euclaise/mathqa_programs huggingface dataset:
Problem: machine a and machine g are each used to manufacture 660 sprockets . it takes machine a 10 hours longer to produce 660 sprockets than machine g . machine g produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: [ reveal ] spoiler : timeg : 660 / x timea : [ 660 / x + 10 ] 660 / x = [ 660 / x + 10 ] * 110 / 100 660 / x = 66 * 11 / x + 10 660 x + 10 = 66 * 11 * x 660 x + 6600 = 66 * 11 * x x = 100 plug in back to timea 660 / 100 + 10 = > 660 / 110 = 6
Answer: a
Python program:
a = 10 / 100
b = a + 1 
c = b * 660
d = c * 10
e = 10 / 100
f = e + 1 
g = f * 660
h = g - 660
i = d / h
j = 660 / i
Problem: for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 7 ] * [ 4 ] equivalent to ?
Options: a ) [ 28 ] , b ) [ 84 ] , c ) [ 42 ] , d ) [ 48 ] , e ) [ 14 ]
Rationale: "[ 7 ] * [ 4 ] = 21 * 2 = 42 = ( 1 / 2 ) ( 84 ) = [ 84 ] the answer is b ."
Answer: b
Python program:
a = 4 / 2
b = 3 * 7
c = a * b
d = c / 3
Problem: what is the tens digit of 6 ^ 21 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 21 has the form 5 n + 1 , so the tens digit of 6 ^ 21 is 5 . the answer is c ."
Answer: c
Python program:
a = 4 + 1 
b = 6 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: machine x and machine b are each used to manufacture 660 sprockets . it takes machine x 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine x . how many sprockets per hour does machine x produces ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: i think the correct answer is a . machine x produces at a speed of x sp / hour and b at a speed of b sp / hour . so , 660 / x = ( 660 / b ) + 10 and x = 1,1 x - - - > 1,1 * 660 = 660 + 11 x - - - > a = 6 , so answer a is correct
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = b * 100
d = 660 / c
Problem: a can do a piece of work in 2 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 3
Rationale: "a ' s 1 hour ' s work = 1 / 2 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 2 + 1 / 3 ) = 5 / 6 . b ' s 1 hour ' s work = ( 5 / 6 - 1 / 2 ) = 1 / 3 . therefore a alone will take 3 hours to do the work . e"
Answer: e
Python program:
a = 1 / 3
b = 1 / 2
c = 1 / 2
d = b - c
e = a - d
f = 1 / e
Problem: the ages of two persons differ by 16 years . 6 years ago , the elder one was 3 times as old as the younger one . what are their present ages of the elder person
Options: a ) 11 , b ) 66 , c ) 28 , d ) 30 , e ) 99
Rationale: "let ' s take the present age of the elder person = x and the present age of the younger person = x – 16 ( x – 6 ) = 3 ( x - 16 - 6 ) = > x – 6 = 3 x – 66 = > 2 x = 60 = > x = 60 / 2 = 30 answer : d"
Answer: d
Python program:
a = 3 * 6
b = 16 - 6
c = a + b 
d = c / 2
e = d + 16
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 10 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.4 % , b ) 9.6 % , c ) 9 % , d ) 9.8 % , e ) 10 %
Rationale: "the amount of chromium in the new 10 + 30 = 40 kg alloy is 0.12 * 10 + 0.08 * 30 = 3.6 kg , so the percentage is 3.6 / 40 * 100 = 9 % . answer : c"
Answer: c
Python program:
a = 12 * 10
b = a / 100
c = 8 * 30
d = c / 100
e = b + d 
f = 10 + 30 
g = e / f
h = g * 100
Problem: an automotive test consisted of driving a car the same distance 3 separate times , first at an average rate of 4 miles per hour , then 5 miles per hour , then 6 miles per hour . if the test took 37 hours to complete , how many miles was the car driven during the entire test ?
Options: a ) 100 , b ) 120 , c ) 180 , d ) 200 , e ) 240
Rationale: x is the segment to be traveled x / 4 + x / 5 + x / 6 = 37 or 74 x / 120 = 37 x = 60 miles . total distance = 3 * 60 = 180 miles c
Answer: c
Python program:
a = 1 / 6
b = 1 / 4
c = 1 / 5
d = b + c 
e = a + d 
f = 37 / e
g = f * 3
Problem: a can do a work in 12 days . b can do the same work in 24 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 12 b rate = 1 / 24 ( a + b ) rate = ( 1 / 12 ) + ( 1 / 24 ) = 1 / 8 a & b finish the work in 8 days correct option is c"
Answer: c
Python program:
a = 12 * 24
b = 12 + 24 
c = a / b
Problem: a , b and c invests rs . 2000 , rs . 3000 and rs . 4000 in a business . after 2 year a removed his money ; b and c continued the business for two more year . if the net profit after 3 years be rs . 4000 , then a ' s share in the profit is ?
Options: a ) 460 , b ) 289 , c ) 220 , d ) 400 , e ) 640
Rationale: "2 * 24 : 3 * 36 : 4 * 36 4 : 9 : 12 4 / 25 * 4000 = 640 answer : e"
Answer: e
Python program:
a = 3000 * 2
b = 4000 * 2
c = a + b 
d = 2000 + c 
e = 2000 / d
f = e * 2000
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 19 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 465 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 19 ) ( x - 8 ) ^ 2 = t + 19 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 465 + 19 = 484 = 22 ^ 2 = ( x - 8 ) ^ 2 hence , x = 30 cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 30 * 31 / 2 = 465 hence , answer is a ."
Answer: a
Python program:
a = 4 * 100
b = 19 - a
c = 4 * 100
d = 19 - c
e = d * 2
f = e + 1 
g = b * f
Problem: the average of 5 quantities is 10 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 19 , b ) 14 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: answer : a ( 5 x 10 - 3 x 4 ) / 2 = 19
Answer: a
Python program:
a = 5 * 10
b = 3 * 4
c = a - b
d = c / 2
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 70 paise per sq m is
Options: a ) rs . 258.80 , b ) rs . 358.80 , c ) rs . 458.80 , d ) rs . 520.80 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 70 / 100 ) = rs . 520.80 answer : d"
Answer: d
Python program:
a = 70 / 100
b = 25 * 12
c = 25 * 6
d = 2 * c
e = 12 * 6
f = e * 2
g = d + f 
h = b + g 
i = a * h
Problem: how many odd factors does 520 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 520 = 2 * 5 * 13 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 520 . answer : b ."
Answer: b
Python program:
a = 4 + 2 
b = a + 1 
c = b + 1
Problem: if the sum of two numbers is 22 and the sum of their squares is 460 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 12 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 460 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 460 + 2 xy so xy = 24 / 2 = 12 answer : c"
Answer: c
Python program:
a = 22 ** 2
b = a - 460
c = b / 2
Problem: what is the value of n if the sum of the consecutive odd integers from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: # of terms = ( n - 1 / 2 ) + 1 { ( last term - first term ) / 2 + 1 | sum = ( 1 + n ) / 2 * # of terms = ( n + 1 ) ^ 2 / 4 = 169 n + 1 = 13 * 2 n + 1 = 26 n = 25 . answer : b
Answer: b
Python program:
a = math.sqrt(169)
b = a * 2
c = 2 * 1
d = b - c
e = d + 1
Problem: the total number of plums that grew during each year on a certain plum tree was equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded to the nearest lower integer . ) during its 3 rd year , this plum tree grew 50 plums . how many plums did it grow during its 6 th year ?
Options: a ) a ) 41 , b ) b ) 38 , c ) c ) 35 , d ) d ) 29 , e ) e ) 28
Rationale: the answer shud be 38 . ( 50 - 3 - 4 - 5 = 38 ) yes , if you go the 50 - 3 way , then it will be 38 . if instead you go the 50 - 4 way ( which they have suggested ) , the answer will be 35 . as i said , there is ambiguity here . answer is c
Answer: c
Python program:
a = 50 - 4
b = 4 + 1 
c = a - b
d = c - 6
Problem: a can finish a work in 8 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 3 / 5 , b ) 3 / 6 , c ) 3 / 7 , d ) 3 / 8 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 8 b ' s 1 day work = 1 / 4 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 8 + 1 / 4 ) = 3 / 8 so in one day 3 / 8 work will be done answer : d"
Answer: d
Python program:
a = 1 / 8
b = 1 / 8
c = b * 2
d = a + c
Problem: donovan and michael are racing around a circular 500 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 500 / 45 = > 100 / 9 2 . speed / rate of michael = distance / time = > 500 / 40 = > 50 / 4 relative speed between them = 50 / 4 - 100 / 9 = > 25 / 36 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 500 , relative rate = 50 / 36 total time taken by micheal to surpass donovan = distance / rate = > 500 * 36 / 50 = > 3600 / 10 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . a"
Answer: a
Python program:
a = 500 / 40
b = 500 / 45
c = a - b
d = 500 / c
e = d / 40
Problem: if m = | | n – 3 | – 2 | , for how many values of n is m = 6 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: "m = | | n – 3 | – 2 | can be 4 only and only when n - 3 = + / - 8 . so there are 2 values of n answer : e"
Answer: e
Python program:
a = 6 + 2 
b = a - 6
Problem: in order to obtain an income of rs . 650 from 10 % stock at rs . 96 , one must make an investment of :
Options: a ) 3488 , b ) 6240 , c ) 2776 , d ) 2889 , e ) 7721
Rationale: "explanation : to obtain rs . 10 , investment = rs . 96 . to obtain rs . 650 , investment = = rs . 6240 answer : b ) 6240"
Answer: b
Python program:
a = 96 / 10
b = a * 650
Problem: in a group of 68 students , each student is registered for at least one of 3 classes – history , math and english . 20 - one students are registered for history , 20 - 6 students are registered for math , and thirty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: a u b u c = a + b + c - ab - bc - ac + abc 68 = 21 + 26 + 34 - ab - bc - ac + 3 = > ab + bc + ac = 16 exactly two classes = ab + bc + ac - 3 abc = 16 - 3 * 3 = 7 hence e
Answer: e
Python program:
a = 20 + 1 
b = 20 + 6 
c = a + b 
d = 20 + 10 
e = d + 4 
f = c + e 
g = f - 68
h = 2 * 3
i = g - h
Problem: 210 reputed college students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .
Answer: b
Python program:
a = 60 + 90 
b = 60 / 3
c = a + b 
d = 210 - c
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 18 kmph , find the speed of the stream ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 7 kmph , d ) 6 kmph , e ) 5 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 18 / 3 = 6 kmph . answer : d"
Answer: d
Python program:
a = 18 * 2
b = a / 3
c = 18 - b
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 62 . if the marks secured by reema was written as 50 instead of 85 then find the correct average marks up to two decimal places .
Options: a ) 63 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 62 = 2170 corrected total marks = 2170 - 50 + 85 = 2205 correct average = 2205 / 35 = 63 answer : a"
Answer: a
Python program:
a = 35 * 62
b = 85 - 50
c = a - b
d = c / 35
Problem: on the xy - coordinate plane , point a lies on the y - axis and point b lies on the x - axis . points a , b , and c form a right triangle with a 90 - degree angle at point c and the triangle has an area of 20 . if ac is parallel to the x - axis , and bc is parallel to the y - axis , which of the following could be the coordinates of point c ?
Options: a ) ( 8 , - 3 )
b ) ( 4 , 5 )
c ) ( - 5 , 7 )
d ) ( - 2 , - 20 )
e ) ( - 15 , - 3 )
Rationale: the area of the triangle formed will be : 1 / 2 * base * height = 1 / 2 * | ( x - coordinate of point c ) | * | ( y - coordinate of point c ) | = 20 thus | product of coordinates of point c | = 40 the answer is d .
Answer: d
Python program:
a = 20 / 2
Problem: 63 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 87 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 97
Rationale: "( 63 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 140 140 – 63 = 77 answer : b"
Answer: b
Python program:
a = 63 * 8
b = a / 30
c = b * 50
d = c / 6
e = d - 63
Problem: steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 90 mph . what is his average speed of travel for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 70 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 90 * 3 = 270 miles . therefore , total distance covered = 80 + 270 = 350 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 350 / 5 = 70 miles per hour . choice d"
Answer: d
Python program:
a = 90 * 3
b = 40 * 2
c = a + b 
d = 3 + 2 
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be odd ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 3 . answer : b ."
Answer: b
Python program:
a = 2 ** 2
b = math.comb(4, 2)
c = math.comb(2, 1)
d = b * c
e = a / d
Problem: in march mrs bil ' s earnings were 80 percent of the bil family ' s total income . in april mrs bil earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs bil ' s earnings were approximately what percent of the bil family ' s total income ?
Options: a ) 83 , b ) 56 , c ) 34 , d ) 12 , e ) 26
Rationale: lets say the family income is 100 in may , lee earned 80 family income is 20 in june , lee earned 20 % more than may , so it is ( 80 + 20 * 80 / 100 = 96 ) family income is same 20 in june lee ' s income percent is 96 * 100 / 116 ~ 83 ans is a
Answer: a
Python program:
a = 100 - 10
b = a / 100
c = b * 80
d = 100 - 80
e = 100 - 10
f = e / 100
g = f * 80
h = d + g 
i = c / h
j = i * 100
k = j + 4
Problem: how many prime numbers are between 29 / 4 and 87 / 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 29 / 4 = 7 . xxx 87 / 5 = 17 . xxx so we need to find prime numbers between 7 ( exclusive ) - 16 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b
Answer: b
Python program:
a = math.floor(2)
Problem: in digging a pond 25 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 1750 , b ) 1000 , c ) 2866 , d ) 2787 , e ) 1121
Rationale: "25 * 10 * 5 = 1750 answer : a"
Answer: a
Python program:
a = 25 * 10
b = a * 5
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 48 kmph , find the speed of the stream ?
Options: a ) 16 kmph , b ) 19 kmph , c ) 14 kmph , d ) 11 kmph , e ) 13 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 48 / 3 = 16 kmph . answer : a"
Answer: a
Python program:
a = 48 * 2
b = a / 3
c = 48 - b
Problem: what is the total number of integers between 100 and 500 ( exclusive ) that are divisible by 5 ?
Options: a ) 51 , b ) 63 , c ) 79 , d ) 66 , e ) 42
Rationale: 105 , 110 , 115 , . . . , 490,495 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 495 - 105 ) / ( 5 ) + 1 = 78 + 1 = 79 answer is c
Answer: c
Python program:
a = 500 - 100
b = a / 5
c = b + 1
Problem: a shopkeeper sold 10 articles at the cost price of 12 articles . then find the profit % or lost %
Options: a ) - 10 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: here 10 articles selling price = 12 articles cost price so the difference = 12 - 10 = 2 % of profit = 2 * 100 / 10 = 20 % correct option is d
Answer: d
Python program:
a = 12 - 10
b = a / 10
c = b * 100
Problem: venus travels around the sun at a speed of approximately 21.9 miles per second . the approximate speed is how many miles per hour ?
Options: a ) 64,420 , b ) 78,840 , c ) 83,160 , d ) 88,970 , e ) 94,320
Rationale: 21.9 * 3600 = 78,840 the answer is b .
Answer: b
Python program:
a = 21 * 9
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: 150 ml solution contains 45 ml sulphuric acid 400 ml solution contains 48 ml sulphuric acid adding 550 ml solution contains 93 ml sulphuric acid 93 / 550 ≈ 90 / 540 = 1 / 6 answer is d
Answer: d
Python program:
a = 150 * 30
b = a / 100
c = 400 * 12
d = c / 100
e = b + d 
f = 150 + 400 
g = e / f
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 18 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 9 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 18 = > x = 3 so deepak age is = 3 ( 3 ) = 9 answer : d"
Answer: d
Python program:
a = 18 - 6
b = a * 3
c = b / 4
Problem: a and b can do a piece of work in 8 days . b and c can do it in 12 days and a and c in 16 days . working together they will complete the work in how many days ?
Options: a ) 3.33 days , b ) 8.33 days , c ) 3.99 days , d ) 7.38 days , e ) 2.88 days
Rationale: a + b = 1 / 8 b + c = 1 / 12 c + a = 1 / 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ( a + b + c ) = 1 / 8 + 1 / 12 + 1 / 16 = 13 / 48 a + b + c = 13 / 96 96 / 13 = 7.38 days answer : d
Answer: d
Python program:
a = 1/(16)
b = 1/(8)
c = 1/(12)
d = b + c 
e = a + d 
f = e / 2
g = 1/(f)
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 19 % home electronics ; 10 % food additives ; 24 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 90 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "14 % microphotonics ; 19 % home electronics ; 10 % food additives ; 24 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 19 + 10 + 24 + 8 ) = 25 % basic astrophysics . 25 % of 360 ° is 90 ° . answer : b ."
Answer: b
Python program:
a = 14 + 19 
b = a + 10 
c = b + 24 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: a will was written such that an estate would be divided among 4 beneficiaries with the remainder donated to charity . one stipulation in the will is that no one beneficiary can receive an amount within 20 % of another ' s amount . if one of the beneficiaries received $ 40000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 4 beneficiaries ?
Options: a ) $ 12436 , b ) $ 13344 , c ) $ 71234 , d ) $ 15736 , e ) $ 19403
Rationale: 1 st - 40,000 . 2 nd - 0.8 * 40,000 = 32,000 3 rd - 0.8 * 32,000 = 25,600 4 th - 0.8 * 25,600 = ~ 20,480 range = 40,000 - 20,480 = 19520 answer : e .
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 40000 * b
d = 20 / 100
e = 1 - d
f = c * e
g = 20 / 100
h = 1 - g
i = f * h
j = 40000 - i