euclaise/mathqa_programs huggingface dataset:
Problem: in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive t difference between n and m ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result t will be 8 - 5 = 3 and answer b"
Answer: b
Python program:
a = 5 - 2
Problem: if the average of 201 , 202 , 204 , 205 , 206 , 209 , 209 , 210 , 212 and x is 207 , what is the value of x ?
Options: a ) 207 , b ) 209 , c ) 211 , d ) 212 , e ) 213
Rationale: sum of the deviations of the numbers in the set from the mean is always zero 201 , 202 , 204 , 205 , 206 , 209 , 209 , 210 , 212 mean is 207 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 207 + 5 = 212 d
Answer: d
Python program:
a = 207 * 10
b = 201 + 202 
c = b + 204 
d = c + 205 
e = d + 206 
f = e + 209 
g = f + 209 
h = g + 210 
i = h + 212 
j = a - i
Problem: in a group of cows and chickens , the number of legs was 20 more than twice the number of heads . the number of cows was :
Options: a ) 5 , 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 20 more than twice the number of heads . therefore , 2 × ( x + y ) + 20 = 4 x + 2 y . or , 2 x + 2 y + 20 = 4 x + 2 y . or , 2 x + 20 = 4 x [ subtracting 2 y from both sides ] . or , 20 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 20 = 2 x . or , x = 10 [ dividing by 2 on both sides ] . therefore , the number of cows = 10 . correct answer : c ) 10"
Answer: c
Python program:
a = 4 - 2
b = 20 / a
Problem: the average marks in mathematics scored by the pupils of a school at the public examination were 39 . if 4 of these pupils who actually scored 25 , 12 , 15 and 19 marks at the examination had not been sent up , the average marks for the school would have been 44 . find the number of pupils sent up for examination from the school ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: 39 x = 25 + 12 + 15 + 19 + ( x – 4 ) 44 39 x = 71 + 44 x - 176 5 x = 105 x = 21 answer : b
Answer: b
Python program:
a = 44 * 4
b = 25 + 12 
c = b + 15 
d = c + 19 
e = a - d
f = 44 - 39
g = e / f
Problem: amanda sees a sale for 30 % off all items , she sees a dress on sale that originally cost $ 50 . how much will it cost amanda to buy the dress after the sale amount of 30 % has been take off ?
Options: a ) $ 40 , b ) $ 35 , c ) $ 50 , d ) $ 65 , e ) $ 15
Rationale: final number = original number - 30 % ( original number ) = 50 - 30 % ( 50 ) = 50 - 15 = $ 35 . answer b
Answer: b
Python program:
a = 30 / 100
b = a * 50
c = 50 - b
Problem: a cricket bat is sold for $ 900 , making a profit of $ 150 . the profit percentage would be
Options: a ) 24 % , b ) 20 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: 150 / ( 900 - 150 ) = 150 / 750 = 0.2 = 20 % . answer : b
Answer: b
Python program:
a = 900 - 150
b = 150 / a
c = b * 100
Problem: of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 28.1 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 4 is 1200 * 1 / 4 so it reduced 300 people , so there is 900 clerical people left but since 300 people left , it also reduced from the total of 3600 so there are 3300 people total since 900 clerical left / 3200 people total answer : b"
Answer: b
Python program:
a = 1 / 3
b = 1 / 4
c = 1 - b
d = a * c
e = 1 / 3
f = 1 / 4
g = 1 - f
h = e * g
i = 1 / 3
j = 1 - i
k = h + j 
l = d / k
m = l * 100
Problem: raja spends 60 % of his monthly income on household items , 10 % of his monthly income on buying cloths , 10 % of his monthly income on medicines and saves the remaining amount which is rs . 5000 . find his monthly income .
Options: a ) rs . 40000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 25000 , e ) none of these
Rationale: "savings 20 % - 5000 expenditure 80 % - 20000 total - 25000 answer : d"
Answer: d
Python program:
a = 60 / 100
b = 10 / 100
c = a + b 
d = 10 / 100
e = c + d 
f = 1 - e
g = 5000 / f
Problem: 22.085 ã — 0.001 = ?
Options: a ) 0.22085 , b ) 2.2085 , c ) 0.022085 , d ) 0.0022085 , e ) none of these
Rationale: "22.085 ã — 0.001 = ? or , ? = 0.022085 answer c"
Answer: c
Python program:
a = 22 / 85
b = a * 100
Problem: 0.99999 + 0.11111 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.1111
Rationale: "0.99999 + 0.00001 = 1 0.1111 + 1 = 1.1111 correct answer is e ."
Answer: e
Python program:
a = 0 / 99999
b = a * 100
Problem: a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.8 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 480 , b ) b . 300 , c ) c . 600 , d ) d . 410 , e ) e . 240
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.8 = 480 answer : a"
Answer: a
Python program:
a = 15 * 12
b = a * 10
c = b / 100
d = c / 100
e = d / 100
f = 1 / 8
g = 0 * 8
Problem: the sector of a circle has radius of 35 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 152.5 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 35 ) + 2 ( 35 ) = 82.5 + 70 = 152.5 cm answer : c"
Answer: c
Python program:
a = 35 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 35
Problem: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 26 ) ?
Options: a ) 23 , b ) 19 , c ) 17 , d ) 13 , e ) 11
Rationale: "f ( 26 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 the greatest prime factor in this list is 13 . the answer is d ."
Answer: d
Python program:
a = 26 / 2
b = a - 1
Problem: what is the remainder when 6 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 1 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? b
Answer: b
Python program:
a = 5 / 2
b = 6 * 6
c = a - b
Problem: two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 108 seconds . the length of each train is :
Options: a ) 82 m , b ) 50 m , c ) 72 m , d ) 150 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 108 secs the total distance traveled is 108 x 25 / 9 = 300 m . therefore the length of each train is = 300 / 2 = 150 m . answer d"
Answer: d
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 108
e = d / 2
Problem: a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 50 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: 50 % is 10 % - points above 40 % and 30 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 3 : 1 . so the team played a total of 30 + 10 = 40 games . the answer is a .
Answer: a
Python program:
a = 40 / 100
b = 30 * a
c = 80 / 100
d = 50 / 100
e = c - d
f = b / e
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 29.85 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 16 ) = 76 cm parameter of the square = 76 cm i . e . 4 a = 76 a = 19 diameter of the semicircle = 19 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 19 ) = 1 / 2 ( 22 / 7 ) ( 19 ) = 418 / 14 = 29.85 cm to two decimal places answer : d"
Answer: d
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 9 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 5 , b ) 1 : 6 , c ) 1 : 7 , d ) 1 : 8 , e ) 1 : 9
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 5 : 9 , thus the smaller number must have a ratio of 1 . the ratio of the smaller number to the larger number is 1 : 9 . the answer is e ."
Answer: e
Python program:
a = 5 / 9
b = 1 / 2
c = a - b
d = c * 2
Problem: if | 5 x - 10 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 3 , d ) - 3 , e ) 4
Rationale: "| 5 x - 10 | = 100 5 x - 10 = 100 or 5 x - 10 = - 100 5 x = 110 or 5 x = - 90 x = 22 or x = - 18 sum = 21 - 18 = 3 answer is c"
Answer: c
Python program:
a = 100 - 10
b = 100 + 10 
c = a - b
d = c - 10
Problem: a is twice as good a workman as b and together they finish a piece of work in 18 days . in how many days will a alone finish the work ?
Options: a ) 31 days , b ) 25 days , c ) 27 days , d ) 29 days , e ) 19 days
Rationale: "if a takes x days to do a work then b takes 2 x days to do the same work . - - > 1 / x + 1 / 2 x = 1 / 18 - - > 3 / 2 x = 1 / 18 - - > x = 27 days . hence , a alone can finish the work in 27 days . answer : c ."
Answer: c
Python program:
a = 1 + 2 
b = a * 18
Problem: it takes avery 2.5 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 15 minutes . , b ) 30 minutes . , c ) 1 hour and 30 minutes . , d ) 1 hour and 40 minutes , e ) 2 hours
Rationale: "avery ' s efficiency is 100 / 2.5 = 40 % tom ' s = 100 / 5 = 20 % they worked together for 1 hour and finished 60 % of the job remaining = 40 % tom will complete 20 % in 60 minutes , 40 % in 120 minutes time taken by tom to finish the remaining on his own = 120 minutes answer : e"
Answer: e
Python program:
a = 1 / 2
b = 1 / 5
c = a + b 
d = 1 - c
e = 1 / 5
f = d / e
g = f * const_60
Problem: a , b and c invests rs . 4000 , rs . 2000 and rs . 6000 in a business . after one year a removed his money ; b and c continued the business for two more year . if the net profit after 3 years be rs . 3300 , then a ' s share in the profit is ?
Options: a ) 6000 , b ) 4000 , c ) 2000 , d ) 600 , e ) 300
Rationale: 4 * 12 : 2 * 36 : 4 * 36 2 : 3 : 6 2 / 11 * 3300 = 600 answer : d
Answer: d
Python program:
a = 2000 * 3
b = 6000 * 3
c = a + b 
d = 4000 + c 
e = 4000 / d
f = e * 4000
Problem: the avg weight of a , b & c is 80 kg . if d joins the group , the avg weight of the group becomes 82 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 81 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 95
Rationale: a + b + c = 3 * 80 = 240 a + b + c + d = 4 * 82 = 328 - - - - ( i ) so , d = 88 & e = 88 + 3 = 91 b + c + d + e = 81 * 4 = 324 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 328 – 324 = 4 a = e + 4 = 91 + 4 = 95 answer : e
Answer: e
Python program:
a = 82 * 4
b = 81 * 4
c = 82 * 4
d = 80 * 3
e = c - d
f = 3 + e 
g = b - f
h = a - g
Problem: rectangular tile each of size 20 cm by 30 cm must be laid horizontally on a rectangular floor of size 100 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 40 , b ) 15 , c ) 25 , d ) 32 , e ) 45
Rationale: "area of tile = 20 * 30 = 600 area of floor = 100 * 150 = 15000 no of tiles = 15000 / 600 = 25 so , the no of tile = 25 answer : c"
Answer: c
Python program:
a = 100 * 150
b = 20 * 30
c = a / b
Problem: 5000 was divided into two parts such a way that when first part was invested at 3 % and the second at 5 % , the whole annual interest from both the investments is rs . 144 , how much was put at 3 % ?
Options: a ) 10600 , b ) 11600 , c ) 12600 , d ) 10680 , e ) 20600
Rationale: "( x * 3 * 1 ) / 100 + [ ( 5000 - x ) * 5 * 1 ] / 100 = 144 3 x / 100 + ( 25000 – 5 x ) / 100 = 144 = > x = 10600 answer : a"
Answer: a
Python program:
a = 5 / 100
b = a * 5000
c = b - 144
d = 5 / 100
e = 3 / 100
f = d - e
g = c / f
Problem: if x is 30 percent more than y and y is 40 percent less than z , then x is what percent of z ?
Options: a ) 78 % , b ) 250 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %
Rationale: "z = 100 ; y = 60 so x = 78 x as % of z = 78 / 100 * 100 = > 78 % answer will be ( a )"
Answer: a
Python program:
a = 30 / 100
b = 1 + a 
c = 100 - 40
d = b * c
Problem: a train running at the speed of 60 km / hr crosses a pole in 12 seconds . find the length of the train .
Options: a ) 150 , b ) 278 , c ) 179 , d ) 200 , e ) 191
Rationale: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 12 = 200 meter answer : d"
Answer: d
Python program:
a = 60 * 1000
b = a / 3600
c = b * 12
Problem: if y > 0 , ( 7 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 7 y / 20 + 6 y / 20 = 13 y / 20 = 65 % answer c"
Answer: c
Python program:
a = 7 / 20
b = 3 / 10
c = a + b 
d = 100 * c
Problem: the value of a machine depreciates at 21 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 257615 , b ) $ 437615 , c ) $ 127615 , d ) $ 117615 , e ) $ 157615
Rationale: "the value of the machine after two years = 0.79 * 0.79 * 1 , 50,000 = $ 96,000 sp such that a profit of $ 24,000 is made = 93,615 + 24,000 = $ 1 , 17,615 d"
Answer: d
Python program:
a = 21 / 100
b = 1 - a
c = 21 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 21 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: what is the cp of rs 100 stock at 9 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 91.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 9 + 1 / 5 91.2 thus the cp is rs 91.2 . answer : c"
Answer: c
Python program:
a = 100 - 9
b = 1 / 5
c = a + b
Problem: the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 8000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,000
Rationale: x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 8000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 8000 ) * t = = = > 3 d = ts + 8000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 8000 t - 2 d = - 2 st + 8000 t 2 d = 2 st - 8000 t d = st - 4000 t x 13 : d = s * t st - 4000 t = s * t s - 4000 = s - 2000 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 8000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 8000 2 = 4000 d = s * t d = 4000 * ( 1 / 2 ) d = 2000 answer : e
Answer: e
Python program:
a = 8000 / 2
b = 1 / 2
c = a * b
Problem: the average of 15 numbers is 75 . average of the first 8 of them is 68 and that of the last 8.00001 is 77 . find the 8.000001 th number ?
Options: a ) 51 , b ) 87 , c ) 35 , d ) 75 , e ) 68
Rationale: sum of all the 15 numbers = 15 * 75 = 1,125 sum of the first 8 of them = 8 * 68 = 544 sum of the last 8 of them = 8 * 77 = 616 so , the 8 th number = 544 + 616 - 1,125 = 35 . answer : c
Answer: c
Python program:
a = 8 * 1
b = 15 * 75
c = 68 * 8
d = b - c
e = a - d
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 5 seconds to pass a telegraph post , then the length of the train is
Options: a ) 110 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 100 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 5 ) m = 100 m answer : option e"
Answer: e
Python program:
a = 12 / 10
b = a - 5
c = 12 / b
Problem: mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 48456 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) none of these
Rationale: ∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 48456 ⁄ 12 = 4038 answer a
Answer: a
Python program:
a = 100 - 60
b = a * 50
c = b / 100
d = c / 100
e = 48456 / d
f = 3 * 4
g = e / f
h = 100 - 60
i = h * 50
j = i / 100
k = j / 100
l = g * k
Problem: what is the sum of all the multiples of 10 between 0 and 100 ?
Options: a ) 500 , b ) 620 , c ) 550 , d ) 340 , e ) 440
Rationale: "the multiples of 10 between 0 and 100 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 and 100 . if these are all added together , the result is 550 . final answer : c"
Answer: c
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 10 
t = 2 + 4 
u = s + t
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 336 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 336 , 2 ( 7 / 5 ) w + 2 w = 336 solve the above equation to find : w = 70 m and l = 98 m . correct answer c ) 70"
Answer: c
Python program:
a = 7 / 5
b = 7 / 5
c = a + b 
d = c + 2 
e = 336 / d
Problem: difference of two numbers is 1650 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2490 , 4150 , e ) 2475 , 4125
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1650 5 * y / 3 – y = 1650 2 * y / 3 = 1650 y = [ ( 1650 * 3 ) / 2 ] = 2475 . one number = 2475 , second number = 5 * y / 3 = 4125 . answer e ."
Answer: e
Python program:
a = 7 / 5
b = 7 / 5
c = 1 - b
d = 1650 / c
e = a * d
Problem: a certain no . when divided by 140 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 11
Rationale: "explanation : 140 + 25 = 165 / 15 = 11 ( remainder ) e"
Answer: e
Python program:
a = 140 - 25
b = a - 4
c = b - 2
Problem: a room of 6 m 00 cm long and 8 m 00 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 12 , b ) 200 , c ) 600 , d ) 800 , e ) 20
Rationale: "explanation : area of the room = 600 * 800 sq cm size of largest square tile = h . c . f of 600 cm and 800 cm = 200 cm area of 1 tile = 200 * 200 sq cm no . of tiles required = ( 600 * 800 ) / ( 200 * 200 ) = 12 answer : a ) 12"
Answer: a
Python program:
a = 6 * 100
b = a + 0 
c = 8 * 100
d = c + 0 
e = b * d
f = 6 * 100
g = f + 0 
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
Problem: an inspector rejects 0.07 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2857 , d ) d ) 3000 , e ) e ) 3100
Rationale: "let the number of meters to be examined be x then , 0.07 % of x = 2 ( 7 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 2857 answer is c"
Answer: c
Python program:
a = 2 * 100
b = a / 0
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 154 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 176.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 154 ) / \ x â ˆ ’ 154 22.50 = > x â ˆ ’ ( 154 / 22.50 ) = 1 . = > x â ˆ ’ 154 = 22.50 . = > x = 176.50 rs . answer : c"
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 154 * b
d = 126 + 135 
e = c - d
f = e / 2
Problem: mother , her daughter and her grand child weighs 110 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 110 kg daughter + child = 60 kg mother = 110 - 60 = 50 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 50 = 10 kg so now daughter = 110 - ( mother + child ) = 110 - ( 50 + 10 ) = 50 kg answer : e"
Answer: e
Python program:
a = 110 - 60
b = a / 5
c = 60 - b