euclaise/mathqa_programs huggingface dataset:
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area t of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Python program:
a = 4 * math.pi
b = 3 / math.pi
c = a * b
d = c / 2
e = 3 / math.pi
f = math.pi * e
g = d + f
Problem: there are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 26 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a"
Answer: a
Python program:
a = 408 + 216 
b = 2 * 2
c = b * 2
d = c * 3
e = a / d
Problem: the number 250 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ?
Options: a ) 18
b ) 22
c ) 21
d ) 20
e ) 19
Rationale: sum of the squares of 3 different positive integers = 250 15 ^ 2 + 3 ^ 2 + 4 ^ 2 = 250 now , sum of these 3 different integers = 15 + 3 + 4 = 22 ans - b
Answer: b
Python program:
a = 250 / 2
b = math.sqrt(a)
c = 2 * b
Problem: 13 ltr of water is added with 11 ltr of a solution containing 16 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 7.33 % , b ) 9 % , c ) 9.67 % , d ) 11 % , e ) 11.5 %
Rationale: "we have an 11 litre solution containing 16 % of alcohol in the water . = > quantity of alcohol in the solution = 11 ã — 16 / 100 now 13 litre of water is added to the solution . = > total quantity of the new solution = 11 + 13 = 24 percentage of alcohol in the new solution = 11 ã — 16 / 100 24 ã — 100 = 11 ã — 1610024 ã — 100 = 11 ã — 0.67 / 100 = 7.33 % a"
Answer: a
Python program:
a = 16 / 100
b = a * 11
c = 13 + 11 
d = b / c
e = 100 * d
Problem: a straight line in the xy - plane has y - intercept of 49 . on this line the x - coordinate of the point is 71 and y - coordinate is 12 then what is the slope of the line ?
Options: a ) 0.5 , b ) 0.51 , c ) - 0.52 , d ) 0.31 , e ) - 0.49
Rationale: "eq of line = y = mx + c c = 49 x = 71 y = 12 substitute given : m = ( y - c ) / x = ( 12 - 49 ) / 71 = - 37 / 71 = - 0.52 correct option is c"
Answer: c
Python program:
a = 12 - 49
b = a / 71
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1116 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 57 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1116 - 640 = 476 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 476 / 28 = 17 total hrs = 40 + 17 = 57 answer b 57"
Answer: b
Python program:
a = 16 * 40
b = 1116 - a
c = 100 + 75 
d = 16 * c
e = d / 100
f = b / e
g = 40 + f
Problem: a train 450 m long running at 126 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 271 , b ) 250 , c ) 350 , d ) 277 , e ) 232
Rationale: "length of the platform = 126 * 5 / 18 * 20 = 700 – 450 = 250 answer : b"
Answer: b
Python program:
a = 126 * const_0_2778
b = 20 * a
c = b - 450
Problem: 200 is increased by 25 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 250 , d ) 190 , e ) 220
Rationale: explanation final number = initial number + 25 % ( original number ) = 200 + 25 % ( 200 ) = 200 + 50 = 250 . answer c
Answer: c
Python program:
a = 25 / 100
b = 200 * a
c = 200 + b
Problem: given that 268 x 74 = 19332 , find the value of 2.68 x . 74 .
Options: a ) 1.9332 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9332 answer a"
Answer: a
Python program:
a = 268 / 100
b = 74 / 100
c = a * b
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 30 % 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 ) 21 % , b ) 22.5 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.3 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 30 % income the savings increased by 100 % . or s = . 3 i or s = 30 % of income d is the answer"
Answer: d
Python program:
a = 100 + 30 
b = a + 100 
c = 2 * 100
d = b - c
e = d / 100
f = e * 100
Problem: the average age of applicants for a new job is 31 , with a standard deviation of 8 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 14 , c ) 15 , d ) 17 , e ) 30
Rationale: "within one standard deviation of the average age means 31 + / - 7 23 - - 31 - - 39 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 total = 17 d"
Answer: d
Python program:
a = 8 * 2
b = a + 1
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 12 weavers in 12 days ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 30 , e ) 36
Rationale: "1 weaver can weave 1 mat in 4 days . 12 weavers can weave 12 mats in 4 days . 12 weavers can weave 36 mats in 12 days . the answer is e ."
Answer: e
Python program:
a = 4 * 4
b = 4 / a
c = 12 * b
d = 12 * c
Problem: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 200 girls , the total number of students in the college is
Options: a ) 420 , b ) 520 , c ) 620 , d ) 620 , e ) none of these
Rationale: explanation : let the boy are 8 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 8 x + 5 x = 13 x = 13 ( 40 ) = 520 answer : b
Answer: b
Python program:
a = 200 / 5
b = a * 8
c = 200 + b
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio q of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore q , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b
Answer: b
Python program:
a = 3 + 2 
b = 3 / a
c = 20 - 10
d = b * c
e = d + 10 
f = e / 20
g = 20 - 10
h = f * g
i = h + 10 
j = 3 + 2 
k = 2 / j
l = 20 - 10
m = k * l
n = m / 20
o = 20 - 10
p = n * o
q = i / p
Problem: a boatman can row 96 km downstream in 8 hr . if the speed of the current is 4 km / hr , then find in what time will be able to cover 8 km upstream ?
Options: a ) 6 hr , b ) 2 hr , c ) 4 hr , d ) 1 hr , e ) none of these
Rationale: "explanation : speed downstream = 96 ⁄ 8 = 12 kmph speed of current = 4 km / hr speed of the boatman in still water = 12 - 4 = 8 kmph speed upstream = 8 - 4 = 4 kmph time taken to cover 8 km upstream = 8 ⁄ 4 = 2 hours . answer : option b"
Answer: b
Python program:
a = 96 / 8
b = a - 4
c = b - 4
d = 8 / c
Problem: the average age of 16 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 26
Rationale: "age of the 15 th student = 16 * 15 - ( 14 * 5 + 16 * 9 ) = 240 - 214 = 26 years answer is e"
Answer: e
Python program:
a = 16 * 15
b = 5 * 14
c = a - b
d = 9 * 16
e = c - d
Problem: a driver goes on a trip of 50 kilometers , the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: "the time for the first part of the trip was 25 / 60 = 5 / 12 hours . the time for the second part of the trip was 25 / 30 = 5 / 6 hours . the total time for the trip was 5 / 12 + 5 / 6 = 15 / 12 = 5 / 4 hours . the average speed for the trip was 50 / ( 5 / 4 ) = 40 kph the answer is c ."
Answer: c
Python program:
a = 25 / 60
b = 50 - 25
c = b / 30
d = a + c 
e = 50 / d
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 2 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 2 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 2 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 6 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 6 w = 6 the answer is b ."
Answer: b
Python program:
a = math.log(2)
b = 12 * a
c = math.log(2)
d = b / c
Problem: 895.7 – 573.07 – 95.007 = ?
Options: a ) 227.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 895.7 - ( 573.07 + 95.007 ) = 895.7 - 668.077 = 227.623 . answer a"
Answer: a
Python program:
a = 573 / 7
b = 895 - 7
Problem: a train ride from two p to town q costs $ 6.85 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.65 . what is the cost of a bus ride from town p to town q ?
Options: a ) $ 1.40 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20
Rationale: "let x be the cost of a bus ride . x + ( x + 685 ) = 965 2 x = 280 x = $ 1.40 the answer is a ."
Answer: a
Python program:
a = 9 - 65
b = a / 2
Problem: how much 60 % of 50 is greater than 42 % of 30 ?
Options: a ) 18 , b ) 91 , c ) 11 , d ) 17.4 , e ) 12
Rationale: "( 60 / 100 ) * 50 – ( 42 / 100 ) * 30 30 - 12.6 = 17.4 answer : d"
Answer: d
Python program:
a = 60 * 50
b = a / 100
c = 42 * 30
d = c / 100
e = b - d
Problem: matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x = 100 i . e . y = 5 new sales = y + 1 = 6 answer : option d
Answer: d
Python program:
a = 1000 - 100
b = 250 - 150
c = 250 - b
d = a / c
Problem: what is the smallest positive integer x for which x 3 + 5 xx 3 + 5 x has a value more than 80 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "4 ^ 3 + 5 * 4 = 64 + 20 = 84 that ' s pretty close to 80 already so i can cancel d and e since they ' ll be more than 80 . b just needs to be checked just in case so . . . 3 ^ 3 + 5 * 3 = 27 + 15 = not close to 80 . therefore , 4 ( c ) is the smallest positive integer x for which x ^ 3 + 5 x has a value more than 80 . answer : c"
Answer: c
Python program:
a = 3 / 10
b = a ** const_0_33
c = 3 / b
d = 3 / 10
e = d ** const_0_33
f = c / e
g = 3 / 10
h = g ** const_0_33
i = 3 / h
j = 3 / 10
k = j ** const_0_33
l = i / k
m = f / l
n = m * 100
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.75 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 12 , b ) 72 , c ) 48 , d ) 99 , e ) 11
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.75 + 1.25 = 3 km = 3000 m . required time = 3000 * 3 / 125 = 72 sec . answer : b"
Answer: b
Python program:
a = 1 * 75
b = 60 * 1000
c = b / 3600
d = a / c
e = 1 * 25
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 13 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 4 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9
Rationale: answer is a . x / x + 36 = 1 / 5 x = 9 13 - 9 = 4
Answer: a
Python program:
a = 20 / 100
b = a * 20
Problem: a cylinder is inserted in a sphere d / h = 2 / 3 . find the surface area of the cylinder ?
Options: a ) 23.12
b ) 24.12
c ) 25.12
d ) 26.12
e ) 27.12
Rationale: take r = 1 , h = 3 = 2 * 3.14 * r * r + 2 * 3.14 * r * h = 2 * 3.14 * r ( r + h ) = 2 * 3.14 * 1 ( 1 + 3 ) = 2 * 3.14 ( 4 ) = 25.12 answer : c
Answer: c
Python program:
a = 2 / 2
b = a + 3 
c = 2 * math.pi
d = b * c
Problem: the measurements obtained for the interior dimensions of a rectangular box are 150 cm by 150 cm by 225 cm . if each of the three measurements has an error of at most 1 centimeter , which of the following is the closes maximum possible difference , in cubic centimeters , between the actual capacity of the box and the capacity computed using these measurements ?
Options: a ) 90,000
b ) 95,000
c ) 93,000
d ) 92,000
e ) 91,000
Rationale: the options are well spread so we can approximate . changing the length by 1 cm results in change of the volume by 1 * 150 * 225 = 33,750 cubic centimeters ; changing the width by 1 cm results in change of the volume by 150 * 1 * 225 = 33,750 cubic centimeters ; changing the height by 1 cm results in change of the volume by 150 * 150 * 1 = 22,500 cubic centimeters . so , approximate maximum possible difference is 33,750 + 33,750 + 22,500 = 90,000 cubic centimeters . answer : a
Answer: a
Python program:
a = 150 * 150
b = 150 * 225
c = a + b 
d = 225 * 150
e = c + d
Problem: what will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?
Options: a ) 1 : 1
b ) 1 : 2
c ) 2 : 3
d ) 2 : 1
e ) none of these
Rationale: explanation : as far as questions of area or volume and surface area are concerned , it is all about formulas and very little logic . so its a sincere advice to get all formulas remembered before solving these questions . lets solve this , area of rectangle = l ∗ b area of triangle = 1 / 2 l ∗ b ratio = l ∗ b : 1 / 2 l ∗ b = 1 : 1 / 2 = 2 : 1 option d
Answer: d
Python program:
a = rectangle_area / (
Problem: if one positive integer is greater than another positive integer by 4 , and the difference of their cubes is 316 , what is their sum ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 7 ^ 3 = 343 the two numbers are 3 and 7 . the answer is c ."
Answer: c
Python program:
a = 3 ** 0
b = 4 ** 4
c = b ** 2
d = 4 ** 4
e = 316 - d
f = e ** 2
g = c + f 
h = math.sqrt(g)
i = a + h 
j = 4 ** 2
k = j * 2
l = i / k
m = 4 ** 4
n = 4 ** 4
o = n ** 2
p = 4 ** 4
q = 316 - p
r = q ** 2
s = o + r 
t = math.sqrt(s)
u = m + t 
v = 4 ** 2
w = v * 2
x = u / w
y = x - 4
z = l + y
Problem: the average age of an adult class is 40 years . 10 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 10 x 32 = ( y + 10 ) x 36 â ‡ ’ 40 y + 320 = 36 y + 360 â ‡ ’ 4 y = 40 â ˆ ´ y = 10 a"
Answer: a
Python program:
a = 40 - 4
b = 10 * a
c = 10 * 32
d = b - c
e = d / 4
Problem: a king has 1000 bottles of wine , a queen wants to kill the king and sends a servant to poison the wine . fortunately the king ' s guard ' s catch d servant after he has only poisoned one bottle and the guard do n ' t know which bottle is poisoned . furthermore it takes one month to have an effect , and there is an anniversary party coming up in 5 weeks time ! the king decides he will get some of the prisoners in his vast dungeons to drink the wine . how many minimum prisoners does it required to sample the wine to find out the poisoned bottle so that the guests will still be able to drink the rest of the wine at his anniversary party in 5 weeks time ?
Options: a ) 1 , b ) 499 , c ) 500 , d ) 999 , e ) 10
Rationale: since you need 10 digits to represent 1000 numbers in binary , you will need 10 prisoners . now the logic is this : every bottle has a unique number from 1 to 1000 and a unique binary representation from 0000000001 to 1111101000 . now you have 10 prisoners . each bottle will be tasted by the prisoners depending on the binary representation of the bottle . wherever there is 1 , the bottle will be tasted by that prisoner ( assuming units digit represents the 1 st prisoner , tens digit the 2 nd prisoner and so on . . . ) 1 st bottle is 0000000001 so it will be tasted by only the 1 st prisoner . 2 nd bottle is 0000000010 so it will be tasted by only the 2 nd prisoner . 3 rd bottle is 0000000011 so it will be tasted by the 1 st and 2 nd prisoners . and so on . . . 1000 th bottle is 1111101000 so it will be tasted by 4 th , 6 th , 7 th , 8 th , 9 th and 10 th prisoners . at the end of a month , we see which prisoners die . say , only the 3 rd prisoner dies . this means the poisoned bottle number is 0000000100 = 3 . say 1 st , 7 th and 9 th prisoners die . this means the poisoned bottle number is 0101000001 = 321 ans : e
Answer: e
Python program:
a = 1000 / 100
Problem: 30 square stone slabs of equal size were needed to cover a floor area of 120 sq . m . find the length of each stone slab ?
Options: a ) 120 cm
b ) 200 cm
c ) 88 cm
d ) 666 cm
e ) 776 cm
Rationale: area of each slab = 120 / 30 m 2 = 4 m 2 length of each slab √ 4 = 2 m = 200 cm b
Answer: b
Python program:
a = 120 / 30
b = math.sqrt(a)
c = b * 100
Problem: if x and y are positive integers and 18 x = 12 y what is the least possible value of xy ?
Options: a ) 14 , b ) 28 , c ) 36 , d ) 84 , e ) 252
Rationale: "18 x = 12 y = > x / y = 2 / 3 = > 3 x = 2 y 3 ( 3 ) = 2 ( 3 ) = > x * y = 9 but it is not given 3 ( 6 ) = 2 ( 6 ) = > x * y = 36 c"
Answer: c
Python program:
a = 12 + 1
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.90 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6468
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.90 ) = rs . 6468 . answer : e ) 6468"
Answer: e
Python program:
a = 13 / 86
b = math.sqrt(a)
c = b * 100
d = circumface * (
Problem: two containers of milk contain mixtures of water and milk in ratio 5 : 4 and 7 : 9 . in what ratio they should be mixed so that mixture is of 6 : 6 ratio ?
Options: a ) 6 : 5 , b ) 7 : 5 , c ) 9 : 8 , d ) 8 : 9 , e ) 8 : 7
Rationale: 6 / 6 - 5 / 4 = = > - 1 / 4 7 / 9 - 6 / 6 = = > - 2 / 9 now , - 1 / 4 = - 2 / 9 = = > 1 / 4 = 2 / 9 = = > 9 : 8 answer : c
Answer: c
Python program:
a = 7 + 9 
b = 9 / a
c = 6 + 6 
d = 6 / c
e = b - d
f = 6 + 6 
g = 6 / f
h = 5 + 4 
i = 4 / h
j = g - i
k = e / j
Problem: 3 , 5 , 7 , 11 , 13 , 17 , 19 , ____
Options: a ) 25 , b ) 36 , c ) 23 , d ) 49 , e ) 27
Rationale: "the sequence is a series of prime numbers , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 . . . . answer : c ."
Answer: c
Python program:
a = negate - (
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 360 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 360 envelopes they will take 360 / 60 mins . i . e . , 6 mins . answer : a"
Answer: a
Python program:
a = 3 / 2
b = 36 / a
c = 36 + b 
d = 360 / c
Problem: if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 4 x years from now ?
Options: a ) 31 , b ) 35 , c ) 30 , d ) 40 , e ) 28
Rationale: "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 4 x years from now , age will be 15 + 4 * 4 = 31 option a"
Answer: a
Python program:
a = 4 * 4
b = a * 4
c = 14 - 1
d = c / 2
e = b - d
Problem: the present population of a town is 220 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 242 , e ) 250
Rationale: "p = 220 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 220 * ( 1 + 10 / 100 ) = 220 * ( 11 / 10 ) = 242 answer is d"
Answer: d
Python program:
a = 220 * 10
b = a / 100
c = 220 + b
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × b = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x b = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b b = 7 ^ 2 = 49 answer d"
Answer: d
Python program:
a = 105 ** 3
b = 21 * 25
c = b * 45
d = a / c
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 2 strokes ?
Options: a ) 3 / 4 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 so removed = 1 - 1 / 4 = 3 / 4"
Answer: a
Python program:
a = 1 / 2
b = 1 / 2
c = b / 2
d = a + c 
e = 1 / 2
f = e / 2
g = f / 2
h = d + g 
i = 1 / 2
j = i / 2
k = j / 2
l = k / 2
m = h + l 
n = 1 / 2
o = n / 2
p = o / 2
q = p / 2
r = q / 2
s = m + r
Problem: a man purchased 3 blankets @ rs . 100 each , 6 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 3 * 100 + 6 * 150 = 1200 1500 – 1200 = 300 a"
Answer: a
Python program:
a = 10 * 150
b = 3 * 100
c = 6 * 150
d = b + c 
e = a - d