euclaise/mathqa_programs huggingface dataset:
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation g of the mean , what percent of the distribution is less than m + g ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d"
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: pradeep has to obtain 35 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 800 , d ) 1000 , e ) 900
Rationale: explanation : let their maximum marks be x . then , 35 % of x = 185 + 25 = > 35 / 100 x = 210 x = ( 210100 / 35 ) x = 600 . answer : b
Answer: b
Python program:
a = 185 + 25 
b = 35 / 100
c = a / b
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 64 , d ) 76 , e ) 88
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.22 ( 800 ) = 264 the answer is c ."
Answer: c
Python program:
a = 160 / 800
b = a * 100
c = 100 - b
d = c - 22
e = 100 - 75
f = d - e
g = f * 800
h = g / 100
i = 100 - 75
j = i * 800
k = j / 100
l = h - k
Problem: a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 120 = 10 * 12 x = 22 the answer is b ."
Answer: b
Python program:
a = 2 * 6
b = 2 * 5
c = a + b 
d = 2 * 5
e = 2 * 6
f = d * e
g = 120 - f
h = 6 * g
i = 2 * 6
j = 2 * 5
k = i + j 
l = k ** 2
m = h + l 
n = math.sqrt(m)
o = c + n 
p = o / 2
Problem: find the area of a parallelogram with base 14 cm and height 24 cm .
Options: a ) 336 , b ) 384 , c ) 345 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 14 * 24 = 336 cm 2 answer : option a"
Answer: a
Python program:
a = 14 * 24
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 35 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 25 % , b ) 28 % , c ) 30 % , d ) 32.5 % , e ) 35 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.35 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 35 % income the savings increased by 100 % . or s = . 35 i or s = 35 % of income e is the answer"
Answer: e
Python program:
a = 100 + 35 
b = a + 100 
c = 2 * 100
d = b - c
e = d / 100
f = e * 100
Problem: how is 5 % expressed as a decimal fraction ?
Options: a ) 0.5 , b ) 0.05 , c ) 0.005 , d ) 0.0005 , e ) 5
Rationale: "5 / 100 = 0.05 answer : b"
Answer: b
Python program:
a = 5 / 100
Problem: 34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 6 feet , and the diagonal of the rectangular plate was 10 ft . what is height of the of the cylinder ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 8 . correct answer c .
Answer: c
Python program:
a = 10 ** 2
b = 6 ** 2
c = a - b
d = math.sqrt(c)
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 160 meters , d ) 850 meters , e ) none of these
Rationale: train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d is the answer .
Answer: d
Python program:
a = 100 - 64
b = a * const_0_2778
c = b * 85
Problem: how many three digit numbers q are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples q - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Python program:
a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: how many numbers from 2 to 9 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 4 , e ) e ) 8
Rationale: "2 / 2 = 1 and 9 / 2 = 4 4 - 1 = 3 3 + 1 = 4 numbers . answer : d"
Answer: d
Python program:
a = 9 / 2
b = math.floor(a)
c = b * 2
d = 2 / 2
e = math.floor(d)
f = e + 1 
g = f * 2
h = c - g
i = h / 2
j = i + 1
Problem: p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is q ' s share ?
Options: a ) 114 , b ) 120 , c ) 134 , d ) 144 , e ) none of these
Rationale: explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 b ' s share = 378 * ( 8 / 21 ) = 18 * 8 = 144 . answer : option d
Answer: d
Python program:
a = 4 * 2
b = 378 * a
c = 10 * 2
d = c + 1 
e = b / d
Problem: if a ( a + 5 ) = 36 and b ( b + 5 ) = 36 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 5 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 4 then b = - 9 or if a = - 9 then b = 4 but in each case a + b = - 9 + 4 = - 5 answer : option b"
Answer: b
Python program:
a = 36 / 10
b = 36 / 10
c = 36 / b
d = a + c
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 2013 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 672
Rationale: "same logic but with application of factorials . 2 * 4 * 6 * 8 * . . . * n = 2 ( 1 * 2 * 3 * 4 * . . . n / 2 ) = 2 * ( n / 2 ) ! now we have : 2 * ( n / 2 ) ! / 2013 = 2 * ( n / 2 ) ! / ( 3 × 11 × 61 ) for the expression 2 * ( n / 2 ) ! to be divisible by 2013 min value of n / 2 should be 61 . so n / 2 = 61 = > n = 122 answer d ."
Answer: d
Python program:
a = 10 + 1 
b = 2013 / a
c = b / 3
d = 2 * c
Problem: billy worked for 3 straight hours on his homework questions . if he solved 132 questions in the third hour , which was twice as many as he solved in the second hour , and 3 times as many questions as he solved in the first hour , how many questions did he solve total ?
Options: a ) 242 , b ) 312 , c ) 424 , d ) 525 , e ) 622
Rationale: total questions solved = questions solved in 3 rd hr + in 2 nd hr + in 1 st hr 132 + 132 / 2 + 132 / 3 = 242 a is the answer
Answer: a
Python program:
a = 10 + 10 
b = a + 2 
c = 1 / 3
d = 132 * c
e = d * 2
f = e + 132 
g = b + f
Problem: if e = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x is between
Options: a ) 0 and 3 , b ) 3 and 6 , c ) 6 and 9 , d ) 9 and 12 , e ) 12 and 15
Rationale: my attempt : if e = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x would be when y is minimum . let y ^ 4 be 0 . now x ^ 4 = 100 . x should be definitely greater than 3 but less than 4 . the only option that fits this range is b hence answer is - - b ) 3 and 6 .
Answer: b
Python program:
a = 4 * 4
b = a + 10 
c = b + 10
Problem: a man buys an item at rs . 750 and sells it at the loss of 10 percent . then what is the selling price of that item
Options: a ) rs . 660 , b ) rs . 675 , c ) rs . 860 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 90 % of 750 = 90 / 100 * 750 = 675 option b"
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = 750 * b
Problem: the average of 13 numbers is 60 . average of the first 7 of them is 55 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 32 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 55 = 385 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 385 - 780 = 32 . answer : a"
Answer: a
Python program:
a = 8 * 61
b = 13 * 60
c = 55 * 7
d = b - c
e = a - d
Problem: how many two - digit numbers yield a remainder of 1 when divided by both 6 and 15 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "easier to start with numbers that are of the form 15 p + 1 - - - > 16,31 , 46,61 , 76,91 . out of these 2 ( 31,61 ) are also of the form 6 q + 1 . thus 2 is the answer . c is the correct answer ."
Answer: c
Python program:
a = 15 * 6
b = 1 + a 
c = 15 * 6
d = b - c
Problem: for what value of â € œ k â €  will the equation ( 2 kx 2 + 3 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 16 / 9
Rationale: for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 3 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 9 answer : e
Answer: e
Python program:
a = 2 + 2 
b = 2 ** a
c = 3 ** 2
d = b / c
Problem: if 9 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 80 , b ) 63 , c ) 120 , d ) 1008 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 9 c 2 for vertical 8 c 2 total parallelogram is 9 c 2 * 8 c 2 = 36 * 28 = 1008 answer : d"
Answer: d
Python program:
a = 9 - 1
b = 9 * a
c = b / 2
d = 8 - 1
e = 8 * d
f = e / 2
g = c * f
Problem: entry fee in an examination was re . 1 . later , this was reduced by 25 % which increased the sale by 20 % . the percentage increase in the number of visitors is
Options: a ) 60 , b ) 50 , c ) 66 , d ) 54 , e ) none
Rationale: sol . let the total original sale be rs . 100 . then , original number of visitors = 100 . new number of visitors = 120 / 0.75 = 160 . ∴ increase % = 60 % . answer a
Answer: a
Python program:
a = 20 * 100
b = a / 100
c = b + 100 
d = 25 / 100
e = 1 - d
f = c / e
g = f - 100
Problem: a , b and c can do a piece of work in 7 days , 21 days and 28 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 8 / 19 , c ) 5 , d ) 67 , e ) 9
Rationale: "1 / 7 + 1 / 21 + 1 / 28 = 19 / 84 = > 84 / 19 = > 4 8 / 19 days answer : b"
Answer: b
Python program:
a = 1/(28)
b = 1/(7)
c = 1/(21)
d = b + c 
e = a + d 
f = 1/(e)
Problem: a retailer bought a machine at a wholesale price of $ 126 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 168
Rationale: my solution : wholesale price = 126 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 126 + 1 / 5 ( 126 ) x = 168 ; answer : e
Answer: e
Python program:
a = 126 * 20
b = a / 100
c = 126 + b 
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
Problem: if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is
Options: a ) 18.20 , b ) 18.33 , c ) 18 , d ) 18.3 , e ) none of these
Rationale: "explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = ( 110 x 20 / 120 ) = rs . 18.33 answer : b"
Answer: b
Python program:
a = 10 + 110 
b = a - 100
c = 10 + 110 
d = b / c
e = 110 * d
Problem: the grade point average of the entire class is 85 . if the average of one third of the class is 97 , what is the average of the rest of the class ?
Options: a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80
Rationale: "let x be the number of students in the class . let p be the average of the rest of the class . 85 x = ( 1 / 3 ) 97 x + ( 2 / 3 ) ( p ) x 255 = 97 + 2 p 2 p = 158 p = 79 . the answer is d ."
Answer: d
Python program:
a = 85 * 4
b = a - 97
c = 4 - 1
d = b / c
Problem: the diameter of a wheel is 0.7 m . how far will it travel in 200 revolutions
Options: a ) 4.4 m , b ) 220 m , c ) 440 m , d ) 560 , e ) 650
Rationale: diameter ( d ) = 0.7 m circumference of the wheel , = 2 * pi * r = d * pi = 0.7 * 3.14 = 2.198 m . in one revolution , wheel will covered = 2.198 m , so , in 200 revolution , it will cover = 200 * 2.198 = 4.396 m = 440 m ( approx ) . answer : option c
Answer: c
Python program:
a = 1000 + const_60 
b = 2 * 10
c = b + 4 
d = a + c 
e = 1000 * 10
f = d / e
g = const_0_25 - f
h = 3 + g 
i = h * 0
j = i * 200
Problem: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 35 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 45 % , b ) 65 % , c ) 85 % , d ) 115 % , e ) 125 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.35 ( 5 b + x ) = b + x 0.75 b = 0.65 x x = 1.15 b the answer is d ."
Answer: d
Python program:
a = 35 * 100
b = 20 * 100
c = a - b
d = 100 - 35
e = c / d
f = e / 20
g = f * 100
Problem: two 6 faced dice are thrown together . the probability that both show the same number on them is ?
Options: a ) 1 / 6 , b ) 1 / 12 , c ) 1 / 18 , d ) 1 / 2 , e ) 1 / 4
Rationale: "it all 3 numbers have to be same basically we want doublets . 11 , 22 , 33 , 44 , 55 and 66 . those are six in number . further the three dice can fall in 6 * 6 = 36 ways . hence the probability is 6 / 36 = 1 / 6 answer : a"
Answer: a
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: if the average marks of 3 batches of 40 , 50 and 60 students respectively is 45 , 55 , 65 , what is the average marks of all the students ?
Options: a ) 56.33 , b ) 34.89 , c ) 23.67 , d ) 54.65 , e ) 43.98
Rationale: average marks of batch 1 = 45 students in batch 1 = 40 total marks of batch 1 = 40 * 45 average marks of batch 2 = 55 students in batch 2 = 50 total marks of batch 2 = 50 × 55 average marks of batch 3 = 65 students in batch 3 = 60 total marks of batch 3 = 65 × 60 total students = 40 + 60 + 50 = 150 average marks of all the students = ( ( 40 * 45 ) + ( 50 × 55 ) + ( 65 × 60 ) ) / 150 = 169 / 3 = 56.333 answer is a .
Answer: a
Python program:
a = 40 * 45
b = 50 * 55
c = a + b 
d = 60 * 65
e = c + d 
f = 40 + 50 
g = f + 60 
h = e / g
Problem: in what ratio must rice of rs . 16 per kg be mixed with rice of rs . 10 per kg so that cost of mixture is rs . 12 per kg ?
Options: a ) 2 : 3 , b ) 5 : 8 , c ) 5 : 6 , d ) 3 : 4 , e ) 1 : 2
Rationale: "( 12 - 10 ) / ( 16 - 12 ) = 2 / 4 = 1 : 2 answer : e"
Answer: e
Python program:
a = 12 - 10
b = 16 - 10
c = a / b
d = 12 - 10
e = 16 - 10
f = d / e
g = 1 - f
h = c / g
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 10 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 91 , d ) 88 , e ) 66
Rationale: right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 10 total people can seat = 81 + 10 = 91 answer : c
Answer: c
Python program:
a = 15 - 3
b = 15 + a 
c = b * 3
d = c + 10
Problem: if 4 < x < 8 < y < 12 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x = 4.1 and y = 11.1 greatest possible difference = 11.1 - 4.1 = 7 answer e"
Answer: e
Python program:
a = 12 - 4
b = a - 1
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 70 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 22 , b ) 10 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 70 ) = 90 ( x - 5 ) 100 = 10 x = > x = 10 . answer : b"
Answer: b
Python program:
a = 90 * 5
b = 5 * 70
c = a - b
d = 90 - 80
e = c / d
Problem: what annual payment will discharge a debt of rs . 6450 due in 4 years at 5 % per annum ?
Options: a ) 1500 , b ) 1400 , c ) 1700 , d ) 1800 , e ) 1600
Rationale: "explanation : he amount needs to be repaid in 4 years = rs . 6450 suppose rs . x is paid annually to repay this debt then , amount paid after 1 st year = rs . x interest for this rs . x for the remaining 3 years = x × 5 × 3 / 100 = 15 x / 100 then , amount paid after 2 nd year = rs . x interest for this rs . x for the remaining 2 years = x × 5 × 2 / 100 = 10 x / 100 amount paid after 3 rd year = rs . x interest for this rs . x for the remaining 1 year = x × 5 × 1 / 100 = 5 x / 100 amount paid after 4 th year = rs . x and this closes the entire debt = > x + 15 x / 100 + x + 10 x / 100 + x + 5 x / 100 + x = 6450 = > 4 x + 30 x / 100 = 6450 = > 4 x + 3 x / 10 = 6450 = > 40 x + 3 x = 64500 = > 43 x = 64500 = > x = 1500 answer : option a"
Answer: a
Python program:
a = 5 / 100
b = a + 1 
c = b ** 4
d = c * 6450
e = d / 4
Problem: in township k each property is taxed at 8 percent of its assessed value . if the assessed value of a property in township k is increased from $ 18,000 to $ 28,000 , by how much will the property tax increase ?
Options: a ) $ 320 , b ) $ 800 , c ) $ 320 , d ) $ 600 , e ) $ 850
Rationale: "increase in house value = $ 28,000 - $ 18,000 = $ 10000 so , tax increase = 8 % of $ 10000 = $ 800 answer : b"
Answer: b
Python program:
a = 3 + 4 
b = a * 4
c = b * 1000
d = 4 + 1 
e = d * 4
f = e * 1000
g = c - f
h = g * 8
i = h / 100
Problem: at a special sale , 8 tickets can be purchased for the price of 6 tickets . if 8 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 8 tickets ?
Options: a ) 25 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 8 tickets cost 800 8 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 200 , % of 6 tickets = ( 200 / 800 ) * 100 = 25 % answer : a"
Answer: a
Python program:
a = 8 * 8
b = 6 * 8
c = a - b
d = c * 100
e = 8 * 8
f = d / e
Problem: the cricket team of 11 members is 29 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 26 , e ) 28
Rationale: "let the average age of the whole team be x years . 11 x - ( 29 + 32 ) = 9 ( x - 1 ) = > 11 x - 9 x = 52 = > 2 x = 52 = > x = 26 . so , average age of the team is 26 years . d"
Answer: d
Python program:
a = 29 + 3 
b = a + 29 
c = 11 - 2
d = b - c
e = 11 - 2
f = 11 - e
g = d / f
Problem: what is the greater of the two numbers whose product is 2560 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 70 , e ) none of these
Rationale: let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2560 / s = 80 . answer : e
Answer: e
Python program:
a = 2 ** 4
b = a * 2
c = 2560 / b
Problem: a cistern which could be filled in 5 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 90 hrs , e ) 10 hrs
Rationale: "1 / 5 - 1 / x = 1 / 10 = > 10 hrs answer : e"
Answer: e
Python program:
a = 1 / 5
b = 1 / 10
c = a - b
d = 1/(c)
Problem: excluding stoppages , the speed of a train is 60 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 12 , b ) b ) 18 , c ) c ) 24 , d ) d ) 30 , e ) e ) 36
Rationale: "explanation : t = 24 / 60 * 60 = 24 answer : option c"
Answer: c
Python program:
a = 36 / 60
b = const_60 * a
c = const_60 - b
Problem: find value for x from below equation ? x + 1 = 3
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 3 - 1 2 . simplify both sides : x = 2 e"
Answer: e
Python program:
a = 3 - 1
Problem: the angle between the minute hand and the hour hand of a clock when the time is 12.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 195 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 12 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 12 − 30 / 5 ) + 30 / 2 = 30 ( 12 − 6 ) + 15 = 30 × 6 + 15 = 195 ° answer is d ."
Answer: d
Python program:
a = 3 * 4
b = 3 * 4
c = b - 1
d = a / c
e = 4 + 1 
f = 3 * 4
g = f - 1
h = e * g
i = d * h
j = const_60 / 2
k = i - j
l = 3 * 4
m = l - 1
n = k * m
o = n / 2
Problem: jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 12 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "check two extreme cases : jane = 18 , child = 9 , years ago = 32 - 18 = 14 - - > child ' s age now = 9 + 14 = 23 ; jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 . answer : d ."
Answer: d
Python program:
a = 18 / 2
b = 32 - 18
c = a + b