euclaise/mathqa_programs huggingface dataset:
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 63 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 63 books , thus 76 - 63 = 12 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 40 . answer : d ."
Answer: d
Python program:
a = 75 - 63
b = 70 / 100
c = 1 - b
d = a / c
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes have no faces coloured ?
Options: a ) 24 , b ) 8 , c ) 16 , d ) 0 , e ) 4
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having only one faces coloured = ( x - 2 ) ^ 3 here , x = side of big cube / side of small cube x = 4 / 1 x = 4 required number = ( 4 - 2 ) ^ 3 = 8 answer : b"
Answer: b
Python program:
a = 64 / 4
b = a / 2
Problem: [ ( 3.242 x 16 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 0.051872 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.242 x 16 = 5.1872 now divide 5.1872 by 100 so , 5.1872 ÷ 100 = 0.051872 ∴ shift the decimal two places to the left as 100 correct option : c"
Answer: c
Python program:
a = 3 * 242
b = a / 100
c = b / 10
Problem: sabrina is contemplating a job switch . she is thinking of leaving her job paying $ 90000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission for each sale made . if each of her sales is for $ 1500 , what is the least number of sales she must make per year if she is not to lose money because of the job change ?
Options: a ) 57 , b ) 177 , c ) 178 , d ) 377 , e ) 200
Rationale: lets say she sales x items so her commission will be : x * 1500 * 15 / 100 = 225 x salary difference is : 90000 - 45000 = 45000 so commission must at least be equal to salary difference i . e . x = 45000 / 225 = 200 ( approx ) . hence answer is e
Answer: e
Python program:
a = 90000 - 45000
b = 1500 * 15
c = b / 100
d = a / c
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 6 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 ) $ 196
Rationale: "by the question , the equation would be 150 p - 86 * 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 = $ 196 . answer e for me ."
Answer: e
Python program:
a = 4 * 4
b = a * 1000
c = 6 * 100
d = b + c 
e = 80 + 6 
f = e * 150
g = d + f 
h = g / 150
Problem: an outlet pipe can empty 2 / 3 of a cistern in 16 minutes . in 8 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 3 / 10
Rationale: 8 / 16 * 2 / 3 = 1 / 3 the answer is b .
Answer: b
Python program:
a = 2 / 3
b = 8 * a
c = b / 16
Problem: if a ã — b = 2 a - 3 b + ab , then 3 ã — 4 + 4 ã — 3 is equal to :
Options: a ) 17 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "explanation : 3 ã — 4 + 4 ã — 3 = ( 2 ã — 3 - 3 ã — 4 + 3 ã — 4 ) + ( 2 ã — 4 - 3 ã — 3 + 4 ã — 3 ) = ( 6 + 8 - 9 + 12 ) = 17 . answer : a"
Answer: a
Python program:
a = 2 * 3
b = 3 * 2
c = a - b
d = 3 * 2
e = c + d 
f = 2 * 2
g = 3 * 3
h = f - g
i = 2 * 3
j = h + i 
k = e + j
Problem: the simple interest on a sum of money will be rs . 1000 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 2000
Rationale: "p - - - 10 - - - - 1000 p - - - 5 - - - - - 500 3 p - - - 5 - - - - - 1500 - - - - - - = > 2000 answer : e"
Answer: e
Python program:
a = 1000 / 10
b = a * 5
c = b * 3
d = 1000 / 10
e = d * 5
f = c + e
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 8 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 54 , d ) 22 : 56 , e ) 52 : 51
Rationale: let c . p . of the article be rs . x . then , required ratio = 104 % of x / 108 % of x = 104 / 108 = 52 / 54 = 52 : 54 answer : c
Answer: c
Python program:
a = 100 + 4 
b = 100 + 8 
c = a / b
Problem: if shares of two persons in profits are rs . 700 and rs . 300 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 7 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 700 / 300 = 7 : 3 answer : c"
Answer: c
Python program:
a = 700 / 300
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 160 square feet and its length is 6 feet longer than its width . if the uniform width between the rug and room is 6 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 456 , c ) 40 , d ) 46 , e ) 104
Rationale: "rug ' s area = 160 which is ( x ) x ( 6 + x ) = 160 so x = 10 rug maintains a uniform distance of 6 feet so room has dimension 10 + 12 and 16 + 12 i . e . 22 and 28 area of room 22 x 28 = 616 area covered is 160 so uncovered area is 616 - 160 = 456 ( answer b )"
Answer: b
Python program:
a = 160 / 10
b = a - 2
c = b + 10 
d = 160 / 10
e = 160 / 10
f = e - 2
g = d + f 
h = c * g
i = h - 160
Problem: an advertising agency finds that , of its 180 clients , 115 use television , 110 use radio and 130 use magazines . also , 85 use television and magazines , 75 use television and radio , 95 use radio and magazines . how many use all the 3 ?
Options: a ) 56 , b ) 70 , c ) 90 , d ) 98 , e ) 80
Rationale: total = 180 television = 115 radio = 110 magazine = 130 all the three = 180 - 115 - 110 - 130 + 85 + 75 + 95 = 80 answer e
Answer: e
Python program:
a = 115 + 110 
b = a + 130 
c = 85 + 75 
d = c + 95 
e = b - d
f = 180 - e
Problem: 8 friends met for lunch at an expensive restaurant , and everyone decided to contribute equally to the total bill of $ 290 . if one of the friends had a coupon for 29 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) $ 90 , b ) $ 70 , c ) $ 45 , d ) $ 37 , e ) $ 25
Rationale: 290 * 0,29 = 84 290 - 84 = 206 206 / 8 = 25 answer e
Answer: e
Python program:
a = 29 / 100
b = a * 290
c = 290 - b
d = c / 8
Problem: for a right angle triangle the hypotenuse is 5 and base is 3 . what is the area of the triangle ?
Options: a ) 6
b ) 7
c ) 8
d ) 9
e ) 10
Rationale: as we know that for a right angle triangle the are is 1 / 2 * base * height we know the base = 3 we need to calculate the height hypotenuse = h = 5 base = b = 3 height = c = ? as per pythagoras h ^ 2 = b ^ 2 + c ^ 2 5 ^ 2 = 3 ^ 2 + c ^ 2 25 = 9 + c ^ 2 c ^ 2 = 25 - 9 c ^ 2 = 16 c = 4 height = 4 area = 1 / 2 * base * height = 1 / 2 * 3 * 4 = 6 square units ans : a
Answer: a
Python program:
a = 1 / 2
b = a * 3
c = 5 ** 2
d = 3 ** 2
e = c - d
f = math.sqrt(e)
g = b * f
Problem: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 210 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 560
Rationale: "easy 560 is the answer . 3 / 4 ( x / 2 ) = 210 x = 210 * 8 / 3 = 560 . answer e"
Answer: e
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 4
d = b * c
e = a + d 
f = 1 - e
g = 210 / f
Problem: a train 1000 m long can cross an electric pole in 200 sec and then find the speed of the train ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "length = speed * time speed = l / t s = 1000 / 200 s = 5 m / sec speed = 5 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 18 kmph answer : d"
Answer: d
Python program:
a = 1000 / 1000
b = 200 / 3600
c = a / b
Problem: joshua and jose work at an auto repair center with 6 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 28 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 8 probability of chosing jose second = 1 / 7 total = 1 / 56 probability of chosing jose first = 1 / 8 probability of chosing josh second = 1 / 7 total = 1 / 56 final = 1 / 56 + 1 / 56 = 1 / 28 c"
Answer: c
Python program:
a = math.factorial(6)
b = math.factorial(2)
c = math.factorial(6)
d = b * c
e = a / d
f = math.factorial(6)
g = e / f
Problem: what is the units digit of 63 ^ 3 * 17 ^ 3 * 49 ^ 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 63 ^ 3 is the units digit of 3 * 3 * 3 = 27 which is 7 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 49 ^ 3 is the units digit of 9 * 9 * 9 = 729 which is 9 . the units digit of 7 * 3 * 9 = 189 is 9 . the answer is e ."
Answer: e
Python program:
a = math.factorial(63)
b = math.factorial(4)
c = a * b
d = math.factorial(63)
e = math.factorial(3)
f = d * e
g = c + f 
h = g / 63
Problem: what is the probability of randomly selecting an arrangement of the letters of the word ` ` mediterranean ' ' in which the first letter is e and the last letter is r ?
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Rationale: there are 13 letters in mediterranean , out of which e appears thrice , n appears twice , a appears twice , and r appears twice . the number of arrangements of mediterranean is therefore 13 ! / 3 ! 2 ! 2 ! 2 ! the number of arrangements in which the first letter is e and the last letter is r is 11 ! / 2 ! 2 ! 2 ! ( we are left with 11 letters out of which e appears twice , n appears twice and a appears twice ) . p = ( 11 ! / 2 ! 2 ! 2 ! ) / ( 13 ! / 3 ! 2 ! 2 ! 2 ! ) = 11 / ! 2 ! 2 ! 2 ! ∗ 3 ! 2 ! 2 ! 2 ! / 13 ! = 3 ! / 12 ∗ 13 = 1 / 26 answer : c .
Answer: c
Python program:
a = 3 * 2
b = const_26 / 2
c = 3 * 2
d = c * 2
e = b * d
f = a / e
Problem: 10 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 75
Rationale: "there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 3 other chairmen for total of 30 handshake . total = 45 + 30 = 75 ans : e"
Answer: e
Python program:
a = 10 - 1
b = 10 * a
c = b / 2
d = 10 * 3
e = c + d
Problem: a goods train runs at a speed of 72 kmph and crosses a 280 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: "s = 280 + x / t 72 * 5 / 18 = 280 + x / 26 x = 240 answer : b"
Answer: b
Python program:
a = 72 * const_0_2778
b = a * 26
c = b - 280
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 100 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 18 , b ) 16 , c ) 17 , d ) 15 , e ) 19
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 100 5 x - 10 = 100 5 x = 90 x = 18 answer : a"
Answer: a
Python program:
a = 100 - 1
b = a - 2
c = b - 3
d = c - 4
e = d / 5
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 3 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 19.5
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 3 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 3 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 3 x = 4.5 since you need a 15 l solution , you must evaporate 19.5 of the original 50 l solution to get a 3 % solution . answer is e ."
Answer: e
Python program:
a = 50 / 100
b = a * 3
c = 50 - b
Problem: average age of 7 members of a family is 29 years . if present age of the youngest member is 5 year , find average age of the remaining members at the time of birth of the youngest member .
Options: a ) 28 , b ) 37 , c ) 29 , d ) 237 , e ) 212
Rationale: average age ( present ) of 7 members = 29 years 5 years ago , average age of 7 members was 29 - 5 = 24 years . since , the youngest member was not born 5 years ago . therefore , average age of remaining 6 members is increased by 246246 = 4 years . therefore , 5 years ago , average age of 6 members was 24 + 4 = 28 years . answer : a
Answer: a
Python program:
a = 7 * 29
b = 7 * 5
c = a - b
d = 7 - 1
e = c / d
Problem: there is a 50 % chance jen will visit chile this year , while there is a 25 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? [ / b ]
Options: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 63.5 % , e ) 75 %
Rationale: "the thing to note in the question is she would not be visiting both . thus p ( chile ) * ( 1 - p ( madagascar ) ) + p ( madagascar ) * ( 1 - p ( chile ) ) which is ( 1 / 2 * 3 / 4 ) + ( 1 / 4 * 1 / 2 ) , 3 / 8 * 1 / 8 = 1 / 2 = 50 % answer : b"
Answer: b
Python program:
a = 2 * 5
b = a ** 2
c = b - 50
d = 2 * 5
e = d ** 2
f = c / e
g = 2 * 5
h = g ** 2
i = 25 / h
j = f * i
k = 2 * 5
l = k ** 2
m = 50 / l
n = 2 * 5
o = n ** 2
p = 25 / o
q = m * p
r = j + q 
s = 2 * 5
t = s ** 2
u = r * t
Problem: thabo owns exactly 200 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 35 , d ) 45 , e ) 50
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 200 3 x + 60 + x = 200 x = 35 answer ( c . )"
Answer: c
Python program:
a = 200 + 20 
b = a / 4
c = b - 20
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 4 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 14 - > t = 20 . c = 6 . mo drinks 4 cups of tea a day then number of days that are not rainy = 20 / 4 = 5 so number of rainy days = 7 - 5 = 2 a is the answer ."
Answer: a
Python program:
a = 4 + 3 
b = 26 + 14 
c = b / 2
d = c / 4
e = a - d
Problem: the market value of a certain machine decreased by 25 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 4,000 , e ) $ 800
Rationale: "d . market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 25 / 100 ) = 8000 - 2000 = $ 6000 market value in 1984 = market value in 1983 - ( 25 % of $ 8000 ) = 6000 - 2000 = $ 4000"
Answer: d
Python program:
a = 100 * 10
b = 2 * 4
c = a * b
d = 100 * 25
e = 2 * 4
f = d * e
g = 25 / 100
h = g * 2
i = f * h
j = c - i
Problem: if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 12 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 12 is 1 . answer : b"
Answer: b
Python program:
a = 3 + 2 
b = a ** 2
c = 12 * 4
d = b - c
Problem: in the manufacture of a certain product , 10 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.25 % , b ) 0.5 % , c ) 0.75 % , d ) 1.25 % , e ) 2.5 %
Rationale: "0.1 * 0.05 = 0.005 = 0.5 % the answer is b ."
Answer: b
Python program:
a = 5 / 100
b = 10 * a
Problem: convert 300 inches into centimeter ?
Options: a ) 762 cm , b ) 750 cm , c ) 650 cm , d ) 710 cm , e ) 754 cm
Rationale: "1 inch = 2.54 cm 300 inches = 300 * 2.54 = 762 cm answer is e"
Answer: e
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 300
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: a boat goes 130 km downstream in 10 hours , and 75 km upstream in 15 hours . the speed of the stream is ?
Options: a ) 3.5 , b ) 3 , c ) 5 , d ) 4 , e ) 8
Rationale: "125 - - - 10 ds = 130 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 13 - 5 ) / 2 = 4 kmph . answer : d"
Answer: d
Python program:
a = 130 / 10
b = 75 / 15
c = a - b
d = c / 2
Problem: pat , kate , and mark charged a total of 135 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 36 , c ) 75 , d ) 90 , e ) 108
Rationale: 75 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 135 = > x = 15 30 : 15 : 90 90 - 15 = 75 answer c
Answer: c
Python program:
a = 1 / 3
b = 1 + a 
c = 3 * 2
d = 1 / c
e = b + d 
f = 135 / e
g = 1 / 3
h = 1 + g 
i = 3 * 2
j = 1 / i
k = h + j 
l = 135 / k
m = 3 * 2
n = l / m
o = f - n
Problem: sum of the squares of 3 no . is 52 and the sum of their products taken two at a time is 72 . find the sum ?
Options: a ) 18 , b ) 21 , c ) 13 , d ) 16 , e ) 14
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 52 + 2 * 72 a + b + c = â ˆ š 196 = 14 answer e"
Answer: e
Python program:
a = 72 * 2
b = 52 + a 
c = math.sqrt(b)
Problem: a bag contains 3 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 3 + 2 + 4 = 9 n ( s ) = 9 c 3 = 84 n ( e ) = 3 c 1 * 2 c 1 * 4 c 1 = 3 * 2 * 4 = 24 probability = 24 / 84 = 2 / 7 answer is a"
Answer: a
Python program:
a = math.comb(4, 2)
b = 3 + 2 
c = math.comb(b, 1)
d = a * c
e = 3 + 2 
f = e + 4 
g = math.comb(f, 3)
h = d / g
Problem: how many seconds will a 650 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 48 km / hr ?
Options: a ) 25 , b ) 45 , c ) 54 , d ) 44 , e ) 48
Rationale: "speed of train relative to man = 48 - 3 = 45 km / hr . = 45 * 5 / 18 = 25 / 2 m / sec . time taken to pass the man = 650 * 2 / 25 = 54 sec . answer : c"
Answer: c
Python program:
a = 48 - 3
b = a * const_0_2778
c = 650 / b
Problem: when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 7 , the remainder is 6 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 6 . . d"
Answer: d
Python program:
a = 100 - reminder
Problem: what is the unit digit in [ ( 6273 ) ^ 1793 x ( 625 ) ^ 317 x ( 341 ) ^ 491 ] ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 5 , e ) none of them
Rationale: unit digit in ( 6374 ) ^ 1793 = unit digit in ( 4 ) ^ 1793 = unit digit in [ ( 4 ^ 2 ) ^ 896 x 4 ] = unit digit in ( 6 x 4 ) = 4 unit digit in ( 625 ) ^ 317 = unit digit in ( 5 ) ^ 317 = 5 unit digit in ( 341 ) ^ 491 = unit digit in ( 1 ) ^ 491 = 1 required digit = unit digit in ( 4 x 5 x 1 ) = 0 answer is 0
Answer: a
Python program:
a = 317 * 341
b = 3 - 3
c = a ** b
Problem: what is the rate percent when the simple interest on rs . 780 amount to rs . 130 in 4 years ?
Options: a ) 4.16 , b ) 5.16 , c ) 6.16 , d ) 7.16 , e ) 8.16
Rationale: "130 = ( 780 * 4 * r ) / 100 r = 4.16 % answer : a"
Answer: a
Python program:
a = 100 * 130
b = 780 * 4
c = a / b
Problem: the cross - section of a river bank is a trapezium in shape . if the river bank is 12 m wide at the top and 8 m wide at the bottom and the area of cross - section is 500 sq m , the depth of river bank is ?
Options: a ) 20 m , b ) 60 m , c ) 40 m , d ) 50 m , e ) 90 m
Rationale: 1 / 2 * d ( 12 + 8 ) = 500 d = 50 answer : d
Answer: d
Python program:
a = 12 + 8 
b = a / 2
c = 500 / b
Problem: what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 2 : 1 , d ) 13 : 11 , e ) 14 : 8
Rationale: correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 6 : 3 = 2 : 1
Answer: c
Python program:
a = 25 - 19
b = 19 - 16
c = a / b
Problem: x can do a piece of work in 20 days . he works at it for 10 days and then y finished it in 12 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 24 , d ) 29 , e ) 30
Rationale: "work done by x in 10 days = 10 * 1 / 20 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by y in 12 days whole work will be done by y in 12 * 2 = 24 days answer is c"
Answer: c
Python program:
a = 10 / 20
b = 1 - a
c = 1/(b)
d = 12 * c
Problem: a man can row upstream at 27 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 31 , b ) 92 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 27 ds = 35 m = ( 35 + 27 ) / 2 = 31 answer : a"
Answer: a
Python program:
a = 27 + 35 
b = a / 2
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum m of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum m = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Python program:
a = 301 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1