euclaise/mathqa_programs huggingface dataset:
Problem: if x ^ 2 + 1 / x ^ 2 = √ 20 what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = √ 20 andsquareboth sides : ( x ² + 1 / x ² ) ² = 20 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 20 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 20 simplify : x ⁴ + 1 / x ⁴ = 18 answer : e"
Answer: e
Python program:
a = 2 ** 2
b = a - 2
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 5 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 7
Rationale: actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 5 miles / gallon . additional 7 miles / gallon is required to match the actual mileage . imo option e .
Answer: e
Python program:
a = 480 / 40
b = a - 5
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 40 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 20 , at what time will they be reading the same page ?
Options: a ) 9 : 30 , b ) 9 : 00 , c ) 8 : 40 , d ) 7 : 50 , e ) 7 : 00
Rationale: "relative speed = jan - tom = 10 pages per hour = 1 / 6 page per minute time diff = 50 minutes by the time jan started tom already finished ( 30 / 60 ) * 50 = 25 pages time taken = 25 / ( 1 / 6 ) = 25 * 6 = 150 minutes = 7 : 50 answer : d"
Answer: d
Python program:
a = 5 - 4
b = 20 - 30
c = b / const_60
d = a + c 
e = d * 30
f = 40 - 30
g = e / f
h = 5 + g 
i = h / 20
Problem: what is the % change in the area of a rectangle when its length increases by 35 % and its width decreases by 35 % ?
Options: a ) 0 %
b ) 20 % increase
c ) 20 % decrease
d ) 12 % decrease
e ) insufficient data
Rationale: ( 135 / 10 ) * ( 65 / 10 ) = 8775 / 100 ~ 88 of original area 0.88 is a 12 % decrease from 100 / 100 - > d
Answer: d
Python program:
a = 100 + 35 
b = 100 - 35
c = a * b
d = c / 100
e = 100 - d
Problem: what is the product between the place values of two 8 ' s in the numeral 780.38
Options: a ) 0.16 , b ) 0.64 , c ) 80.08 , d ) 64 , e ) 6.4
Rationale: required product = 80 x 0.08 = 6.4 answer is e
Answer: e
Python program:
a = 780 / 38
b = math.floor(a)
c = b * 100
d = 780 - 38
e = math.floor(d)
f = 780 * 38
g = 780 * 38
h = math.floor(g)
i = f - h
j = i / 10
k = e * j
Problem: two numbers are 30 % and 37 % are less than a third number . how much percent is the second number less than the first ?
Options: a ) 19 % , b ) 80 % , c ) 10 % , d ) 90 % , e ) 15 %
Rationale: i ii iii 70 63 100 70 - - - - - - - - 7 100 - - - - - - ? = > 10 % answer : c
Answer: c
Python program:
a = 100 - 30
b = 100 - 37
c = a - b
d = 100 - 30
e = c / d
f = e * 100
Problem: a train is 360 meter long is running at a speed of 30 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 87 , b ) 69 , c ) 60 , d ) 72 , e ) 21
Rationale: "speed = 30 km / hr = 30 * ( 5 / 18 ) m / sec = 25 / 3 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 3 / 25 ) = 60 seconds answer : c"
Answer: c
Python program:
a = 360 + 140 
b = 30 * 1000
c = b / 3600
d = a / c
Problem: the total car population in a chennai is 9000 out of which 5000 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red
Options: a ) 22.5 % , b ) 21.5 % , c ) 20.5 % , d ) 12.5 % , e ) 10.5 %
Rationale: total honda brand red cars = 90 / 100 * 5000 = 4500 total red cars = 60 / 100 * 9000 = 5400 no . of non - honda cars = 9000 - 5000 = 4000 no . of non - honda red cars = 5400 - 4500 = 900 % of non - honda red cars = 900 / 4000 * 100 = 22.5 % answer : a
Answer: a
Python program:
a = 12 + 12 
b = 90 * 1
c = b + 3 
d = 90 * 1
e = c - d
f = e / 2
g = a - f
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 29 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 14.5 minutes , b ) 29 minutes , c ) 35 minutes , d ) 58 minutes , e ) 87 minutes
Rationale: danny ' s time is 29 minutes . the time to reach halfway is 14.5 minutes . steve ' s time is 58 minutes . the time to reach halfway is 29 minutes . the time difference is 29 - 14.5 = 14.5 minutes the answer is a .
Answer: a
Python program:
a = 29 / 2
Problem: find the fraction which has the same ratio to 1 / 2 that 2 / 5 has to 3 / 7
Options: a ) 1 / 2 , b ) 2 / 12 , c ) 14 / 30 , d ) 3 / 8 , e ) 7 / 9
Rationale: "a : 1 / 2 = 2 / 5 : 3 / 7 as the product of the means is equal to the product of the extremes . a * 3 / 7 = 1 / 2 * 2 / 5 a * 3 / 7 = 2 / 10 a = 14 / 30 = > a = 14 / 30 answer : c"
Answer: c
Python program:
a = 2 / 5
b = 3 / 7
c = a / b
d = 1 / 2
e = c * d
Problem: the average of 7 consecutive numbers a , b , c , d , e , f and g is 9 . what percent of g is a ?
Options: a ) 42.0 , b ) 48.0 , c ) 50.0 , d ) 52.2 , e ) 54.0
Rationale: explanation : in such a case the middle number ( d ) is the average ∴ d = 9 and a = 6 and g = 12 required percentage = 6 / 12 x 100 = 50.0 answer : option c
Answer: c
Python program:
a = 7 / 2
b = math.floor(a)
c = 9 + b 
d = 7 / 2
e = math.floor(d)
f = 9 - e
g = c - f
h = 7 / 2
i = math.floor(h)
j = 9 + i 
k = g / j
l = k * 100
Problem: a hen leaps 6 leaps for every 8 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?
Options: a ) 1 : 1 , b ) 3 : 8 , c ) 4 : 3 , d ) 8 : 9 , e ) 1 : 3
Rationale: given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 6 / 3 * 8 = 1 : 1 ' ' answer : 1 : 1 ;
Answer: a
Python program:
a = 6 / 8
b = 3 / 4
c = a / b
Problem: amar takes as much time in running 24 meters as a car takes in covering 60 meters . what will be the distance covered by amar during the time the car covers 2.2 km ?
Options: a ) 700 m , b ) 500 m , c ) 870 m , d ) 880 m , e ) 840 m
Rationale: "distance covered by amar = 24 / 60 ( 2.2 km ) = 2 / 5 ( 2200 ) = 880 m answer : d"
Answer: d
Python program:
a = 2 * 2
b = 24 * a
c = b / 60
Problem: of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents b watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is 3.5 % of 600 , b is 21 . d is the correct answer
Answer: d
Python program:
a = 40 / 100
b = 600 * a
c = 50 / 100
d = 600 * c
e = b + d 
f = 35 / 100
g = 600 * f
h = e + g 
i = h - 600
j = 18 / 100
k = 600 * j
l = i - k
m = l / 2
Problem: the product of two numbers is 336 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 336 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 336 ) = 961 x + y = 31 . option d"
Answer: d
Python program:
a = 2 * 336
b = 289 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 336
f = d + e 
g = math.sqrt(f)
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 12,375 , d ) rs . 16,500 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 600 x 20.625 ) = rs . 12,375 . answer c"
Answer: c
Python program:
a = 5 * 5
b = 600 * a
Problem: x and y together can completes a work in 12 days and y complete the same work in 24 days . then the number of days x required to complete the work will be ?
Options: a ) 15 days . , b ) 12 days . , c ) 24 days . , d ) 13 days . , e ) 16 days .
Rationale: x and y complete in one day = 1 / 12 part , y completes in one day = 1 / 24 parts . therefore x alone can do in one day = 1 / 24 part . therefore the work can be finished by x = 24 days . ans : c
Answer: c
Python program:
a = 1/(12)
b = 1/(24)
c = a - b
d = 1/(c)
Problem: if 204 ÷ 12.75 = 16 , then 2.04 ÷ 1.275 = ?
Options: a ) 16 , b ) 1.6 , c ) 0.16 , d ) 0.016 , e ) none of these
Rationale: explanation : ( 204 / 12.75 ) = 16 ⇒ ( 20.4 ) / ( 1.275 ) = 16 ( ∵ divided numerator and denominator by 10 ) ⇒ 2.04 / 1.275 = 1.6 ( ∵ divided lhs and rhs by 10 ) answer : option b
Answer: b
Python program:
a = 2 / 4
Problem: if n is an integer and 101 n ^ 2 is less than or equal to 3600 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 5 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 3600 n ^ 2 < = 3600 / 101 which will be less than 81 since 3600 / 100 = 36 which is the square of 9 next closest value of n where n ^ 2 < = 36 is 5 ans b"
Answer: b
Python program:
a = 3600 / 101
b = math.sqrt(a)
c = math.floor(b)
Problem: the simple form of the ratio 4 / 3 : 3 / 7 is ?
Options: a ) 7 : 3 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3
Rationale: "4 / 3 : 3 / 7 = 21 : 9 = 7 : 3 answer : a"
Answer: a
Python program:
a = 3 / 7
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 105 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3200 , c ) $ 3500 , d ) $ 6400 , e ) $ 9600
Rationale: let x be the monthly salary 15 % of 1 / 5 * x = 105 x = 3500 answer c
Answer: c
Python program:
a = 3 + 2 
b = 100 * a
c = 30 + 20 
d = c + 35 
e = 100 - d
f = 105 / e
g = b * f
Problem: what is 12 percent of 80 ?
Options: a ) 11.21 , b ) 9.6 , c ) 8.66 , d ) 12.23 , e ) 13.1
Rationale: "we assume that 80 is 100 % assume ' x ' is value we looking for here , 80 = 100 % and x = 12 % therefore , 80 / x = 100 % / 12 % 80 / x = 8.33 x = 9.6 b"
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 12 * n
p = o / 100
Problem: if the average ( arithmetic mean ) of 5 b , 6 b + 47 b , 8 b - 4 and 2 b is 140 , what is the value of b ?
Options: a ) 20 , b ) 22 , c ) 25 , d ) 30 , e ) 48
Rationale: am of 5 b , 6 b + 47 b , 8 b - 4 and 2 b = 5 b + 6 b + 4 + 7 b + 8 b - 4 + 2 b = 28 b / 5 given that 28 b / 5 = 140 b = 25 answer is c
Answer: c
Python program:
a = 140 / 6
b = a + 2
Problem: you buy a piece of land with an area of â ˆ š 400 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 20 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 400 . answer d"
Answer: d
Python program:
a = math.sqrt(400)
Problem: find the number , difference between number and its 3 / 5 is 62 .
Options: a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 62 , = > ( 2 / 5 ) x = 62 = > 2 x = 62 * 5 , = > x = 155 answer : option d"
Answer: d
Python program:
a = 62 / 2
b = a * 5
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 90 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 86 % , d ) 97 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 90 % more than company a ' s assets which is 190 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 95 a + b = 195 kw = 190 kw / ( a + b ) * 100 = 190 / 195 * 100 = 97.43 % or 97 % d"
Answer: d
Python program:
a = 100 + 90 
b = 100 + 90 
c = b / 2
d = 100 + c 
e = a / d
f = e * 100
Problem: if $ 200 invested at a certain rate of simple interest amounts to $ 240 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 210
Rationale: "200 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 200 + 200 * ( r / 100 ) * ( 3 ) = 240 = > r = 20 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 210 answer is e ."
Answer: e
Python program:
a = 150 * 6
b = 240 - 200
c = b * 200
d = c / 200
e = d / 3
f = a * e
g = f / 200
h = 150 + g
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 60 to incur a loss 20 % ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 60 * ( 100 % + 20 % ) = $ 72 number of articles to be sold for $ 72 to incur a 20 % loss : $ 72 / $ 2.40 = 30 thus , solution a is correct ."
Answer: a
Python program:
a = original_price_before_loss / (
Problem: a train 200 m long crosses a platform 200 m long in 40 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 36 kmph
Rationale: "d = 200 + 200 = 400 t = 40 s = 400 / 40 * 18 / 5 = 36 kmph answer : e"
Answer: e
Python program:
a = const_60 * 0
b = 40 * a
c = b - 200
Problem: a shopkeeper sold 30 articles at the cost price of 25 articles . then find the profit % or lost %
Options: a ) 15 % , b ) 18 % , c ) 20 % loss , d ) 25 % , e ) 30 %
Rationale: "here 30 articles selling price = 25 articles cost price so the difference = 25 - 30 = - 5 % of loss = 5 * 100 / 25 = 20 % correct option is c"
Answer: c
Python program:
a = 25 - 30
b = a / 30
c = b * 100
Problem: the sum of three consecutive even numbers is 30 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 25 , e ) 34
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 30 6 p = 30 = > p = 5 . the middle number is : 5 p = 25 . answer : d"
Answer: d
Python program:
a = 30 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 30 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 30 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 30 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: if x is the median of the set { 9 / 2 , 10 / 3 , 27 / 9 , 21 / 5 , x } , x could be
Options: a ) 16 / 5 , b ) 17 / 5 , c ) 28 / 7 , d ) 30 / 7 , e ) 31 / 7
Rationale: "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 10 / 3 = 3 . something , 27 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( c )"
Answer: c
Python program:
a = 9 / 2
b = 10 / 3
c = a + b 
d = 27 / 9
e = c + d 
f = 21 / 5
g = e + f 
h = g / 4
i = 10 / 100
j = h + i 
k = 10 / 100
l = j + k
Problem: james and david work at a grocery shop with 12 other workers . for an internal review , 2 of the 12 workers will be randomly chosen to be interviewed . what is the probability that james and david will both be chosen ?
Options: a ) 1 / 26 , b ) 1 / 36 , c ) 1 / 46 , d ) 1 / 66 , e ) 1 / 56
Rationale: probability that james and david will both be chosen out of 12 workers = ( 2 / 12 ) * ( 1 / 11 ) = 1 / 66 answer d
Answer: d
Python program:
a = 1 / 12
b = 12 - 1
c = 1 / b
d = a * c
e = 2 * d
Problem: bookman purchased 40 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 300 , how many paperback copies were sold ?
Options: a ) 6 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "the bookman had 10 hardback ad 40 - 10 = 30 paperback copies ; 14 copies were sold , hence 40 - 14 = 26 copies were left . let # of paperback copies left be p then 10 p + 20 ( 26 - p ) = 300 - - > 10 p = 220 - - > p = 22 # of paperback copies sold is 30 - 22 = 8 answer : c"
Answer: c
Python program:
a = 40 - 10
b = a * 10
c = 10 * 20
d = b + c 
e = d - 300
f = math.gcd(40, 10)
g = f * 20
h = e - g
i = h / 10
Problem: a candidate got 35 % of the votes and lost to the rival by 1800 votes . how many votes were cast ?
Options: a ) 5500 , b ) 6000 , c ) 6500 , d ) 7000 , e ) 7500
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1800 10 % = 600 100 % of the votes = 6000 answer : b"
Answer: b
Python program:
a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 1800 / d
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number d of people surveyed by the company ?
Options: a ) 46 , b ) 80 , c ) d . 90 , d ) d . 100 , e ) 200
Rationale: 100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .
Answer: d
Python program:
a = 100 - 23
b = a + 23 
c = b + 20 
d = c / 2
e = d - 20
f = 100 - 23
g = f + 23 
h = g + 20 
i = h / 2
j = e + i
Problem: two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 54 seconds . the length of each train is :
Options: a ) 82 m , b ) 50 m , c ) 75 m , d ) 80 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 54 secs the total distance traveled is 54 x 25 / 9 = 150 m . therefore the length of each train is = 150 / 2 = 75 m . answer c"
Answer: c
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 54
e = d / 2
Problem: if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 7 m of the same rod ?
Options: a ) 22.8 kg , b ) 26.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 7 : : 42.75 : x = > 11.25 x x = 7 x 42.75 = > x = ( 7 x 42.75 ) / 11.25 = > x = 26.6 answer : b"
Answer: b
Python program:
a = 7 * 42
b = a / 11
Problem: if a farmer wants to plough a farm field on time , he must plough 160 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 600 , b ) 490 , c ) 448 , d ) 435 , e ) 679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 160 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 160 x = 85 ( x + 2 ) + 40 75 x = 210 x = 2.8 so the farmer planned to have the work done in 6 days , and the area of the farm field is 160 ( 2.8 ) = 448 hectares correct answer c"
Answer: c
Python program:
a = 2 * 85
b = 40 + a 
c = 160 - 85
d = b / c
e = d * 160
Problem: a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 10 % salt solution . what is the value of x ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 10 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 10 ) / ( 10 - 0 ) = 5 / 1 1 / x = 5 / 1 x = 1 / 5 answer : a"
Answer: a
Python program:
a = 60 - 10
b = 10 / a
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 36 pages per hour . if tom starts reading a novel at 4 : 00 , and jan begins reading an identical copy of the same book at 4 : 48 , at what time will they be reading the same page ?
Options: a ) 7 : 18 , b ) 7 : 48 , c ) 8 : 18 , d ) 8 : 48 , e ) 9 : 18
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 24 pages in the first 48 minutes . jan can catch tom at a rate of 6 pages per hour , so it will take 4 hours to catch tom . the answer is d ."
Answer: d
Python program:
a = 4 - 4
b = 48 - 0
c = b / const_60
d = a + c 
e = d * 30
f = 36 - 30
g = e / f
h = 4 + g 
i = h / 48
Problem: bhatia , ashtikar and singh begin to play with rs 70 each . at the end the ratio of the amounts left with ashtikar and singh is 1 : 2 and of those with singh and bhatia is 4 : 1 . what is singh ' s gain ( in rs ) ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 53
Rationale: we have b + a + s = 210 and s = 2 a , s = 4 b and a = 2 b solving these eqs we got that singh have rs . 120 in the end bhatia have 30 and astikar have 60 . so singh ' s profit is 120 - 70 = 50 answer : d
Answer: d
Python program:
a = 70 * 3
b = a * 4
c = 4 + 1 
d = c + 2 
e = b / d
f = e - 70
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 7 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 47
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 7 ^ 2 - 2 = 47 . thus , the answer is e ."
Answer: e
Python program:
a = 2 ** 2
b = a - 2
Problem: the floor of a rectangular room is 19 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 144 m 2 , b ) 140 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 23 ã — 16 = 368 m 2 area of the inner rectangle = 19 ã — 12 = 228 m 2 required area = ( 368 â € “ 228 ) = 140 m 2 answer b"
Answer: b
Python program:
a = 2 * 2
b = a + 19 
c = 2 * 2
d = 12 + c 
e = rectangle_area - (
Problem: the price of a tv was increased by 30 percent . the new price was then increased by 20 percent . a single increase of what percent is equivalent to these two successive increases ?
Options: a ) 50 % , b ) 60 % , c ) 65 % , d ) 56 % , e ) 45 %
Rationale: consider base price - $ 100 25 % increase = 1.30 * 100 = $ 130 another 20 % increase on new price = 1.2 * 130 = $ 156 so final price of radio - $ 156 therefore a 56 % increase correct option - d
Answer: d
Python program:
a = 100 + 30 
b = a / 100
c = 20 + 100 
d = c / 100
e = b * d
f = e - 1
g = f * 100