euclaise/mathqa_programs huggingface dataset:
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 500 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 8 = 256 < 500 , then the greatest possible length of integer z is 8 . the answer is c ."
Answer: c
Python program:
a = 2 ** 10
b = math.log(a)
Problem: after decreasing 50 % in the price of an article costs rs . 620 . find the actual cost of an article ?
Options: a ) 1400 , b ) 1240 , c ) 1200 , d ) 1100 , e ) 1500
Rationale: "cp * ( 50 / 100 ) = 620 cp = 12.4 * 100 = > cp = 1240 answer : b"
Answer: b
Python program:
a = 50 / 100
b = 1 - a
c = 620 / b
Problem: if the compound interest on a certain sum of money for 7 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 2100 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 7 yrs = ( 3000 x 10 x 7 ) / 100 = 2100 / - answer : d ."
Answer: d
Python program:
a = 3 * 0
b = a * 10
c = b * 10
d = c * 7
e = d / 100
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 4 + 3 and * 4 + 4 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 4 would be divisible by all numbers from 1 to 4 . = > * 4 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 4 is divisible by 3 ) in fact adding anyprimenumber between 1 to 4 to * 4 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 4 + 3 and * 4 + 11 then the answer would be 1 . for * 4 + 3 and * 4 + 13 , it is 2 and so on . . . a"
Answer: a
Python program:
a = 4 * 3
b = a * 2
c = b * 4
d = c + 4 
e = 4 * 3
f = e * 2
g = f * 4
h = g + 3 
i = d - h
j = i - 1
Problem: in the hillside summer camp there are 50 children . 85 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 20 . , b ) 45 . , c ) 50 . , d ) 30 . , e ) 25 .
Rationale: given there are 50 students , 84 % of 50 = 42 boys and remaining 8 girls . now here 84 % are boys and 16 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 8 % . . if we add 50 to existing 45 then the count will be 92 and the girls number will be 8 as it . now boys are 92 % and girls are 8 % . ( out of 100 students = 92 boys + 8 girls ) . imo option c is correct .
Answer: c
Python program:
a = 100 - 5
b = a / 100
c = b * 50
d = 5 / 100
e = d * 50
f = c + e
Problem: 4 , 5 , 7 , 11 , 19 , ( . . . )
Options: a ) 32 , b ) 22 , c ) 35 , d ) 27 , e ) 28
Rationale: "4 4 × 2 - 3 = 5 5 × 2 - 3 = 7 7 × 2 - 3 = 11 11 × 2 - 3 = 19 19 × 2 - 3 = 35 answer is c"
Answer: c
Python program:
a = negate - (
Problem: a set s = { x , - 8 , - 5 , - 2 , 2 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) - 1 , e ) can not be determined
Rationale: "median of the set = ( - 2 + 2 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 17 - 15 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c"
Answer: c
Python program:
a = 9 + 8 
b = a + 2 
c = b - 2
d = c - 5
e = d - 8
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many acres q were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn q = 4 * 94 = 376 correct option - c
Answer: c
Python program:
a = 1000 * 1
b = 10 * 3
c = b + 4 
d = a + c 
e = 5 + 2 
f = e + 4 
g = d / f
h = g * 4
Problem: a sum fetched a total simple interest of $ 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8925
Rationale: "e 8925 principal = $ 100 x 4016.25 / 9 x 5 = $ 401625 / 45 = $ 8925 ."
Answer: e
Python program:
a = 4016 * 25
b = a / 9
c = b / 5
Problem: a train running at 1 / 2 of its own speed reached a place in 8 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 4 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: time taken if run its own speed = 1 / 2 * 8 = 4 hrs time saved = 8 - 4 = 4 hrs answer : c
Answer: c
Python program:
a = 1 / 2
b = a * 8
Problem: the ratio 6 : 5 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 120 % , d ) 125 % , e ) none
Rationale: "solution 6 : 5 = 6 / 5 = ( 6 / 5 x 100 ) % . = 120 % . answer c"
Answer: c
Python program:
a = 6 / 5
b = a * 100
Problem: find the area of a parallelogram with base 20 cm and height 16 cm ?
Options: a ) 198 cm 2 , b ) 320 cm 2 , c ) 279 cm 2 , d ) 128 cm 2 , e ) 297 cm 2
Rationale: "area of a parallelogram = base * height = 20 * 16 = 320 cm 2 answer : b"
Answer: b
Python program:
a = 20 * 16
Problem: a part of certain sum of money is invested at 10 % per annum and the rest at 16 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 8 : 5 , b ) 4 : 9 , c ) 4 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: 16 : 10 = 8 : 5 answer : a
Answer: a
Python program:
a = 16 / 100
b = a * 10
Problem: the h . c . f of two numbers is 12 and their l . c . m is 6600 . if one of the numbers is 288 , then the other is ?
Options: a ) 255 , b ) 260 , c ) 265 , d ) 270 , e ) 275
Rationale: "other number = ( 12 * 6600 ) / 288 = 275 . answer : e"
Answer: e
Python program:
a = 12 * 288
Problem: the unit digit in the product ( 624 * 708 * 913 * 463 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 8 * 3 * 3 ) = 8 answer : d"
Answer: d
Python program:
a = 624 * 708
b = a * 913
c = b * 463
d = 624 * 708
e = d * 913
f = e * 463
g = 4 + 4 
h = f - g
i = c - h
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 450 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 678 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is b : 678 solution : total number of students studying both are 450 + 226 - 134 = 542 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 542 , so 100 % is approx . 678 ."
Answer: b
Python program:
a = 226 + 450
Problem: the volume of the sphere q is ( 37 / 64 ) % less than the volume of sphere p and the volume of sphere r is ( 19 / 27 ) % less than that of sphere q . by what is the surface area of sphere r less than the surface area of sphere p ?
Options: a ) 77.77 %
b ) 75 %
c ) 67.5 %
d ) 87.5 %
e ) none of these
Rationale: explanation : let the volume of sphere p be 64 parts . therefore volume of sphere q = > 64 − ( 37 / 64 ) % of 64 . = > 64 − 37 = 27 parts . the volume of r is : - = > 27 − ( 19 / 27 ) × 27 . = > 27 − 19 = 8 parts . volume ratio : = > p : q : r = 64 : 27 : 8 . radius ratio : = > p : q : r = 4 : 3 : 2 . the surface area will be 16 : 9 : 5 . surface area of r is less than the surface area of sphere p . = > 16 k − 4 k = 12 k . now , = > ( 12 k / 16 k ) × 100 . = > 75 % . hence , the surface area of sphere r is less than the surface area of sphere p by 75 % . answer : b
Answer: b
Python program:
a = 1 / 3
b = 64 ** a
c = 64 / b
d = 1 / 3
e = 64 ** d
f = c - e
g = 1 / 3
h = 64 ** g
i = 64 / h
j = f / i
k = j * 100
Problem: what is the radius of a circle that has a circumference of 3.14 meters ?
Options: a ) 2.5
b ) 2
c ) 1.5
d ) 1
e ) 0.5
Rationale: circumference of a circle = 2 π r . given , circumference = 3.14 meters . therefore , 2 π r = circumference of a circle or , 2 π r = 3.14 . or , 2 ? 3.14 r = 3.14 , [ putting the value of pi ( π ) = 3.14 ] . or , 6.28 r = 3.14 . or , r = 3.14 / 6.28 . or , r = 0.5 . answer : 0.5 meter . correct answer e
Answer: e
Python program:
a = 2 * math.pi
b = 3 / 14
Problem: the difference between a two - digit number and the number obtained by interchanging the digit is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 8 , b ) 15 , c ) 14 , d ) 12 , e ) 10
Rationale: since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let the ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 * 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer a
Answer: a
Python program:
a = 2 * 10
b = a + 1 
c = b - 10
d = c - 2
e = 36 / d
f = 2 * 10
g = f + 1 
h = g - 10
i = h - 2
j = 36 / i
k = j * 2
l = e + k 
m = 2 * 10
n = m + 1 
o = n - 10
p = o - 2
q = 36 / p
r = q * 2
s = 2 * 10
t = s + 1 
u = t - 10
v = u - 2
w = 36 / v
x = r - w
y = l - x
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "first ratio = 3 / 20 = 15 % second ratio = ( 3 + 12 ) / ( 9 + 108 ) = 15 / 117 = 12,8 % decrease = 2,2 % 2,2 % / 15 % = 15 % approximately . answer : b"
Answer: b
Python program:
a = 3 / 20
b = a * 100
Problem: the difference of two numbers is 11 and one fifth of their sum is 9 . the numbers are :
Options: a ) 31 , 20 , b ) 30 , 19 , c ) 29 , 18 , d ) 28 , 17 , e ) none
Rationale: "x − y = 11 , x + y = 5 × 9 x − y = 11 , x + y = 45 , y = 17 , x = 28 answer : d"
Answer: d
Python program:
a = 10 / 2
b = a * 9
c = 10 / 2
d = c * 9
e = 11 + d 
f = e / 2
g = b - f
h = 10 / 2
i = g + h
Problem: an internet recently hired 8 new network , in addvertisement 20 network already employed . all new network cam from university a . in addition 75 % of computer addvertisement came from same university a . what fraction of original 20 network addvertisement came from same univerity a ? pls help to solve
Options: a ) 13 / 20 , b ) 15 / 20 , c ) 14 / 20 , d ) 12 / 20 , e ) 11 / 20
Rationale: new networks = 8 already employed networks = 20 total networks = 28 computer advt . from uni . a = 28 * ( 75 / 100 ) = 21 out 28 networks 21 came from uni . a among these 21 we know 8 are newly hired so 21 - 8 = 13 networks among previously employed networks came from uni . a answer is : 13 / 20 answer : a
Answer: a
Python program:
a = 8 + 20 
b = 75 / 100
c = a * b
d = c - 8
e = d / 20
Problem: dividing by 3 ⁄ 9 and then multiplying by 5 ⁄ 6 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 5 / 2 , e ) 5 ⁄ 16
Rationale: "say x / 3 / 9 * 5 / 6 = x * 9 / 3 * 5 / 6 = x * 5 / 2 d"
Answer: d
Python program:
a = 9 / 3
b = 5 / 6
c = a * b
Problem: if it takes a machine 1 ⁄ 3 minute to produce one item , how many items will it produce in 2 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 80 , d ) 120 , e ) 360
Rationale: "1 item takes 1 / 3 min so it takes 120 min to produce x x / 3 = 120 the x = 360 answer : e"
Answer: e
Python program:
a = 2 * const_60
b = 1 / 3
c = a / b
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many s apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons s = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Python program:
a = 10 + 10 
b = a + 2 
c = 1430 / b
d = c + 45 
e = 1430 / d
f = e + 9
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 7700 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 7700 x ( 2 / 11 ) ) = rs . 1400 . answer is c"
Answer: c
Python program:
a = 2 * 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 3 
f = 2 / e
g = 7700 * f
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 5 ] ] ?
Options: a ) 39 , b ) 9 , c ) 15 , d ) 19 , e ) 25
Rationale: "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 5 ] ] = 5 ^ 2 + 2 * 5 + 4 = 39 . option a"
Answer: a
Python program:
a = 5 ** 2
b = 2 * 2
c = a + b 
d = c + 4
Problem: sobha ' s father was 38 years of age when she was born while her mother was 36 years old when her brother 4 years younger to her was born . what is the difference between the ages of her parents ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 2
Rationale: age of sobha ' s father when sobha was born = 38 age of sobha ' s mother when sobha was born = 36 − 4 = 32 required difference of age = 38 − 32 = 6 answer is b .
Answer: b
Python program:
a = 38 + 4 
b = a - 36
Problem: if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 74 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 74 a = 28 the answer is c ."
Answer: c
Python program:
a = 74 * 2
b = 16 - 8
c = a - b
d = 2 + 3 
e = c / d
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 7 . what is the ratio of the smaller number to the larger number ?
Options: a ) 2 : 3 , b ) 2 : 5 , c ) 3 : 7 , d ) 4 : 9 , e ) 5 : 6
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 5 : 7 , thus the smaller number must have a ratio of 3 . the ratio of the smaller number to the larger number is 3 : 7 . the answer is c ."
Answer: c
Python program:
a = 5 / 7
b = 1 / 2
c = a - b
d = c * 2
Problem: find number which is 60 % less than 120 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 48 , e ) 98
Rationale: "explanation : 60 % less is 40 % of the given number therefore , 40 % of 120 is 48 . answer : d"
Answer: d
Python program:
a = 120 * 60
b = a / 100
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 182 votes . find the total number of valid votes ?
Options: a ) 455 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 182 = > 4 x / 10 = 182 = > 4 x = 1820 = > x = 455 . answer : a"
Answer: a
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 182 / c
Problem: find the number which is nearest to 457 and is exactly divisible by 11 .
Options: a ) 450 , b ) 451 , c ) 460 , d ) 462 , e ) none
Rationale: "solution on dividing 457 by 11 , remainder is 6 . required number is either 451 or 462 nearest to 456 is = 462 . answer d"
Answer: d
Python program:
a = 11 - reminder
b = 457 + a
Problem: a cycle is bought for rs . 450 and sold for rs . 520 , find the gain percent ?
Options: a ) 18 , b ) 14 , c ) 20 , d ) 15 , e ) 15.55
Rationale: "450 - - - - 70 100 - - - - ? = > 15.55 % answer : e"
Answer: e
Python program:
a = 520 - 450
b = a / 450
c = b * 100
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration r of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration r would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 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: 12.1212 + 17.0005 - 9.1103 = ?
Options: a ) 20.0015 , b ) 20.0105 , c ) 20.0115 , d ) 20.0114 , e ) none
Rationale: solution given expression = ( 12.1212 + 17.0005 ) - 9.1103 = ( 29.1217 - 9.1103 ) = 20.0114 . answer d
Answer: d
Python program:
a = 12 + 1212 
b = a - 9
Problem: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 104 . what was the number he chose ?
Options: a ) 123 , b ) 121 , c ) 277 , d ) 267 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 104 2 â ‹ … x â ˆ ’ 138 = 104 x = 121 answer : b"
Answer: b
Python program:
a = 104 + 138 
b = a / 2
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 18 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 10 and 7 , d ) 3 and 10 , e ) 10 and 10
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 18 cm 2 more than the first area . therefore a 1 + 18 = a 2 x ( x − 3 ) + 18 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 18 = x 2 + x − 2 x − 2 2 x = 20 x = 10 . so , the sides of the rectangle are 10 cm and ( 10 − 3 ) = 7 cm long . so answer is c ."
Answer: c
Python program:
a = 18 / 2
b = a + 1 
c = b - 3
Problem: john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 75 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 25 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 75 = 25 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 25 / 100 ) * 100 = ( 0.25 ) * 100 = 25 % . d"
Answer: d
Python program:
a = 100 - 75
Problem: an investment compounds annually at an interest rate of 30 % what is the smallest investment period by which time the investment will more than double in value ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "1 year : 100 / 3 = 33.33 approx $ 34 : total : 134 2 nd year : 134 / 3 = 45 : total : 134 + 45 = 179 3 rd year : 179 / 3 = 60 : total : 179 + 60 = 239 > 2 ( 100 ) ; 3 years ; answer : a"
Answer: a
Python program:
a = math.log(3)
b = 30 / 100
c = 1 + b 
d = math.log(c)
e = a / d
f = math.floor(e)
g = f + 1
Problem: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.25 as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 2050 , e ) 2060
Rationale: in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 2060 : ri = 120 , ro = 150 thus ans : e
Answer: e
Python program:
a = 4 + 3 
b = 1 + 25 
c = 1950 + b
Problem: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord q , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . q = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d
Answer: d
Python program:
a = 30 / 3
Problem: a person crosses a 300 m long street in 4 minutes . what is his speed in km per hour ?
Options: a ) 1.6 , b ) 4.5 , c ) 8.2 , d ) 6.5 , e ) 2.9
Rationale: "distance = 300 meter time = 4 minutes = 4 x 60 seconds = 240 seconds speed = distance / time = 300 / 240 = 1.25 m / s = 1.25 ã — 18 / 5 km / hr = 4.5 km / hr answer : b"
Answer: b
Python program:
a = 300 / 1000
b = 4 * const_60
c = b / 3600
d = a / c
Problem: jerry and michelle play a card game . in the beginning of the game they have an equal number of cards . each player , at her turn , gives the other a third of her cards . michelle plays first , giving jerry a third of her cards . jerry plays next , and michelle follows . then the game ends . jerry ended up with 28 more cards than michelle . how many cards did each player have originally ?
Options: a ) 51 , b ) 52 , c ) 53 , d ) 54 , e ) 56
Rationale: "gamemichelle jerry initially 54 54 assume after game 1 36 72 after game 2 60 48 after game 3 40 68 now merry has 28 cards more than michelle . this option gives us exactly what number of cards they had initially . so the answer is d"
Answer: d
Python program:
a = 28 * 3
b = a - 28
Problem: if albert ’ s monthly earnings rise by 26 % , he would earn $ 693 . if , instead , his earnings rise by only 20 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 660 , d ) 690 , e ) 693
Rationale: = 693 / 1.26 ∗ 1.2 = 660 = 660 answer is c
Answer: c
Python program:
a = 26 / 100
b = 1 + a 
c = 693 / b
d = 20 / 100
e = 1 + d 
f = c * e
Problem: what is the normal price of an article sold at $ 36 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 45 , b ) $ 48 , c ) $ 50 , d ) $ 54 , e ) $ 56
Rationale: "0.8 * 0.9 * cost price = $ 36 cost price = $ 50 the answer is c ."
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
f = 36 / e
Problem: if | x + 3 | = 5 , what is the sum of all the possible values of x ?
Options: a ) - 16 , b ) - 12 , c ) - 8 , d ) - 6 , e ) 12
Rationale: "there will be two cases x + 3 = 5 or x + 3 = - 5 = > x = 2 or x = - 8 sum of both the values will be - 8 + 2 = - 6 answer : d"
Answer: d
Python program:
a = 3 + 5
Problem: in a group of cows and hens , the number of legs are 14 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 14 2 x = 14 x = 7 . answer : c"
Answer: c
Python program:
a = 14 - 4
Problem: a and b invests rs . 3000 and rs . 6000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 3 : 8 , c ) 3 : 1 , d ) 9 : 9 , e ) 3 : 4
Rationale: "( 3 * 6 + 6 * 6 ) : ( 6 * 12 ) 18 : 24 = > 3 : 4 . answer : e"
Answer: e
Python program:
a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 6000 * e
g = d / f