euclaise/mathqa_programs huggingface dataset:
Problem: if integer k is equal to the sum of all even multiples of 25 between 200 and 600 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 50 between 200 and 600 . using arithmetic progression to find n : 600 = 200 + ( n - 1 ) 50 400 + 50 = 50 n 450 = 50 n = > n = 9 the sum would be : 9 * mean mean = [ 600 + 200 ] / 2 = 400 9 * 400 = 3600 d"
Answer: d
Python program:
a = 600 / 25
b = math.floor(a)
c = b * 25
d = 200 / 25
e = math.floor(d)
f = e * 25
g = c - f
h = g / 25
i = h + 1 
j = i / 2
Problem: how many integers between 324,700 and 448,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 8,030 , c ) 1,253 , d ) 1,252 , e ) 1,239
Rationale: "the integers are : 324,713 324,813 etc . . . 448,513 the number of integers is 4486 - 3247 = 1239 the answer is e ."
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 448 - 600
Problem: g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( r ) is divisible by 4 ^ 11 , what is the smallest possible value for r ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: "g ( r ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
Answer: b
Python program:
a = 2 * 12
Problem: if 1 / 12 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 3 are from africa , 1 / 6 are from asia and the remaining 35 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 110 , b ) 115 , c ) 120 , d ) 125 , e ) 130
Rationale: 1 / 12 + 1 / 8 + 1 / 3 + 1 / 6 = ( 2 + 3 + 8 + 4 ) / 24 = 17 / 24 let x be the number of passengers on the ship . 35 = ( 7 / 24 ) x x = 120 the answer is c .
Answer: c
Python program:
a = 1 / 12
b = 1 / 8
c = a + b 
d = 1 / 3
e = c + d 
f = 1 / 6
g = e + f 
h = 1 - g
i = 35 / h
Problem: 54671 - 14456 - 33466 = ?
Options: a ) 2449 , b ) 5449 , c ) 6749 , d ) 6449 , e ) 6468
Rationale: "c if we calculate we will get 6749"
Answer: c
Python program:
a = 54671 / 100
b = a * 14456
c = 1 / 3
d = 54671 / 100
e = d * 14456
f = c * e
g = b - f
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 13 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 3 more or 3 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 2,240 , d ) $ 1,920 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 13 : x + x - 3 = 13 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : c ."
Answer: c
Python program:
a = 3 * 1000
b = 13 + 3 
c = b / 3
d = c * 20
e = 13 + 2 
f = e / 3
g = f - 3
h = g * 100
i = d + h 
j = a - i
Problem: the ages of two person differ by 20 years . if 7 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 32 , 12 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 7 ) = ( x + 20 - 7 ) = > 4 x = 48 = > x = 12 their present ages are 32 years and 12 year . answer : b"
Answer: b
Python program:
a = 5 * 7
b = 20 - 7
c = a + b 
d = 5 - 1
e = c / d
f = e + 20
Problem: how many integers between 1 and 10 ^ 18 are such that the sum of their digits is 2 ?
Options: a ) 161 , b ) 171 , c ) 181 , d ) 191 , e ) 201
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 17 and there are 18 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 17 thus , the total number of integers is 1 + 2 + . . . + 17 + 18 = 18 * 19 / 2 = 171 the answer is b ."
Answer: b
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 10 - e
Problem: how many positive integers less than 27 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 20 , e ) 22
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 11 - 1 = 22 . answer : e ."
Answer: e
Python program:
a = 27 - 2
b = a - 1
c = b - 1
Problem: in a corporation , 50 percent of the male employees and 40 percent of the female employees are at least 35 years old . if 42 percent of all the employees are at least 35 years old , what fraction of the employees in the corporation are females ?
Options: a ) 3 / 5 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: you can use the weighted averages formula for a 10 sec solution . no of females / no of males = ( 50 - 42 ) / ( 42 - 40 ) = 4 / 1 no of females as a fraction of total employees = 4 / ( 4 + 1 ) = 4 / 5 ; answer : d
Answer: d
Python program:
a = 50 - 42
b = 50 - 40
c = a / b
Problem: if 4 men working 10 hours a day earn rs . 1400 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 1890 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1400 : x hence 4 * 10 * x = 9 * 6 * 1400 or x = 9 * 6 * 1400 / 4 * 10 = 1890 answer : d"
Answer: d
Python program:
a = 9 * 6
b = 4 * 10
c = a / b
d = c * 1400
Problem: if a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 120 and a perimeter of 46 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 120 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 120 , let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 120 . . . . 120 / 8 = 15 = the longer side perimeter = 8 + 8 + 15 + 15 = 46 c"
Answer: c
Python program:
a = 46 / 2
b = 46 / 2
c = b ** 2
d = 4 * 120
e = c - d
f = math.sqrt(e)
g = a - f
h = g / 2
Problem: a car gets 33 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 16 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 168 , b ) 172 , c ) 176 , d ) 180 , e ) 184
Rationale: "originally , the distance the car could go on a full tank was 16 * 33 = 528 miles . after it has been modified , the car can go 33 / 0.75 = 44 miles per gallon . on a full tank , the car can go 16 * 44 = 704 miles , thus 176 miles more . the answer is c ."
Answer: c
Python program:
a = 33 / 75
b = a * 100
c = b * 16
d = 33 * 16
e = c - d
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 2 / 7 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 2 / 7 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 2 / 7 = 5 / 7 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 5 / 7 = 1 / 3 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 5 / 7 * 2 / 3 = 1 / 2 ans c"
Answer: c
Python program:
a = 2 / 7
b = 1 - a
c = 2 / 7
d = 1 - c
e = d / 2
f = 1 - e
g = b * f
Problem: shekar scored 76 , 65 , 82 , 67 and 55 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 55 ) / 5 = 375 / 5 = 69 hence average = 69 answer : b"
Answer: b
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 55 
e = 1 + 4 
f = d / e
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 2500 resolutions ?
Options: a ) 1187 m , b ) 1704 m , c ) 2179 m , d ) 3520 m , e ) 4297 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 2500 resolutions . = 2500 * 2 * 22 / 7 * 22.4 = 352000 cm = 3520 m answer : d"
Answer: d
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 2500
i = h / 100
Problem: the average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?
Options: a ) 20 , b ) 27 , c ) 72 , d ) 28 , e ) 82
Rationale: "sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b"
Answer: b
Python program:
a = 23 * 4
Problem: if a person has two rectangular fields . the larger field has thrice the length and 4 times the width of the smaller field . if the smaller field has a length 50 % more than the width . if a person takes 20 minutes to complete one round of a smaller field then what is the time required to complete one round of a larger field ?
Options: a ) 69 minutes , b ) 68 minutes , c ) 58 minutes , d ) 48 minutes , e ) 67 minutes
Rationale: let the width of the smaller rectangle is 4 units then , the length of the smaller rectangle is 6 units ( that is 50 % more than the width ) now the perimeter of the rectangle is 2 ( 6 + 4 ) = 20 units so , 20 units is covered in 20 units , implies covers one unit in one minute so now coming to the larger rectangle the width = 16 units , length = 18 units , perimeter = 2 ( 16 + 18 ) 68 units thus , to cover the larger field , 68 minutes required to cover the rectangle . answer : b
Answer: b
Python program:
a = 50 / 100
b = 4 * a
c = 20 * b
d = c + 20 
e = d + 4 
f = e + 4
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 7 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 7 miles / gallon . additional 5 miles / gallon is required to match the actual mileage . imo option c ."
Answer: c
Python program:
a = 480 / 40
b = a - 7
Problem: some of 40 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 20 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 1
Rationale: "let total paint = 1 let amount replaced = x 40 ( 1 - x ) + 20 x = 20 x = 1 / 1 answer : e"
Answer: e
Python program:
a = 20 / 100
b = 40 / 100
c = a - b
d = 20 / 100
e = 40 / 100
f = d - e
g = c / f
Problem: there are two concentric circles with radii 10 and 6 . if the radius of the outer circle is increased by 20 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ?
Options: a ) 11 , b ) 111 , c ) 211 , d ) 311 , e ) 411
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 100 pi . the area of the small circle is 36 pi . the area a 1 between the circles is 64 pi . when the big circle ' s radius increases , the new area is 144 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 135 pi . the ratio of a 2 / a 1 is 135 / 64 = 2.11 which is an increase of 111 % . the answer is b ."
Answer: b
Python program:
a = 100 + 20 
b = a / 100
c = 10 * b
d = c ** 2
e = 100 - 50
f = e / 100
g = 6 * f
h = g ** 2
i = d - h
j = 10 ** 2
k = 6 ** 2
l = j - k
m = i - l
n = 10 ** 2
o = 6 ** 2
p = n - o
q = m / p
r = q * 100
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 3.2 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 20 , c ) 50 , d ) 8.6 , e ) 40
Rationale: "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 3.2 km / hr hence , speed of the man = 15 - 3.2 = 11.8 km / hr man ' s speed against the current = speed of the man - speed of the current = 11.8 - 3.2 = 8.6 km / hr answer is d ."
Answer: d
Python program:
a = 15 - 3
b = a - 3
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 46,875 , how much profit did the business make ?
Options: a ) $ 55,000 , b ) $ 75,000 , c ) $ 95,000 , d ) $ 115,000 , e ) $ 125,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 46875 p = $ 75,000 the answer is b ."
Answer: b
Python program:
a = 1 + 4 
b = 100 * a
c = 100 * b
d = 25 / 100
e = 25 / 100
f = 25 / 100
g = 1 - f
h = e * g
i = h * 2
j = d + i 
k = c / j
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 24 days . how long will y take to complete the work ?
Options: a ) 30 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 24 days whole work will be done by y in 24 * 5 / 4 = 30 days answer is a"
Answer: a
Python program:
a = 8 / 40
b = 1 - a
c = 1/(b)
d = 24 * c
Problem: linda bought 3 notebooks at $ 1.20 each ; a box of pencils at $ 1.50 and a box of pens at $ 1.70 . how much did linda spend ?
Options: a ) $ 6.80 , b ) $ 8.40 , c ) $ 7.70 , d ) $ 4.70 , e ) $ 3.90
Rationale: linda spent 1.20 ? 3 = $ 3.60 on notebooks the total amount of money that linda spent is equal to 3.60 + 1.50 + 1.70 = $ 6.80 correct answer a
Answer: a
Python program:
a = 3 * 1
b = a + 1 
c = b + 1
Problem: a park square in shape has a 3 metre wide road inside it running along its sides . the area occupied by the road is 1764 square metres . what is the perimeter along the outer edge of the road ?
Options: a ) 576 metres
b ) 589 metres
c ) 600 metres
d ) 700 metres
e ) none
Rationale: solution let the length of the outer edges be x metres . then , length of the inner edge = ( x - 6 ) m . ∴ x 2 - ( x - 6 ) 2 = 1764 ‹ = › x 2 - ( x 2 - 12 x + 36 ) = 1764 ‹ = › 12 x = 1800 ‹ = › x = 150 . ∴ required perimeter = ( 4 x ) m ‹ = › ( 4 x 150 ) m = 600 m . answer c
Answer: c
Python program:
a = 3 * 2
b = a ** 2
c = 1764 + b 
d = 3 * 2
e = 2 * d
f = c / e
g = f * 4
Problem: two numbers are respectively 20 % and 50 % more than a third number . the percentage that is first of the second is ?
Options: a ) 45 % , b ) 80 % , c ) 78 % , d ) 94 % , e ) 68 %
Rationale: "i ii iii 120 150 100 150 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 80 % answer : b"
Answer: b
Python program:
a = 20 + 100 
b = 50 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22932 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 30 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22932 / - - 17640 / - = rs . 5292 / - rate of interest = ( 5292 / 22932 ) × ( 100 / 1 ) = > 30 % answer : option e"
Answer: e
Python program:
a = 22932 - 17640
b = a / 17640
c = b * 100
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 60 ?
Options: a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 60 4 n < 53 n < 13 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 13 ) combining the two - 1.5 < n < 13.25 n = 1 to 13 ( 48 integers ) and n = - 1 and 0 so 15 integers . b"
Answer: b
Python program:
a = 60 - 7
b = a / 4
c = math.floor(b)
d = 1 - 7
e = d / 4
f = math.floor(e)
g = c - f
Problem: the average of first 25 natural numbers is ?
Options: a ) 14 , b ) 13 , c ) 15 , d ) 18 , e ) 12
Rationale: "sum of 25 natural no . = 650 / 2 = 325 average = 325 / 25 = 13 answer : b"
Answer: b
Python program:
a = 25 + 1
Problem: r = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set r and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs r , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Python program:
a = 4 / 4
b = 1 / 5
c = a * b
Problem: a $ 79.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: "listed selling price of chair = 79.95 $ discounted selling price of chair = 59.95 $ discount = 79.95 - 59.95 = 20 $ % decrease in price of chair = ( 20 / 79.95 ) * 100 % = 25 % approx answer c"
Answer: c
Python program:
a = 79 - 95
b = a / 79
c = b * 100
Problem: 5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 16 days . how many additional pipes , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: this is an inverse proportional problem . . . . . . 5 pipes in 16 days ; so for 4 days , it will be = 16 x 5 / 4 = 20 so , 20 - 5 = 15 answer e
Answer: e
Python program:
a = 4 * 5
b = a - 5
Problem: a heap of grapes is divided into groups of 3 , 5 and 7 and each time one coconut is left over . the least number of grapes in the heap is ? a . 31 b . 41 c . 51 d . 61
Options: a ) a ) 31 , b ) b ) 41 , c ) c ) 106 , d ) d ) 61 , e ) e ) 71
Rationale: lcm = 105 = > 105 + 1 = 106 answer : c
Answer: c
Python program:
a = math.lcm(3, 5)
b = math.lcm(a, 7)
Problem: three 6 faced dice are thrown together . the probability that no two dice show the same number on them is
Options: a ) 5 / 0 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 6
Rationale: "explanation : no two dice show same number would mean all the three faces should show different numbers . the first can fall in any one of the six ways . the second die can show a different number in five ways . the third should show a number that is different from the first and second . this can happen in four ways . thus 6 * 5 * 4 = 120 favourable cases . the total cases are 6 * 6 * 6 = 216 . the probability = 120 / 216 = 5 / 9 . answer : b"
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively .
Options: a ) 121 , b ) 124 , c ) 127 , d ) 122 , e ) 129
Rationale: "required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 _______ 1651 ) 2032 ( 1 1651 1651 _______ 381 ) 1651 ( 4 1524 _________ 127 ) 381 ( 3 381 0 required number = 127 . answer is c ."
Answer: c
Python program:
a = 1657 - 6
b = 2037 - 5
c = math.gcd(a, b)
Problem: ram - leela has $ 100 in her piggy bank . how much will she have in her bank 52 weeks from now if she puts $ 1 in the bank next week , $ 2 two weeks from now , $ 3 3 weeks from now , and continues to increase the amount that she puts in by $ 1 each week ?
Options: a ) 1478 , b ) 1578 , c ) 1678 , d ) 1778 , e ) 1798
Rationale: the dollar deposits are in an a . p . 1,2 , 3,4 . . . 52 with common difference 1 sum of the terms is n ( n + 1 ) / 2 i . e 52 * ( 52 + 1 ) / 2 = 52 * 53 / 2 = 1378 total deposit therefore with chiu - lihas is 100 + 1378 = 1478 $
Answer: a
Python program:
a = 100 / 2
b = a + 3 
c = b * 52
d = c / 2
e = d + 100
Problem: a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 350 pounds of the mixture ?
Options: a ) 250 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: almonds : walnuts = 5 : 2 total mixture has 7 parts in a 350 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 350 = 250 pounds answer ( a )
Answer: a
Python program:
a = 5 * 350
b = 5 + 2 
c = a / b
Problem: if x = - 5 / 4 and y = - 3 / 2 , what is the value of the expression - 2 x – y ^ 2 ?
Options: a ) 1 / 4 , b ) - 1 , c ) 5 / 4 , d ) 3 / 2 , e ) 3 / 4
Rationale: x = - 5 / 4 and y = - 3 / 2 = = > - 2 ( - 5 / 4 ) - ( 3 / 2 ) ^ 2 = 10 / 4 - 9 / 4 = 1 / 4 ans : a
Answer: a
Python program:
a = 5 / 4
b = 2 * a
c = 3 / 2
d = c ** 2
e = b - d
Problem: which expression is the greatest
Options: a ) 3252 / 3257 , b ) 3456 / 3461 , c ) 3591 / 3596 , d ) 3641 / 3656 , e ) 3453 / 3458
Rationale: "options can be re - written as ( x - 5 ) x = > 1 - ( 5 / x ) a ) 1 - ( 5 / 3257 ) b ) 1 - ( 5 / 3461 ) c ) 1 - ( 5 / 3596 ) d ) 1 - ( 5 / 3656 ) e ) 1 - ( 5 / 3458 ) to get the largest among these second half should be the least and so denominator to be largest . hence ' d ' ."
Answer: d
Python program:
a = 3 * 3
b = 3600 - a
c = 3600 - 4
d = b / c
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 78 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 86 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 78 * 3 = 234 jerry wants the average to be = 80 hence total score on 4 tests should be = 80 * 4 = 320 score required on the fourth test = 320 - 234 = 86 option c"
Answer: c
Python program:
a = 78 + 2 
b = 4 * a
c = 78 * 3
d = b - c