euclaise/mathqa_programs huggingface dataset:
Problem: a rich aristocrat decided that he would give every man rs . 45 and every women rs . 60 . only one nineth of the man and only one twelfth of the women collected their dues . can u tell me how much money thath aristocrat spent if their were 3552 people in total
Options: a ) 17760 , b ) 18540 , c ) 16320 , d ) 14640 , e ) 15640
Rationale: iman = 45 and 1 women = 60 then 1 / 9 man = 1 / 9 * 45 = 5 and 1 / 12 of women = 1 / 12 * 60 = 5 total people 3552 = 3552 * 5 = 17760 answer : a
Answer: a
Python program:
a = 2 * 10
b = 4 * 10
c = b * 10
d = 100 * 100
e = 3600 * 2
f = d + e 
g = 4 * 10
h = f + g 
i = c + h 
j = i + 100 
k = a + j 
l = k * 1
Problem: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour slower than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 6 m / h - - > 3 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 3 ^ 2 d ^ 2 = 25 = 5 answer option a
Answer: a
Python program:
a = 1 / 2
b = 8 * a
c = b ** 2
d = 8 - 2
e = 1 / 2
f = d * e
g = f ** 2
h = c + g 
i = math.sqrt(h)
Problem: a fill pipe can fill 1 / 3 of cistern in 20 minutes in how many minutes , it can fill 3 / 4 of the cistern ?
Options: a ) 15 min , b ) 45 min , c ) 25 min , d ) 40 min , e ) 50 min
Rationale: "1 / 3 of the cistern can fill in 20 min 3 / 4 of the cistern can fill in = 20 * 3 * 3 / 4 = 45 min answer is b"
Answer: b
Python program:
a = 20 / 1
Problem: a cube is divided into 125 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "each side of the cube has 5 x 5 = 25 cubelets . only the interior cubelets are painted one colour . on each side , 3 x 3 = 9 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 9 = 54 the answer is d ."
Answer: d
Python program:
a = 4 * 2
b = a * 3
c = 125 - b
d = c / 2
Problem: indu gave bindu rs . 3750 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 4 , e ) 9
Rationale: "3750 = d ( 100 / 4 ) 2 d = 6 answer : c"
Answer: c
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 3750 * c
e = d - 3750
f = 4 / 100
g = 3750 * f
h = g * 2
i = e - h
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 37 , the mean is how much greater than the median ?
Options: a ) 6 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 37 ) / 5 = ( 5 x + 50 ) / 5 = x + 10 median = x + 4 thus mean - median = x + 10 - ( x + 4 ) = 6 answer = a"
Answer: a
Python program:
a = 2 + 4 
b = a + 7 
c = b + 37 
d = 4 + 1 
e = c / d
f = e - 4
Problem: the flow of water through a drainage pipe was monitored for a 3 - hour period . in the second hour , the rate of flow was 36 gallons per hour , which was 50 percent faster than the rate of flow for the first hour . if 25 percent more water flowed through the pipe in the third hour than it did in the second , how many gallons of water flowed through the pipe during the entire 3 hours ?
Options: a ) 106.25 , b ) 105.5 , c ) 105.75 , d ) 106 , e ) 105.0
Rationale: rate of flow of water in second hour = 36 gallons per hour rate of flow of water in first hour = 36 / ( 3 / 2 ) = 24 gallons per hour rate of flow of water in third hour = ( 125 / 100 ) * 36 = ( 5 / 4 ) * 36 = 45 gallons per hour number of gallons of water that flowed through the pipe during the entire 3 hours = 24 + 36 + 45 = 105 gallons answer e
Answer: e
Python program:
a = 3 / 2
b = 36 / a
c = const_0_25 * 36
d = 36 + c 
e = b + d 
f = e + 36
Problem: running at the same constant rate , 6 identical machines can produce a total of 330 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2200 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 330 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 330 x = ( 10 x 4 x 330 ) / ( 6 ) x = 2200 . answer : c"
Answer: c
Python program:
a = 330 / 6
b = a * 4
c = b * 10
Problem: if a light flashes every 6 seconds , how many times will it flash in 1 / 4 of an hour ?
Options: a ) 51 , b ) 151 , c ) 251 , d ) 351 , e ) 451
Rationale: "in 1 / 4 of an hour there are 15 * 60 = 900 seconds the number of 6 - second intervals = 900 / 6 = 150 after the first flash , there will be 150 more flashes for a total of 151 . the answer is b ."
Answer: b
Python program:
a = 3600 / 4
b = a * 3
c = b / 6
Problem: a sum of rs . 1360 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 13660 = > 17 x / 12 = 13660 = > 13660 x 12 / 17 = rs . 960 hence , b ’ s share = rs . ( 960 / 4 ) = rs . 240 . answer c"
Answer: c
Python program:
a = 1360 / 10
b = a * 2
c = b - 12
d = c - 12
Problem: find the compound interest on $ 20000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 1648.64 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: "principle = $ 20000 rate = 2 % half yearly = 4 half years amount = 20000 * ( 1 + 2 / 100 ) ^ 4 = 20000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 21648.64 c . i . = 21648.64 - 20000 = $ 1648.64 answer is b"
Answer: b
Python program:
a = 4 / 100
b = a / 2
c = b + 1 
d = c ** 4
e = d * 20000
f = e - 20000
Problem: 78 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 26 , d ) 15 , e ) 16
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 78 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 78 x 5 x 12 x = ( 78 x 5 x 12 ) / ( 30 x 6 ) x = 26 . answer : c"
Answer: c
Python program:
a = 78 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: can you find a 6 digit number under 5 lakh such that the sum of it ' s digits is 43 ?
Options: a ) 588338 , b ) 499449 , c ) 399826 , d ) 788392 , e ) 622975
Rationale: b the required number is 499449 . the maximum sum of a number under 5 lakh will be of the number 499999 i . e . 49 . thus the required number must be close to 499999 . the root of 499999 ~ 707.106 by calculating the square of 707 , we get 499849 which is the answer .
Answer: b
Python program:
a = 6 + 1 
b = a * 100
c = 6 + 1 
d = b + c 
e = d ** 2
Problem: a real estate agent received a 6 % commission on the selling price of a house . if his commission was $ 8880 , what was the selling price of the house ?
Options: a ) $ 234000 , b ) $ 227000 , c ) $ 148000 , d ) $ 479000 , e ) $ 337,000
Rationale: 6 % x = 8,880 : x = selling price of house . x = $ 148,000 : solve for x correct answer c .
Answer: c
Python program:
a = 6 / 100
b = 8880 / a
Problem: there is a total of 84 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 2 / 7 . what is the probability that the marble will be either red or blue ?
Options: a ) 3 / 7 , b ) 11 / 14 , c ) 13 / 28 , d ) 19 / 28 , e ) 29 / 42
Rationale: p ( red or blue ) = 1 - p ( white ) - p ( green ) = 28 / 28 - 7 / 28 - 8 / 28 = 13 / 28 the answer is c .
Answer: c
Python program:
a = 1 / 4
b = 2 / 7
c = a + b 
d = 1 - c
Problem: ( x + 7 ) is a factor in x ^ 2 - mx - 35 . what is the value of m ?
Options: a ) - 3 , b ) - 2 , c ) - 4 , d ) - 5 , e ) - 6
Rationale: "i solved the second degree equation and found it like this : x ^ 2 - mx - 35 ( x - 5 ) ( x + 7 ) x = 5 or x = - 7 substituting both values for x in the equation we find : x ^ 2 - mx - 35 = > ( - 7 ) ^ 2 - m ( - 7 ) = 35 = > 49 + 7 m = 35 = > 7 m = 35 - 49 = - 14 = > m = - 2 and with 5 , using a similar process we end up with : ( 5 ) ^ 2 - m ( 5 ) = 35 - 10 = 5 m m = - 2 ao , ans b"
Answer: b
Python program:
a = 35 / 7
b = a - 7
Problem: the product of two positive integers is 575 and their difference is 2 . what is the bigger number ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "let ' s use trial and error to find the two numbers . 27 * 25 = 675 ( too high ) 25 * 23 = 575 the answer is c ."
Answer: c
Python program:
a = 575 / 2
b = 575 / a
c = b * 4
d = c + 10 
e = d - 1
Problem: at a certain pizza parlor , the diameter of a large pizza is 40 % larger than the diameter of a small pizza . what is the percent increase in total amount of pizza , from a small to a large ?
Options: a ) 20 % , b ) 40 % , c ) 64 % , d ) 80 % , e ) 96 %
Rationale: a real world problem — - yum ! — - but again , the specifics of the shape don ’ t matter . diameter increases 40 % , so k = 1.4 in this case . “ amount of pizza ” just means the area of the circle , so k ^ 2 = ( 1.4 ) ^ 2 = 1.96 , which is the multiplier for a 96 % increase . that ’ s the percent increase in area . answer = e
Answer: e
Python program:
a = 100 + 40 
b = a ** 2
c = 100 ** 2
d = b - c
e = d / 100
Problem: on a map , 2.5 inches represent 40 miles . how many miles approximately is the distance if you measured 155 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 990.4 , b ) 970 , c ) 972 , d ) 976.4 , e ) 975
Rationale: "1 inch = 2.54 cm 2.5 inch = 2.54 * 2.5 cm 6.35 cm = 40 miles 155 cms = 40 / 6.35 * 155 = 976.4 miles answer : d"
Answer: d
Python program:
a = 155 / 2
b = 40 / 2
c = a * b
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 48 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: 20 x + 48 = 21 ( x – 5 ) x = 57 answer : c
Answer: c
Python program:
a = 20 + 1 
b = a * 5
c = b - 48
Problem: if two integers x , y ( x > y ) are selected from - 4 to 4 ( inclusive ) , how many cases are there ?
Options: a ) 27 , b ) 30 , c ) 33 , d ) 36 , e ) 39
Rationale: "there are 9 integers from - 4 to 4 inclusive . 9 c 2 = 36 . the answer is d ."
Answer: d
Python program:
a = 4 + 4 
b = 4 + 2 
c = a + b 
d = 4 + 1 
e = c + d 
f = e + 4 
g = f + 4 
h = g + 2 
i = h + 1
Problem: a man is 24 years older than his son . in four years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 4 = 2 ( x + 4 ) â € ¹ = â € º x + 28 = 2 x + 8 x = 20 . answer c"
Answer: c
Python program:
a = 2 * 2
b = a - 2
c = 24 - b
d = 2 - 1
e = c / d
Problem: a car is purchased on hire - purchase . the cash price is $ 23 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly instalments . interest is charged at 12 % p . a . what is the monthly instalment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 515 , d ) $ 543 , e ) $ 552
Rationale: "explanation : cash price = $ 23 000 deposit = 10 % ã — $ 23 000 = $ 2300 loan amount = $ 23000 â ˆ ’ $ 2300 number of payments = 60 = $ 20700 i = p * r * t / 100 i = 12420 total amount = 20700 + 12420 = $ 33120 regular payment = total amount / number of payments = 552 answer : e"
Answer: e
Python program:
a = 23 * 1000
b = 10 / 100
c = 1 - b
d = a * c
e = d / 60
f = 12 / 100
g = f / 12
h = 23 * 1000
i = 10 / 100
j = 1 - i
k = h * j
l = g * k
m = e + l
Problem: on the number line , if x is halfway between - 8 and 4 , and if y is halfway between - 2 and 6 , what number is halfway between x and y ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: x = - 2 and y = 2 . the answer is c .
Answer: c
Python program:
a = negate + (
Problem: a survey was sent to 90 customers , 15 of whom responded . then the survey was redesigned and sent to another 50 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 28 % , e ) 63 %
Rationale: "rate of first survey = 15 / 90 rate of second survey = 9 / 50 % response rate increase ( 9 / 50 - 15 / 90 ) / ( 15 / 90 ) = 8 % answer is c = 8 %"
Answer: c
Python program:
a = 9 / 50
b = 15 / 90
c = a - b
d = c * 100
e = math.floor(d)
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 50 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 86 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 50 % more than company a ' s assets which is 150 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 75 a + b = 175 kw = 150 kw / ( a + b ) * 100 = 150 / 175 * 100 = 85.7 % or 86 % answer : c"
Answer: c
Python program:
a = 100 + 50 
b = 100 + 50 
c = b / 2
d = 100 + c 
e = a / d
f = e * 100
Problem: a rectangular field is to be fenced on three sides leaving a side of 80 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 44 ft , b ) 97 ft , c ) 22 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 80 x breadth = 680 breadth = 8.5 feet area to be fenced = 2 b + l = 2 ( 8.5 ) + 80 = 97 feet answer : b ) 97 ft"
Answer: b
Python program:
a = 680 / 80
b = a * 2
c = b + 80
Problem: rs . 120 are divided among a , b , c such that a ' s share is rs . 20 more than b ' s and rs . 20 less than c ' s . what is b ' s share
Options: a ) rs 10 , b ) rs 20 , c ) rs 24 , d ) rs 28 , e ) none of these
Rationale: explanation : let c = x . then a = ( x � 20 ) and b = ( x � 40 ) . x + x - 20 + x - 40 = 120 or x = 60 . a : b : c = 40 : 20 : 60 = 2 : 1 : 3 . b ' s share = rs . 120 * ( 1 / 6 ) = rs . 20 answer : b
Answer: b
Python program:
a = 120 - 20
b = 20 + 20 
c = a - b
d = c / 3
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 5 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 5 so sum of 3 should be 15 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 6 and 6 so a has to be 3 b"
Answer: b
Python program:
a = 3 * 5
b = a - 10
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 10 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 20 , d ) 16 , e ) 12
Rationale: "7 * 5 : 10 * x = 7 : 10 x = 20 answer : c"
Answer: c
Python program:
a = 7 / 5
b = 10 / 7
c = a * b
d = c * 10
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 25 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 5 . hence , c is the correct answer ."
Answer: c
Python program:
a = 40 - 25
b = 40 - 19
c = a / b
Problem: if x is an integer such that 0 < x < 12 , 1 < x < 15 , 10 > x > 5 , 11 > x > 8 , and x + 2 < 12 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "0 < x < 12 , 1 < x < 15 , - 5 < x < 10 8 < x < 11 x < 10 from above : 8 < x < 10 - - > x = 9 . answer : d ."
Answer: d
Python program:
a = 12 - 2
b = a - 2
Problem: a sum of money lent out at s . i . amounts to rs . 660 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 540 , d ) s . 740 , e ) s . 516
Rationale: "s . i for 5 years = ( 1020 - 660 ) = rs . 360 . s . i . for 2 years = 360 / 5 * 2 = rs . 144 . principal = ( 660 - 144 ) = rs . 516 . answer : e"
Answer: e
Python program:
a = 1020 - 660
b = a / 5
c = b * 2
d = 660 - c
Problem: what number has a 5 : 1 ratio to the number 8 ?
Options: a ) 22 , b ) 40 , c ) 88 , d ) 52 , e ) 12
Rationale: 5 : 1 = x : 8 x = 40 answer : b
Answer: b
Python program:
a = 8 * 5
Problem: for an agricultural experiment , 500 seeds were planted in one plot and 200 were planted in a second plot . if exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 35.7 % , b ) 25 % , c ) 32 % , d ) 30.8 % , e ) 60 %
Rationale: "from the first plot 0.30 * 500 = 150 ; from the second plot 0.50 * 200 = 100 ; total percent = ( 150 + 100 ) / ( 500 + 200 ) = 0.357 . answer : a ."
Answer: a
Python program:
a = 30 / 100
b = a * 500
c = 50 / 100
d = c * 200
e = b + d 
f = 500 + 200 
g = e / f
h = g * 100
Problem: what is the total number of prime numbers less than 70 ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: solution prime numbers less than 70 are = 12 . 2,3 , 5,7 , 11,13 , 17,19 , 23,29 , 31,37 , 41,43 , 47,53 , 59,61 , and 67 their number is 19 . answer c
Answer: c
Python program:
a = 10 + 3 
b = a + 4 
c = 10 + 3 
d = c + 4 
e = d + 2 
f = max(b)
Problem: 3 / 5 of all married couples have more than one child . 1 / 2 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 1 / 2 of 100 couples have more than 3 kids = 50 couples . this implies that 50 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 40 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 50 = 10 . fraction will be 10 / 100 = 1 / 10 . option b"
Answer: b
Python program:
a = 3 / 5
b = 2 / 5
c = a - b
Problem: at a special sale , 6 tickets can be purchased for the price of 3 tickets . if 6 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 6 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 50 % , e ) 66.6 %
Rationale: let the price of a ticket be rs . 100 , so 3 tickets cost 300 & 6 tickets cost 600 6 tickets purchased at price of 3 tickets ie . , for 300 , so amount saved s rs . 300 , % of 6 tickets = ( 300 / 600 ) * 100 = 50 % answer : d
Answer: d
Python program:
a = 6 * 6
b = 3 * 6
c = a - b
d = c * 100
e = 6 * 6
f = d / e
Problem: a 4 - digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1 , 2 , 4 , and 6 at all . if repeated digits are allowed , what is the probability that it has at least one even digit ?
Options: a ) 23 / 24 , b ) 31 / 36 , c ) 55 / 64 , d ) 65 / 81 , e ) 75 / 121
Rationale: p ( no even digits ) = 2 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 16 / 81 p ( at least one even digit ) = 1 - 16 / 81 = 65 / 81 the answer is d .
Answer: d
Python program:
a = 10 - 4
b = a ** 4
c = 4 ** 4
d = b - c
e = 10 - 4
f = e ** 4
g = d / f
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 15 % ?
Options: a ) 228 , b ) 480 , c ) 267 , d ) 288 , e ) 544
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 96 sp = cp - loss = 640 - 96 = rs . 544 answer : e"
Answer: e
Python program:
a = 800 * 100
b = 25 + 100 
c = a / b
d = 800 * 100
e = 25 + 100 
f = d / e
g = f * 15
h = g / 100
i = c - h
Problem: the speed of a train is 120 kmph . what is the distance covered by it in 10 minutes ?
Options: a ) 26 kmph , b ) 20 kmph , c ) 28 kmph , d ) 30 kmph , e ) 40 kmph
Rationale: "120 * 10 / 60 = 20 kmph answer : b"
Answer: b
Python program:
a = 10 / const_60
b = a * 120
Problem: from a total of 4 boys and 4 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 36 , c ) 60 , d ) 120 , e ) 240
Rationale: "answer = b = 36 no of 4 person committees that can be formed = 4 c 2 * 4 c 2 = 36 answer b"
Answer: b
Python program:
a = 3 * 4
b = 4 * 2
c = a * b
Problem: if an article is sold at 20 % profit instead of 14 % profit , then the profit would be rs . 180 more . what is the cost price ?
Options: a ) rs . 1000 , b ) rs . 2000 , c ) rs . 3000 , d ) rs . 4000 , e ) rs . 5200
Rationale: "explanation : let the cost price of an article be rs . x . ( 20 % of x ) - ( 14 % of x ) = 180 20 x / 100 - 14 x / 100 = 105 = > 6 x = 180 * 100 = > x = 3000 cost price = rs . 3000 answer : c"
Answer: c
Python program:
a = 180 / 14
b = a * 100
Problem: find the greatest number that exactly divides 35 , 91 and 840 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the greatest number that exactly divides 35 , 91 and 840 is the hcf of the three numbers . so , calculating hcf we get the answer 7 . answer : c"
Answer: c
Python program:
a = 840 - 91
b = a - 35
c = 91 - 35
d = math.gcd(b, c)
e = 840 - 91
f = math.gcd(d, e)
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 3 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 168 , b ) 144 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 3 ) * 360 = 120 gallons . remaning paint = 240 gallons paint used in the second week = ( 1 / 5 ) * 240 = 48 gallons total paint used = 168 gallons . option a"
Answer: a
Python program:
a = 360 / 3
b = a * 1
c = 360 / 3
d = c * 1
e = 360 - d
f = e / 5
g = b + f