euclaise/mathqa_programs huggingface dataset:
Problem: if n is a positive integer and n ^ 2 is divisible by 134 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 24 , is n divisible by 48 ? no . so , n is not always divisible by 48 . c"
Answer: c
Python program:
a = 134 / 2
b = math.sqrt(a)
c = b * 2
Problem: in a group of 400 players some are outdoor players , some are indoor players and some plays both . 350 plays outdoors and 110 plays indoor . how many plays indoor as well as outdoor games .
Options: a ) 70 , b ) 60 , c ) 90 , d ) 100 , e ) 110
Rationale: consider total number of players n ( o u i ) = 400 players who plays outdoors n ( o ) = 350 players who plays indoors n ( i ) = 110 players who plays both n ( o â ˆ © i ) = ? n ( o u i ) = n ( o ) + n ( i ) - n ( o â ˆ © i ) 400 = 350 + 110 - n ( o â ˆ © i ) n ( o â ˆ © i ) = 460 - 400 n ( o â ˆ © i ) = 60 so people read both science fiction and literacy works are 60 answer : b
Answer: b
Python program:
a = 350 + 110 
b = a - 400
Problem: if 50 % of x equals the sum of y and 20 , then what is the value of x – 2 y ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 90
Rationale: explanation : given , 50 % of x equals the sum of y and 20 . = > ( 50 / 100 ) × x = y + 20 . = > x / 2 = y + 20 . = > x = 2 y + 40 . = > x – 2 y = 40 . answer : b
Answer: b
Python program:
a = 50 / 100
b = 20 / a
Problem: weights of two friends ram and shyam are in the ratio of 4 : 5 . ram ’ s weight increases by 10 % and the total weight of ram and shyam together becomes 82.8 kg , with an increase of 15 % . by what per cent did the weight of shyam increase ?
Options: a ) 12.5 % , b ) 17.5 % , c ) 19 % , d ) 21 % , e ) none of these
Rationale: let the weights of ram and shyam be 4 x and 5 x . now , according to question , 4 x × 110 / 100 + shyam ? snewwt 4 x × 110100 + shyam ? s new wt = 82.8 . . . . . . . . ( i ) and 4 x + 5 x = 9 x + 115 / 100 = 82.8 . . . . . . . . ( ii ) from ( ii ) , x = 8 putting in ( i ) , we get shyam ’ s new wt = ( 82.8 – 35.2 ) = 47.6 % increase in shyam ’ s wt = ( 47.6 − 40 / 40 × 100 ) = 19 answer c
Answer: c
Python program:
a = 4 / 5
b = 15 - 10
c = a * b
d = c + 15
Problem: 1397 x 1397
Options: a ) 1951609 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1397 x 1397 = ( 1397 ) 2 = ( 1400 - 3 ) 2 = ( 1400 ) 2 + ( 3 ) 2 - ( 2 x 1400 x 3 ) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609 . answer : option a"
Answer: a
Python program:
a = 1397 / 1397
b = a * 100
Problem: if n divided by 9 has a remainder of 8 , what is the remainder when 2 times n is divided by 9 ?
Options: a ) 1 , b ) 7 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 9 p + 8 for some integer p hence 2 n = > 18 q + 16 but again , 16 can be divided by 9 to get remainder 7 for some integer q hence b"
Answer: b
Python program:
a = 2 * 8
Problem: barbata invests $ 2400 in the national bank at 4 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 2400 , d ) 3600 , e ) 2450
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.04 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.04 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.04 ) x = 2400 * 0.02 / 0.02 = 2400 ans : c"
Answer: c
Python program:
a = 6 / 100
b = a * 2400
c = 4 / 100
d = 2400 * c
e = b - d
f = 8 / 100
g = 6 / 100
h = f - g
i = e / h
Problem: what is the value of ( 4 ) ^ - 5 ?
Options: a ) 1 / 602 , b ) 1 / 120 , c ) 1 / 650 , d ) 1 / 1024 , e ) 1 / 1000
Rationale: "4 ^ - 5 = 1 / ( 4 ) ^ 5 = 1 / 1024 answer : d"
Answer: d
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 12 - m ) then m = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2 m = 12 - m 3 m = 12 m = 4 the answer is d ."
Answer: d
Python program:
a = 2 + 1 
b = 12 / a
Problem: p and q are the only two applicants qualified for a short - term research project that pays 540 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 9 , b ) $ 15 , c ) $ 18 , d ) $ 21 , e ) $ 27
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 540 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 540 / 30 = $ 18 p ' s hourly wage is 540 / ( t - 10 ) = $ 27 which is $ 9 per hour more . the answer is a ."
Answer: a
Python program:
a = 3 / 2
b = a - 1
c = 10 / b
d = 540 / c
e = 3 / 2
f = e - 1
g = 10 / f
h = g + 10 
i = 540 / h
j = d - i
Problem: the average of the marks of 12 students in a class is 50 . if the marks of each student are doubled , find the new average ?
Options: a ) 160 , b ) 120 , c ) 100 , d ) 150 , e ) 170
Rationale: "sum of the marks for the 12 students = 12 * 50 = 600 . the marks of each student are doubled , the sum also will be doubled . the new sum = 600 * 2 = 1200 . so , the new average = 1200 / 12 = 100 . answer : c"
Answer: c
Python program:
a = 50 * 2
Problem: if 75 percent of a class answered the first question on a certain test correctly , 25 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 25 % - { both } + 20 % - - > { both } = 20 % . answer : b ."
Answer: b
Python program:
a = 75 + 25 
b = a + 20 
c = b - 100
Problem: pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 8 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 24 , c ) 18 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 8 = > 1 / x = 1 / 6 - 1 / 8 = ( 4 - 3 ) / 24 = 1 / 24 = > x = 24 . answer : b"
Answer: b
Python program:
a = 8 * 6
b = 8 - 6
c = a / b
Problem: if the sum of two numbers is 55 and the h . c . f . and l . c . m . of these numbers are 5 and 120 respectively , then the sum of the reciprocals of the numbers is equal to :
Options: a ) 11 / 122 , b ) 11 / 120 , c ) 11 / 121 , d ) 11 / 140 , e ) 11 / 111
Rationale: explanation : let the numbers be a and b . then , a + b = 55 and ab = 5 x 120 = 600 . the required sum answer : b ) 11 / 120
Answer: b
Python program:
a = 55 / 5
b = a / 120
Problem: in a factory , there are 60 % technicians and 100 % non - technicians . if the 60 % of the technicians and 100 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 85 % , e ) 42 %
Rationale: "total = 160 t = 60 nt = 100 60 * ( 100 / 100 ) = 37.5 100 * ( 60 / 100 ) = 37.5 37.5 + 37.5 = 75 = > 160 - 75 = 85 % answer : d"
Answer: d
Python program:
a = 100 / 100
b = 60 * a
c = 60 / 100
d = c * 100
e = b + d 
f = 100 - e
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8200 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4500 , d ) 5700 , e ) 6711
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8200 = 32800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 800 salary of may is rs . 6500 salary of january = rs . 5700 . answer : d"
Answer: d
Python program:
a = 8000 * 4
b = 8200 * 4
c = b - 6500
d = a - c
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 12 years and that of the other 9 students is 16 years . the age of the 15 th student is ?
Options: a ) 11 years , b ) 17 years , c ) 21 years , d ) 14 years , e ) 12 years
Rationale: "age of the 15 th student = [ 15 * 15 - ( 12 * 5 + 16 * 9 ) ] = ( 225 - 204 ) = 21 years . answer : c"
Answer: c
Python program:
a = 15 * 15
b = 5 * 12
c = 9 * 16
d = b + c 
e = a - d
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 800 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 20 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 800 = x * 1 x / 2 x ² = 1600 x = 40 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 40 / 2 = 20 m answer : d"
Answer: d
Python program:
a = 1 / 2
b = 800 / a
c = math.sqrt(b)
d = c / 2
Problem: what decimal fraction is 20 ml of a litre ?
Options: a ) . 2 , b ) 0.002 , c ) . 05 , d ) . 02 , e ) none of these
Rationale: "answer required fraction = 20 / 1000 = 2 / 100 = . 02 correct option : d"
Answer: d
Python program:
a = 20 / 1000
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 210 , what is the least possible value of n ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 14
Rationale: "210 = 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is a ."
Answer: a
Python program:
a = 210 / 2
b = a / 3
c = b / 4
d = 10 / 2
e = c / d
Problem: a man covers a distance on scooter . had he moved 3 kmph faster he would have taken 40 min less . if he had moved 2 kmph slower , he would have taken 40 min more . the distance is .
Options: a ) 30 km , b ) 60 km , c ) 80 km , d ) 20 km , e ) 40 km
Rationale: e 40 km let distance = x m usual rate = y kmph x / y – x / y + 3 = 40 / 60 hr 2 y ( y + 3 ) = 9 x - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ( 1 ) x / y - 2 – x / y = 40 / 60 hr y ( y - 2 ) = 3 x - - - - - - - - - - - ( 2 ) divide 1 & 2 equations by solving we get x = 40 km
Answer: e
Python program:
a = 100 * 40
b = a / 40
c = 40 / 2
d = c * 3
e = b - d
Problem: p is 50 % more efficient than q . p can complete a work in 25 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "the work done by p in 1 day = 1 / 25 let work done by q in 1 day = q q × ( 150 / 100 ) = 1 / 25 q = 100 / ( 25 × 150 ) = 10 / ( 25 × 15 ) the work done by p and q in 1 day = 1 / 25 + 10 / ( 25 × 15 ) = 25 / ( 25 × 15 ) = 1 / 15 p and q together can do the work in 15 days . the answer is c ."
Answer: c
Python program:
a = 50 / 100
b = a + 1 
c = b * 25
d = 50 / 100
e = d + 1 
f = e + 1 
g = c / f
Problem: a can do a piece of work in 4 hours . a and c together can do it in just 2 hours , while b and c together need 3 hours to finish the same work . b alone can complete the work in - - - hours .
Options: a ) 65 , b ) 85 , c ) 48 , d ) 12 , e ) 25
Rationale: explanation : work done by a in 1 hour = 1 / 4 work done by b and c in 1 hour = 1 / 3 work done by a and c in 1 hour = 1 / 2 work done by a , b and c in 1 hour = 1 / 4 + 1 / 3 = 7 / 12 work done by b in 1 hour = 7 / 12 – 1 / 2 = 1 / 12 = > b alone can complete the work in 12 hours answer : d
Answer: d
Python program:
a = 1/(3)
b = 1/(2)
c = 1/(4)
d = b - c
e = a - d
f = 1/(e)
Problem: beginning in town a , biker bob rides his bike 12 miles west , 6 miles north , 4 miles east , and then 12 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 18.97 miles , b ) 20 miles , c ) 22 miles , d ) 23 miles , e ) 25 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 12 + 6 = 18 m other being the base ie distance traveled west - distance traveled eat = 12 - 6 = 6 m now this third side or the distance between town a and town b = 18 ^ 2 + 6 ^ 2 = sq root 360 = 18.97 mile answer : a"
Answer: a
Python program:
a = 6 + 12 
b = a ** 2
c = 4 ** 2
d = b + c 
e = math.sqrt(d)
Problem: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 60.5 . when one student dropped the class , the average of the remaining scores increased to 64.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 8 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 60.50 = 968 total score of 15 students is 15 * 64 = 960 so , the score of the person who left is 8 ( 968 - 960 ) answer will be ( a"
Answer: a
Python program:
a = 16 * 60
b = 16 - 1
c = b * 64
d = a - c
Problem: median w of price of the car is 52000 . which could be the median of the other two . 35000 , 44000 , x , y , 57000 .
Options: a ) 38000 , b ) 47000 , c ) 48000 , d ) 51000 , e ) 56000
Rationale: median of the car is 52000 therefore 52000 is the middle number . assuming y > = x , x will have to be the median value i . e . 52000 . therefore the remaining value would have to be between 52000 and 57000 inclusive . the only answer choice that fits is w = 56000 . e
Answer: e
Python program:
a = 100 * 10
b = 57000 - a
Problem: each man in a gang of 100 investors has investments ineither equities or securities or both . exactly 2525 of the investors in equities haveinvestments in securities , exactly 4040 of the investorsin securities have investments inequities . how many have investmentsin equities ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120
Rationale: the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let xx , yy , and zz denote the number of people in the respective categories . since the total number of investors is 110 , we have x + y + z = 110 x + y + z = 110 - - - - - - - - - - - - - ( 1 ) also , the number of people with investments in equities is x + zx + z and the number of people with investments in securities is y + zy + z . since exactly 25 % 25 % of the investors in equities have investments in securities , we have the equation 25100 × ( x + z ) = z 25100 × ( x + z ) = z 25100 × x = 25100 × z 25100 × x = 25100 × z x = 3 zx = 3 z - - - - - - - - - - - - - - - - - - - ( 2 ) since exactly 40 % 40 % of the investors in securities have investments in equities , we have the equation 40100 × ( y + z ) = z 40100 × ( y + z ) = z ( y + z ) = 5 z 2 ( y + z ) = 5 z 2 y = 3 z 2 y = 3 z 2 substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) yields 3 z + 3 z 2 + z = 1103 z + 3 z 2 + z = 110 11 z 2 = 11011 z 2 = 110 z = 110 × 211 = 20 z = 110 × 211 = 20 hence , the number of people with investments in equities is : x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 = 80 b
Answer: b
Python program:
a = 100 + 10 
b = 4 * 10
c = b / 100
d = 2 + 3 
e = 2 + 3 
f = d * e
g = f / 100
h = c / g
i = 1 + h 
j = 4 * 10
k = j / 100
l = i - k
m = a / l
n = 4 * 10
o = n / 100
p = 2 + 3 
q = 2 + 3 
r = p * q
s = r / 100
t = o / s
u = m * t
Problem: a certain country had a total annual expenditure of $ 9.6 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 4,000
Rationale: total expenditure / population = per capita expenditure hence , ( 9,6 x 10 ^ 11 ) / 240 000 000 = ( 9,6 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 4 x 10 ^ ( 11 - 8 ) = 4 x 10 ^ 3 = 4000 . answer is e .
Answer: e
Python program:
a = 10 ** 11
b = 9 * 6
c = 4 + 2 
d = 10 ** c
e = 240 * d
f = b / e
Problem: in the manufacture of a certain product , 6 percent of the units produced are defective and 4 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 ) 0.125 % , b ) 0.24 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 6 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 6 / 100 ) * 100 % = ( 24 / 10000 ) * 100 % = ( 24 / 100 ) % = . 24 % answer b"
Answer: b
Python program:
a = 4 / 100
b = 6 * a
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.10 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 732.6 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.1 = 732.6 answer : c"
Answer: c
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
Problem: the distance between 2 cities a and b is 1000 km . a train starts from a at 8 a . m . and travels towards b at 100 km / hr . another starts from b at 9 a . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 8 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 8 + 5 = 1 p . m . answer is e"
Answer: e
Python program:
a = 2 + 9 
b = 8 + 9 
c = a / b
d = c + 1000
Problem: 445 , 221 , 109 , 53 , . . .
Options: a ) 8 , b ) 7 , c ) 42 , d ) 25 , e ) 63
Rationale: "explanation : to obtain next number , subtract 3 from the previous number and divide the result by 2 445 ( 445 - 3 ) / 2 = 221 ( 221 - 3 ) / 2 = 109 ( 109 - 3 ) / 2 = 53 ( 53 - 3 ) / 2 = 25 answer : d"
Answer: d
Python program:
a = negate - (
Problem: car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 5 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 52 : 35 , c ) 13 : 7 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 65 ã — 8 = 520 km distance travelled by car b = 70 ã — 5 = 350 km ratio = 520 / 350 = 52 : 35 b"
Answer: b
Python program:
a = 65 * 8
b = 70 * 5
c = a / b
Problem: find the least number must be subtracted from 568219 so that remaining no . is divisible by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "on dividing 568219 by 5 we get the remainder 4 , so 4 should be subtracted e"
Answer: e
Python program:
a = 568219 / 5
b = math.floor(a)
c = b * 5
d = 568219 - c
Problem: if the cost price of 40 articles is equal to the selling price of 25 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 60 % profit , e ) 75 % profit
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 40 articles = 40 * 1 = $ 40 the selling price of 25 articles = cost price of 40 articles = $ 40 . now , we know the selling price of 25 articles . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = $ 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 40 - 25 = $ 15 . as the profit is in the positive , the merchant has made a profit of $ 15 . therefore , % loss = loss / cp * 100 % loss = 15 / 25 * 100 = 60 % profit . d"
Answer: d
Python program:
a = 100 * 25
b = a / 40
c = 100 - b
d = 100 * 25
e = d / 40
f = c / e
g = 100 * f
Problem: the numbers 272738 and 232342 , when divided by n , a two digit number , leave a remainder of 13 and 17 respectively . find the sum of the digits of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 4 , e ) 5
Rationale: from the given information , ( 272738 - 13 , 232342 - 17 ) are exactly divisible by that two digit number . we have to find the hcf of the given numbers 272725 , 232325 . hcf = 25 . so sum of the digits = 7 . answer : a
Answer: a
Python program:
a = 272738 - 13
b = 232342 - 17
c = math.gcd(a, b)
d = reminder + (
Problem: find the area of a parallelogram with base 36 cm and height 18 cm ?
Options: a ) 287 cm 2 , b ) 887 cm 2 , c ) 384 cm 2 , d ) 268 cm 2 , e ) 648 cm 2
Rationale: "area of a parallelogram = base * height = 36 * 18 = 648 cm 2 answer : e"
Answer: e
Python program:
a = 36 * 18
Problem: if the number is divided by 3 , it reduced by 42 . the number is
Options: a ) a ) 51 , b ) b ) 63 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 42 = > 2 x / 3 = 42 = > x = 63 answer : option b"
Answer: b
Python program:
a = 42 * 3
b = 3 - 1
c = a / b
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 6 ?
Options: a ) 82,650 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 6 seeing the options after dividing an finding the reminder of 2 my answer was a"
Answer: a
Python program:
a = 1000 - 3
b = 3 * 3
c = b * 10
d = 3 * 3
e = c + d 
f = e + 3 
g = a - f
h = g / 6
i = h + 1 
j = i / 2
k = 1000 - 3
l = 3 * 3
m = l * 10
n = 3 * 3
o = m + n 
p = o + 3 
q = k + p 
r = j * q
Problem: how many bricks , each measuring 50 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 2400 , c ) 5500 , d ) 7400 , e ) 3200
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 50 x 11.25 x 6 ) = 3200 answer : e"
Answer: e
Python program:
a = 8 * 100
b = 6 * 100
c = a * b
d = c * 22
e = 50 * 11
f = e * 6
g = d / f