euclaise/mathqa_programs huggingface dataset:
Problem: there are 760 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 425 , d ) 475 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 760 . hence 3 x + 5 x = 760 solve for x 8 x = 760 x = 95 number of boys 3 x = 3 × 95 = 285 number of girls 5 x = 5 × 95 = 475 d"
Answer: d
Python program:
a = 760 / 5
b = a * 3
Problem: a contractor is engaged for 30 days on the condition that he receives rs . 25 for eachday he works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was heabsent ?
Options: a ) 5 , b ) 10 , c ) 17 , d ) 25 , e ) 30
Rationale: "30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b"
Answer: b
Python program:
a = 30 * 7
b = a + 425 
c = 25 + 7 
d = b / c
e = 30 - d
Problem: if a dozen of oranges cost $ 5 , what would be the cost of 10 oranges ?
Options: a ) 3.56 , b ) 4.16 , c ) 4.86 , d ) 5.1 , e ) 5.2
Rationale: the cost of one orange = 5 / 12 = 0.416 the cost of ten oranges = 0.416 x 10 = $ 4.16 answer : b
Answer: b
Python program:
a = 10 * 5
b = 10 + 2 
c = a / b
Problem: the perimeter of one square is 48 cm and that of another is 36 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 12 √ 4 , e ) 15 √ 2
Rationale: "4 a = 48 4 a = 36 a = 12 a = 9 a 2 = 144 a 2 = 81 combined area = a 2 = 225 = > a = 15 d = 15 √ 2 answer : e"
Answer: e
Python program:
a = 48 / 4
b = a ** 2
c = 36 / 4
d = c ** 2
e = b + d 
f = e * 2
g = math.sqrt(f)
Problem: light glows for every 14 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 381 , b ) 382 , c ) 383 , d ) 384 , e ) 355
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 14 = 354 so total 355 times light ll glow answer : e"
Answer: e
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 14
Problem: if 36 men can do a piece of work in 20 hours , in how mwny hours will 15 men do it ?
Options: a ) 22 , b ) 48 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 20 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 20 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 20 } { 15 } = 48 hence , 15 men can do it in 48 hours . answer : b ) 48"
Answer: b
Python program:
a = 36 * 20
b = a / 15
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours z will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) z = 4 . , c ) z = 5 . , d ) 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double z = 6 hrs . . so closest to that option is 5 ."
Answer: c
Python program:
a = 3 * 20
b = a / 12
Problem: find the simple interest on rs . 580 for 11 months at 9 paisa per month ?
Options: a ) 574 , b ) 270 , c ) 566 , d ) 266 , e ) 121
Rationale: "i = ( 580 * 11 * 9 ) / 100 = 574 answer : a"
Answer: a
Python program:
a = 11 / 100
b = 580 * a
Problem: every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` rat ' ' ?
Options: a ) 108 , b ) 111 , c ) 114 , d ) 117 , e ) 120
Rationale: ` ` rat ' ' = ( 18 + 1 + 20 ) * 3 = 117 . the answer is d .
Answer: d
Python program:
a = 2 * 10
b = a - 2
c = b + 1 
d = 2 * 10
e = c + d 
f = e * 3
Problem: a train 100 m long crosses a platform 125 m long in 2 sec ; find the speed of the train ?
Options: a ) 36 , b ) 405 , c ) 200 , d ) 302 , e ) 404
Rationale: "d = 100 + 125 = 225 t = 2 s = 225 / 2 * 18 / 5 = 405 kmph answer : b"
Answer: b
Python program:
a = 125 * const_0_2778
b = 2 * a
c = b - 100
Problem: 0.0015 ÷ ? = 0.003
Options: a ) 0.05 , b ) 0.005 , c ) 0.5 , d ) 5 , e ) 50
Rationale: "let 0.0015 / x = 0.003 x = 0.0015 / 0.003 = 0.5 answer : c"
Answer: c
Python program:
a = 0 / 15
b = a * 100
Problem: √ ( 9 ) ^ 2
Options: a ) 3 , b ) 14 , c ) 9 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 9 ) ^ 2 = ? or , ? = 9 answer c"
Answer: c
Python program:
a = 9 ** 2
b = math.sqrt(a)
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 $ 39,375 , how much profit did the business make ?
Options: a ) $ 54,000 , b ) $ 57,000 , c ) $ 60,000 , d ) $ 63,000 , e ) $ 66,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 39,375 p = $ 63,000 the answer is d ."
Answer: d
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: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e"
Answer: e
Python program:
a = 2 * 12
b = 15 + 25 
c = a * b
d = 6 * 3
e = c - d
f = 4 * 3
g = 3 * f
h = e - g
i = h * 3
Problem: a car that moves at an average speed of 60 kmph , reaches its destination on time . when its average speed becomes 50 kmph , then it reaches its destination 45 minutes late . find the length of journey .
Options: a ) 189 km , b ) 225 km , c ) 255 km , d ) 199 km , e ) none
Rationale: sol . difference between timings = 45 min = 3 / 4 hr . let the length of journey be x km . then , x / 50 - x / 60 = 1 / 4 â ‡ ” 6 x - 5 x = 225 â ‡ ” x = 225 km . answer b
Answer: b
Python program:
a = 45 / const_60
b = 50 * a
c = 60 - 50
d = b / c
e = d * 60
Problem: one pipe can fill a tank in 15 hour . but because of hole in a tank , this tank fill in 20 hour . so in how much time this hole will empty the full tank ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: in 1 hour hole empty = [ 1 / 15 - 1 / 20 ] = 1 / 60 so total time taken to empty the full tank through hole = 60 hour . answer d
Answer: d
Python program:
a = 1 / 15
b = 1 / 20
c = a - b
d = 1/(c)
Problem: the ratio of the volumes of two cubes is 125 : 1728 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 9 : 11 , c ) 25 : 144 , d ) 27 : 121 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 125 : â ³ â ˆ š 1728 = 5 : 12 ratio of surface areas = 5 ^ 2 : 12 ^ 2 = 25 : 144 answer : c"
Answer: c
Python program:
a = 125 / 1728
b = 1 / 3
c = a ** b
Problem: moli buys 3 ribbons , 7 clips and 1 soap for rs . 120 exactly . at the same place it would cost rs . 164 for 4 ribbons , 10 clips and one soap . how much would it cost for one ribbon , one clip and one soap ?
Options: a ) 36 , b ) 34 , c ) 38 , d ) 32 , e ) 31
Rationale: explanation : let us consider , ribbon is denoted by r clips is denoted by c soaps is denoted by s now according to the question , = > 3 r + 7 c + s = 120 - - - - - - - - ( 1 ) = > 4 r + 10 c + s = 164 - - - - - - - - ( 2 ) ( 1 ) - ( 2 ) = > ( 3 r - 4 r ) + ( 7 c - 10 c ) + ( s - s ) = 120 - 164 = > - r - 3 c = - 44 multily the equation by - 1 , it becomes = > r + 3 c = 44 - - - - - - - ( 3 ) now perform this operation 2 * ( 1 ) - ( 2 ) = > 2 r + 4 c + s = 76 - - - - - - - ( 4 ) finaly ( 4 ) - ( 3 ) = > r + c + s = 32 hence , the cost of 1 ribbon , 1 clip and 1 saop would be 32 rs . answer : d
Answer: d
Python program:
a = 164 - 120
b = 10 + 2 
c = a - b
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 5 minutes ?
Options: a ) 7.5 , b ) 66 , c ) 77 , d ) 52 , e ) 42
Rationale: "90 * 5 / 60 = 7.5 kmph answer : a"
Answer: a
Python program:
a = 5 / const_60
b = a * 90
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 124 billion gallons to 140 billion gallons . if the storm increased the amount of water in the reservoirs to 80 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 51 , b ) 48 , c ) 55 , d ) 63 , e ) 65
Rationale: "let total capacity be x we know 140 = 0.80 x x = 140 / 0.80 = 175 prior to storm , we had 124 bn gallons 175 - 124 = 51 answer : a"
Answer: a
Python program:
a = 140 * 100
b = a / 80
c = b / 2
Problem: if ( m - 8 ) is a factor of m ^ 2 - km - 24 , then k =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - km - 24 a = - 3 k = 8 + a = 5 = b"
Answer: b
Python program:
a = 24 / 8
b = 8 - a
Problem: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 70 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 30 %
Rationale: solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 70 % = 70 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 70 - c = 100 c = 30 option e .
Answer: e
Python program:
a = 60 + 70 
b = a - 100
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability w that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) w = 5 / 6 . answer : c
Answer: c
Python program:
a = 5 / 6
Problem: how many 4 - digit positive integers are there , where each digit is positive , and no 4 adjacent digits are same ?
Options: a ) 1236 , b ) 3024 , c ) 4096 , d ) 4608 , e ) 6561
Rationale: "first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities fourth digit , 6 possibilities . 9 * 8 * 7 * 6 = 3024 . b"
Answer: b
Python program:
a = 4 + 4 
b = 4 + 4 
c = a * b
d = 4 + 4 
e = 4 * 4
f = d * e
g = c * f
Problem: p can do a work in 15 days and q cando the same work in 20 days . if they can work together for 4 days , what is the fraction of work left ?
Options: a ) 6 / 15 , b ) 7 / 13 , c ) 8 / 15 , d ) 9 / 17 , e ) 2 / 13
Rationale: amount of work p can do in 1 day = 1 / 15 amount of work q can do in 1 day = 1 / 20 amount of work p and q can do in 1 day = 1 / 15 + 1 / 20 = 7 / 60 amount of work p and q can together do in 4 days = 4 × ( 7 / 60 ) = 7 / 15 fraction of work left = 1 – 7 / 15 = 8 / 15 c
Answer: c
Python program:
a = const_60 / 15
b = const_60 / 15
c = const_60 / 20
d = b + c 
e = a * d
f = const_60 - e
g = f / const_60
Problem: how many of the integers between 25 and 95 are even ?
Options: a ) 35 , b ) 90 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 25 to 95 is 70 numbers half of them is even . . which is 35 answer : a"
Answer: a
Python program:
a = 95 - 25
b = a / 2
Problem: the sale price shirts listed for rs . 400 after successive discount is 10 % and 5 % is ?
Options: a ) 280 , b ) 290 , c ) 342 , d ) 250 , e ) 253
Rationale: 400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 c
Answer: c
Python program:
a = 400 * 10
b = a / 100
c = 5 * 400
d = c / 100
e = b + d 
f = 400 - e
Problem: village x has a population of 78000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 78000 - 1200 p = 42000 + 800 p 2000 p = 36000 p = 18 answer is d ."
Answer: d
Python program:
a = 78000 - 42000
b = 800 + 1200 
c = a / b
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 4000 , the number of valid votes that the other candidate got , was :
Options: a ) 3500 , b ) 1200 , c ) 1650 , d ) 3700 , e ) 1800
Rationale: "number of valid votes = 80 % of 4000 = 3200 . valid votes polled by other candidate = 45 % of 4000 = ( 45 / 100 ) x 4000 = 1800 answer = e"
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 4000
Problem: a invested $ 300 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 300 * 12 : 200 * 6 a : b = 3 : 1 a ' s share = 100 * 3 / 4 = $ 75 answer is b"
Answer: b
Python program:
a = 200 / 2
b = 200 / 2
c = 300 + b 
d = a / c
e = 1 - d
f = 100 * e
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 336,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,625 , e ) $ 2,250
Rationale: "number of boxes = total volume / volume of one box = 336,000 / ( 8 * 10 * 12 ) = 350 one box costs 7.50 , so 350 box will cost = 350 * 7.5 = 2625 d is the answer"
Answer: d
Python program:
a = 3 * 100
b = 8 * 10
c = a + b 
d = c + 4 
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 7
j = i / 1000
Problem: the sum of 77 consecutive integers is 7777 . what is the greatest integer in the set ?
Options: a ) 139 , b ) 141 , c ) 143 , d ) 145 , e ) 147
Rationale: "let x be the first integer in the set . then x + 76 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 76 ) = 77 x + 76 * 77 / 2 = 77 ( x + 38 ) then x + 38 = 101 x = 63 the largest integer in the set is 63 + 76 = 139 the answer is a ."
Answer: a
Python program:
a = 77 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 77 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 77 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 77 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: a group of boy scouts and girls scouts is going on a rafting trip . 80 % of the scouts arrived with signed permission slips . if 40 % of the scouts were boy scouts and 75 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .
Options: a ) 79 , b ) 81 , c ) 82 , d ) 83 , e ) 85
Rationale: "40 % were boy scouts so 60 % ( 100 - 40 = 60 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 75 % of 40 % of the total going ) + ( ? % of 60 % of the total going ) = 80 % of the total going we can let the ` ` total going ' ' = 100 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 75 * . 40 * 100 + x * . 60 * 100 = . 80 * 100 30 + x * 60 = 80 60 x = 50 x = 50 / 60 x = . 833333 converting this to a percent , we have 83 % d"
Answer: d
Python program:
a = 40 * 75
b = a / 100
c = 80 - b
d = 100 - 40
e = c / d
f = e * 100
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 3 years . what is the sum ?
Options: a ) 122762 , b ) 132877 , c ) 122882 , d ) 133875 , e ) 132887
Rationale: "principal = ( 100 * 4016.25 ) / ( 1 * 3 ) = rs . 133875 . answer : d"
Answer: d
Python program:
a = 4016 * 25
b = a / 1
c = b / 3
Problem: pipe a can fill a tank in 12 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 36
Rationale: "let the pipe b be closed after x minutes . 30 / 12 - x / 24 = 1 = > x / 24 = 30 / 12 - 1 = 3 / 2 = > x = 3 / 2 * 24 = 36 . answer : e"
Answer: e
Python program:
a = 30 / 12
b = a - 1
c = b * 24
Problem: sandy is younger than molly by 18 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 18 x = 9 sandy is 63 years old . the answer is d ."
Answer: d
Python program:
a = 9 - 7
b = 7 / a
c = b * 18
Problem: score interval - - - - - - - - - - - - - - - - number of scores 50 - 59 - - - - - - - - - - - - - - - - - - - - - - - - - - 2 60 - 69 - - - - - - - - - - - - - - - - - - - - - - - - - - 4 70 - 79 - - - - - - - - - - - - - - - - - - - - - - - - - - 10 80 - 89 - - - - - - - - - - - - - - - - - - - - - - - - - - 27 90 - 99 - - - - - - - - - - - - - - - - - - - - - - - - - - 18 the table above shows the distribution of test scores for a group of management trainees . which score interval contains the median of the 61 scores ?
Options: a ) 30 , b ) 32 , c ) 31 th ( 80 - 89 ) , d ) 34 , e ) 36
Rationale: total scores = 2 + 4 + 10 + 27 + 18 = 61 , which is odd , therefore the median is the floor ( 61 / 2 ) + 1 = 31 th score . and the 31 th score is in the 80 - 89 range , because 50 - 79 only reference 28 scores . c
Answer: c
Python program:
a = 70 - 79
Problem: a side of beef lost 20 percent of its weight in processing . if the side of beef weighed 640 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 800 , d ) 840 , e ) 900
Rationale: "let weight of side of beef before processing = x ( 80 / 100 ) * x = 640 = > x = ( 640 * 100 ) / 80 = 800 answer c"
Answer: c
Python program:
a = 640 * 100
b = 100 - 20
c = a / b
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds . the ratio of their speeds is ?
Options: a ) 3 / 7 , b ) 3 / 2 , c ) 3 / 5 , d ) 3 / 1 , e ) 3 / 3
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : b"
Answer: b
Python program:
a = 27 - 23
b = 23 - 17
c = a / b
Problem: the cost price of 16 articles is the same as the selling price of 12 articles . find the loss / profit percentages .
Options: a ) 30 % , b ) 32.50 % , c ) 33 1 / 3 % , d ) 40 % , e ) 50 %
Rationale: "explanation : the gain is 4 out of 12 articles . therefore , gain percentage = 4 x 100 / 12 = 100 / 3 = 33 1 / 3 % answer : option c"
Answer: c
Python program:
a = 16 * 4
b = 4 + 1 
c = a / b
Problem: selling an kite for rs . 30 , a shop keeper gains 30 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 17 % , e ) 20 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 130 * 30 = rs . 23.07 sale price = 90 % of rs . 30 = rs . 27 required gain % = 3.92 / 23.07 * 100 = 17 % . answer : d"
Answer: d
Python program:
a = 30 / 100
b = 100 - 10
c = a * b
d = 30 * 100
e = 30 + 100 
f = d / e
g = c - f
h = 30 * 100
i = 30 + 100 
j = h / i
k = g / j
l = k * 100
Problem: the manufacturing cost of a shoe is rs . 220 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 222 , b ) s 216 , c ) s 220 , d ) s 270 , e ) s 217
Rationale: "explanation : total cost of a watch = 220 + ( 500 / 100 ) = 225 . gain = 20 % = > sp = 1.2 cp = 1.2 x 225 = 270 answer : d"
Answer: d
Python program:
a = 500 / 100
b = 220 + a 
c = 20 / 100
d = 500 / 100
e = 220 + d 
f = c * e
g = b + f
Problem: a grocer has a sale of rs . 5124 , rs . 5366 , rs . 5808 , rs . 5399 and rs . 6124 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5400 ?
Options: a ) 4079 , b ) 4579 , c ) 5579 , d ) 5679 , e ) 5779
Rationale: "total sale for 5 months = rs . ( 5124 + 5366 + 5808 + 5399 + 6124 ) = rs . 27821 . required sale = rs . [ ( 5400 x 6 ) - 27821 ] = rs . ( 32400 - 27821 ) = rs . 4579 . answer : b"
Answer: b
Python program:
a = 5 + 1 
b = a * 5400
c = 5124 + 5366 
d = c + 5808 
e = d + 5399 
f = e + 6124 
g = b - f
Problem: one bacterium splits into 8 bacteria of the next generation . but due to environment , only 50 % of one generation can produced the next generation . if the seventh generation number is 4096 million , what is the number in first generation ?
Options: a ) 1 million , b ) 2 million , c ) 4 million , d ) 8 million , e ) none of these
Rationale: solution : let the number of bacteria in the 1 st generation be x , then number of bacteria in 2 nd , 3 rd , 4 th . . . . . generation would be 8 ( x / 2 ) , 8 ( 4 x / 2 ) , 8 ( 16 x / 2 ) . . . . and so on . as x , 4 x , 16 x , 64 x . . . . . it is in gp with common ratio 4 . hence , 7 th term of gp , x ( 4 ) 6 = 4096 or , x = 1 or 1 million . answer : option a
Answer: a
Python program:
a = 8 / 2
b = 8 - 2
c = a ** b
d = 8 / 2
e = 8 - 2
f = d ** e
g = c / f
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 1 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 1 / 3 ) * ( 3 / 8 ) = 1 / 32 . ans . a ."
Answer: a
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 5 / 8
e = 1 - d
f = c * e