .
Answer: c
Python program:
a = 4 + 1 
b = 380 / a
c = 4 + 1 
d = 380 - c
e = 4 + 1 
f = e ** 2
g = d / f
h = b + g 
i = 4 + 1 
j = 380 - i
k = 4 + 1 
l = k ** 3
m = j / l
n = h + m
Problem: find the least number which when divided by 38 and 3 leaves a remainder of 1 in each case .
Options: a ) 107 , b ) 109 , c ) 111 , d ) 113 , e ) 115
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 38 , 3 ) + 1 = 115 . answer : e"
Answer: e
Python program:
a = math.lcm(38, 3)
b = 1 + a