euclaise/mathqa_programs huggingface dataset:
Problem: in a certain circle there are 10 points . what is the number of the triangles connecting 2 points of the 10 points ?
Options: a ) 40 , b ) 45 , c ) 108 , d ) 120 , e ) 132
Rationale: "imo : b here we have to select 2 points out of 10 points . order is not important so the answer will be 10 c 2 = 45 answer b"
Answer: b
Python program:
a = math.factorial(10)
b = 10 / 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: a 8000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 48
Rationale: in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 4,000 by that net inflow to get the minutes ) - 48 min . answer e .
Answer: e
Python program:
a = 6 + 4 
b = a + 2 
c = 8000 / 2
d = b * c
e = d / 1000
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 124 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1800
Rationale: "$ 120 for 2 years = $ 60 per year . extra $ 4 yearned with the compound interest is the percent yearned on percent . so , $ 4 is yearned on $ 60 , which means that the interest = 15 % . this on the other hand means that half of the savings = 60 * 15 = $ 900 . twice of that = $ 1,800 . answer : e ."
Answer: e
Python program:
a = 124 - 120
b = 2 * a
c = b / 120
d = 120 / c
Problem: abcd is a square where ab = â ˆ š 6000 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 6000 / 2 = 3000 . correct answer e"
Answer: e
Python program:
a = 6000 / 2
Problem: mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8410 / - . find out the amount that he borrowed .
Options: a ) s . 5266 , b ) s . 5269 , c ) s . 5461 , d ) s . 5218 , e ) s . 52192
Rationale: explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8410 = p + ( 54 p / 100 ) 8410 = ( 100 p + 54 p ) / 100 8410 = 154 p / 100 p = ( 8410 * 100 ) / 154 = rs . 5461.039 answer : c
Answer: c
Python program:
a = 6 * 9
b = a / 100
c = 1 + b 
d = 8410 / c
Problem: the perimeter of a semi circle is 108 cm then the radius is ?
Options: a ) 17 , b ) 21 , c ) 19 , d ) 11 , e ) 12
Rationale: "36 / 7 r = 108 = > r = 21 answer : b"
Answer: b
Python program:
a = 2 + math.pi 
b = 108 / a
Problem: the length of a rectangle is one - sixth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1296 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 560 sq . units
b ) 360 sq . units
c ) 260 sq . units
d ) 460 sq . units
e ) 160 sq . units
Rationale: given that the area of the square = 1225 sq . units = > side of square = √ 1296 = 36 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 36 * 10 = 360 sq . units answer : b
Answer: b
Python program:
a = math.sqrt(1296)
b = a * 10
Problem: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 35 inclusive .
Options: a ) 288 , b ) 364 , c ) 410 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 13 to 35 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 35 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 33 = 48 now we have proof that there is no middle term . we have 6 bunches of 48 . 6 ( 48 ) = 288 a"
Answer: a
Python program:
a = 35 + 1 
b = a / 2
c = b ** 2
d = 13 - 2
e = d + 1 
f = e / 2
g = f ** 2
h = c - g
Problem: the function f ( n ) is defined as the product of all the consecutive positive integers between 4 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 4 answer : d
Answer: d
Python program:
a = 2 ** 2
Problem: in a shower , 5 cm of rain falls . the volume of water that falls on 1.5 hectares of ground is :
Options: a ) 75 cu . m
b ) 750 cu . m
c ) 7500 cu . m
d ) 75000 cu . m
e ) none of these
Rationale: solution area = ( 1.5 × 10000 ) m 2 = 45000 m 2 . depth = m = m . ∴ volume = ( area × depth ) = m 3 = 750 m 3 . answer b
Answer: b
Python program:
a = 5 / 100
b = 1 * 5
c = b * 10
d = a * c
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 200 ?
Options: a ) 48 , b ) 49 , c ) 50 , d ) 51 , e ) 52
Rationale: from first constraint 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 < 200 4 n < 193 n < 48 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 48 ( 48 integers ) and n = - 1 and 0 so 50 integers . c is the answer
Answer: c
Python program:
a = 200 - 7
b = a / 4
c = math.floor(b)
d = 1 - 7
e = d / 4
f = math.floor(e)
g = c - f
Problem: in the first 10 overs of a cricket game , the run rate was only 2.1 . what should be the rate in the remaining 30 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 8.28 , c ) 6.11 , d ) 8.7 , e ) 8.11
Rationale: "required run rate = [ 282 - ( 2.1 * 10 ) ] / 30 = 261 / 30 = 8.70 answer : d"
Answer: d
Python program:
a = 10 * 2
b = 282 - a
c = b / 30
Problem: 5216 x 51 = ?
Options: a ) 212016 , b ) 266016 , c ) 266436 , d ) 216314 , e ) 216318
Rationale: "normal way of multiplication may take time . here are one alternative . 5216 x 51 = ( 5216 x 50 ) + 5216 = ( 5216 x 100 ) / 2 + 5216 = 521600 / 2 + 5216 = 260800 + 5216 = 266016 answer is b"
Answer: b
Python program:
a = 5216 / 51
b = a * 100
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 70 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1857.14
Rationale: "300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 70 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 70 = 1857.14 e is the answer"
Answer: e
Python program:
a = 300 * 100
b = a / 30
c = b + 300 
d = 70 / 100
e = c / d
Problem: a car takes 6 hours to cover a distance of 720 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 , b ) 50 , c ) 80 , d ) 70 , e ) 65
Rationale: "time = 6 distance = 720 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 720 / 9 = 80 kmph answer c ."
Answer: c
Python program:
a = 6 * 3
b = a / 2
c = 720 / b
Problem: by selling 15 pencils for a rupee a man loses 15 % . how many for a rupee should he sell in order to gain 15 % ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 89 , e ) 81
Rationale: "85 % - - - 15 115 % - - - ? 15 / 115 * 15 = 11 answer : c"
Answer: c
Python program:
a = 100 + 15 
b = 100 - 15
c = 1 / b
d = a * c
e = 1 / d
f = e * 15
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 50 kmph its consumption is 1 litre per hour . if each litre costs $ 50 and other expenses per hous is $ 50 , then what would be the minimum expenditure required to cover a distance of 500 km ?
Options: a ) 800 , b ) 950 , c ) 900 , d ) 1000 , e ) 1250
Rationale: "50 kmph consumption is 1 lt / hr so 500 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 50 so 10 lt costs $ 500 extra expenses for 1 hr - $ 50 10 hrs - $ 500 total expense - $ 500 + $ 500 = $ 1000 answer : d"
Answer: d
Python program:
a = 500 / 50
b = a * 50
c = 500 / 50
d = c * 50
e = b + d
Problem: a man can row at 5 kmph in still water . if the velocity of current is 2 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.1 km , b ) 2.9 km , c ) 3.4 km , d ) 4.4 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 2 ) = 7 kmph speed upstream = ( 5 - 2 ) = 3 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 7 + x / 3 = 1 â ‡ ’ 3 x + 7 x = 21 â ‡ ’ 10 x = 21 â ‡ ’ x = 2.1 km answer : option a"
Answer: a
Python program:
a = 5 - 2
b = a * 3
c = b / 5
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: clearly d a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . 96 has more number of smaller prime factor thats the clue ! ! = d
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b
Problem: a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 24 inches . find b .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 24 ( 2 ^ 3 * 3 ) , sob = 2 ^ 3 or 2 ^ 3 * 3 ( 8 or 24 ) . combining 2 premises shows the answer is a ( 8 ) ."
Answer: a
Python program:
a = 24 / 4
b = a ** 2
c = 12 ** 2
d = b - c
e = math.sqrt(d)
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 7000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 28000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 7,000 * 2 ) * 2 = $ 28,000 ( after 9 years investment will become $ 7,000 * 2 = $ 14,000 and in another 9 years it ' ll become $ 14,000 * 2 = $ 28,000 ) . answer : a ."
Answer: a
Python program:
a = 7000 * 2
b = a * 2
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1480 ?
Options: a ) 228 , b ) 217 , c ) 100 , d ) 288 , e ) 772
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1480 74 x = 1480 = > x = 20 5 x = 100 rs . answer : c"
Answer: c
Python program:
a = 6 * 3
b = 9 * 4
c = a + b 
d = 4 * 5
e = c + d 
f = 1480 / e
g = 5 * f
Problem: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of m + 2 n ?
Options: a ) 11 , b ) 18 , c ) 20 , d ) 25 , e ) 40
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 10 + 15 * 2 = 40 answer : e"
Answer: e
Python program:
a = 3 ** 2
b = 4 * a
Problem: if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 14 , b ) 8 , c ) 12 , d ) 4 , e ) 18
Rationale: "let length of rectangle = l 4 ^ 2 = l * 4 = > l = 16 / 4 = 4 answer d"
Answer: d
Python program:
a = 4 ** 2
b = a / 4
Problem: what is the average ( arithmetic mean ) of the numbers 21 , 22 , 23 , 23 , 24 , and 25 ?
Options: a ) 23.0 , b ) 22.5 , c ) 21 , d ) 24 , e ) 23
Rationale: "{ 21 , 22 , 23 , 23 , 24 , 25 } = { 23 - 2,23 - 1 , 23 , 23,23 + 1,23 + 2 } - - > the average = 23 . answer : e ."
Answer: e
Python program:
a = 21 + 23 
b = 23 - 21
c = b / 21
d = c + 1 
e = a * d
f = e / 2
g = 23 - 21
h = g / 21
i = h + 1 
j = f / i
Problem: the average age of 28 students in a group is 16 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 45 , b ) 36 , c ) 41 , d ) 51 , e ) 48
Rationale: "sol . age of the teacher = ( 29 ã — 17 â € “ 28 ã — 16 ) years = 45 years . answer a"
Answer: a
Python program:
a = 28 + 1
Problem: a and b are two stations 390 km apart . a train starts from a at 10 a . m . and travels towards b at 65 kmph . another train starts from b at 11 a . m . and travels towards a at 35 kmph . at what time do they meet ?
Options: a ) 2.15 pm , b ) 1.15 pm , c ) 4.15 pm , d ) 3.15 pm , e ) 12.15 pm
Rationale: suppose they meet x hours after 10 a . m . then , ( distance moved by first in x hrs ) + [ distance moved by second in ( x - 1 ) hrs ] = 390 . 65 x + 35 ( x - 1 ) = 390 = > 100 x = 425 = > x = 17 / 4 so , they meet 4 hrs . 15 min . after 10 a . m i . e . , at 2.15 p . m . answer a
Answer: a
Python program:
a = 390 + 35 
b = 65 + 35 
c = a / b
d = c + 10 
e = 10 + 2 
f = d - e
Problem: in a group of cows and chickens , the number of legs was 16 more than twice the number of heads . the number of cows was :
Options: a ) 8 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 16 more than twice the number of heads . therefore , 2 × ( x + y ) + 16 = 4 x + 2 y . or , 2 x + 2 y + 16 = 4 x + 2 y . or , 2 x + 16 = 4 x [ subtracting 2 y from both sides ] . or , 16 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 16 = 2 x . or , x = 8 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 . correct answer : a ) 8"
Answer: a
Python program:
a = 4 - 2
b = 16 / a
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 5000 and b rs . 1000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 8160 , e ) 7291
Rationale: "5000 : 1000 = > 5 : 1 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 5 / 6 = 7200 + 960 = 8160 answer : d"
Answer: d
Python program:
a = 10 / 100
b = 1 - a
c = 9600 * b
d = 5000 + 1000 
e = 1000 / d
f = c * e
g = 9600 - f
Problem: how much 90 % of 40 is greater than 80 % of 30 ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 17 , e ) 18
Rationale: "( 90 / 100 ) * 40 – ( 80 / 100 ) * 30 36 - 24 = 12 answer : a"
Answer: a
Python program:
a = 90 * 40
b = a / 100
c = 80 * 30
d = c / 100
e = b - d
Problem: an auction house charges a commission of 20 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 190,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.2 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 190,000 ( 20 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : b ."
Answer: b
Python program:
a = 20 * 10
b = a + 10
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 3 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 1
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 3 ) = 36 / 12 = 3 / 1 . answer : e ."
Answer: e
Python program:
a = 4 + 1 
b = 45 / a
c = 45 - b
d = 4 + 1 
e = 45 / d
f = e + 3 
g = c / f
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 8 % p . a . was rs . 2828.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned ?
Options: a ) 19828.29 , b ) 19828.2 , c ) 19828.8 , d ) 19828.88 , e ) 19828.21
Rationale: "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : c"
Answer: c
Python program:
a = 8 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = 2828 / 80
f = e + 2828
Problem: a man took loan from a bank at the rate of 13 % p . a . s . i . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was ?
Options: a ) rs . 1846 , b ) rs . 18846 , c ) rs . 13846 , d ) rs . 2000 , e ) rs . 14846
Rationale: "principal = ( 100 * 5400 ) / ( 13 * 3 ) = rs . 13846 answer : c"
Answer: c
Python program:
a = 5400 * 100
b = a / 3
c = b / 13
Problem: a sum amounts to rs . 4410 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) rs . 4000 , b ) rs . 5000 , c ) rs . 4500 , d ) rs . 4800 , e ) rs . 5800
Rationale: ci = 4410 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 4410 = p [ 21 / 20 ] ^ 2 4410 [ 20 / 21 ] ^ 2 4000 answer : a
Answer: a
Python program:
a = 5 / 100
b = a + 1 
c = b ** 2
d = 4410 / c
Problem: a man can row downstream at 18 kmph and upstream at 8 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 8 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 26 = > x = 13 , y = 5 . answer : b"
Answer: b
Python program:
a = 18 + 8 
b = a / 2
c = b / 2
Problem: the compound ratio of 2 / 3 , 6 / 7 , 1 / 5 and 1 / 8 is given by ?
Options: a ) 7 / 98 , b ) 1 / 48 , c ) 1 / 98 , d ) 3 / 350 , e ) 1 / 68
Rationale: "2 / 3 * 6 / 7 * 1 / 5 * 1 / 8 = 12 / 1400 = 3 / 350 answer : d"
Answer: d
Python program:
a = 2 * 7
b = 1/(a)
Problem: how many of the positive factors of 14 are not factors of 21 ?
Options: a ) 4 , b ) 3 , c ) 1 , d ) 2 , e ) 0
Rationale: "factors of 14 - 1 , 2 , 7 , 14 , factors of 21 - 1 , 3 , 7 , 21 , comparing both , we have three factors of 14 which are not factors of 21 - 2,14 the answer is c"
Answer: c
Python program:
a = 21 / 14
Problem: how much water must be added to 60 litres of milk at 1.5 litres for rs . 20 so as to have a mixture worth rs . 32 / 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) 21 litres
Rationale: c . p . of 1 litre of milk = rs . 20 × 2 / 3 = rs . 40 / 3 . c . p . of 1 litre of water = rs 0 . mean price = rs . 32 / 3 . by the rule of alligation , we have : c . p of 1 litre c . p of 1 litre of water of milk ( 0 ) ( rs . 40 / 3 ) \ / mean price ( rs . 32 / 3 ) / \ 40 / 3 − 32 / 3 32 / ( 3 − 0 ) 8 / 3 32 / 3 the ratio of water and milk = 8 / 3 : 32 / 3 . = 8 : 32 = 1 : 4 . thus , quantity of water to be added to 60 litres of milk : = ( 1 / 4 ) × 60 litres . = 15 litres . answer : c
Answer: c
Python program:
a = 32 / 3
b = 20 / 1
c = 32 / 3
d = b - c
e = a / d
f = 60 / e
Problem: a cricket bat is sold for $ 850 , making a profit of $ 255 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 43 %
Rationale: "255 / ( 850 - 255 ) = 255 / 595 = 51 / 119 = 43 % . answer : e ."
Answer: e
Python program:
a = 850 - 255
b = 255 / a
c = b * 100
Problem: a car covers a distance of 624 km in 2 3 / 5 hours . find its speed ?
Options: a ) 104 kmph , b ) 194 kmph , c ) 109 kmph , d ) 174 kmph , e ) 240 kmph
Rationale: 624 / 2 3 / 5 = 240 kmph answer : e
Answer: e
Python program:
a = 3 / 5
b = 2 + a 
c = 624 / b
Problem: three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 30 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters , b ) 36 square meters , c ) 42 square meters , d ) 45 square meters , e ) 120 square meters
Rationale: "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 30 = 90 sq m of the wallpaper overlaps in three layers . 90 sq m makes two extra layers hence the area over which it makes two extra layers is 45 sq m . answer ( d ) ."
Answer: d
Python program:
a = 300 - 180
b = a - 30
c = b / 2
Problem: the average of first three prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50
Rationale: "23 + 29 + 31 = 83 / 3 = 27.7 answer : d"
Answer: d
Python program:
a = 20 + 1
Problem: if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 40 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 60 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
Options: a ) $ 50 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 3 x + 4 y + 2 z = 40 7 x + 2 y + 2 z = 60 adding both the equations = 10 x + 6 y + 4 z = 100 5 x + 3 y + 2 z = 50 ans a"
Answer: a
Python program:
a = 60 + 40 
b = a / 2
Problem: the heights of 3 individuals are in the ratio 4 : 5 : 6 . if the sum of the heights of the heaviest and the lightest boy is 150 cm more than the height of the third boy , what is the weight of the lightest boy ?
Options: a ) 120 cm , b ) 150 cm , c ) 160 cm , d ) 190 cm , e ) of these
Rationale: let the heights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 150 = > 5 k = 150 = > k = 30 therefore the height of the lightest boy = 4 k = 4 ( 30 ) = 120 cm . answer : a
Answer: a
Python program:
a = 4 + 6 
b = a - 5
c = 150 / b
d = c * 4