euclaise/mathqa_programs huggingface dataset:
Problem: if m and n are positive integers and n ≠ 1 , then mn ( n − 1 ) is
Options: a ) m - n , b ) m + n , c ) mn , d ) mn ^ 2 - mn , e ) mn ^ 2
Rationale: "mn ( n - 1 ) = mn ^ 2 - mn answer : d"
Answer: d
Python program:
a = 1 * 2
b = a ** const_0_33
c = math.floor(b)
Problem: two numbers are in the ratio of 5 : 7 . if 20 is subtracted from each number , they are in the ratio of 5 : 9 . what are the two numbers ?
Options: a ) 35 , 49 , b ) 40 , 56 , c ) 45 , 63 , d ) 50 , 70 , e ) 55 , 77
Rationale: "( 5 x - 20 ) : ( 7 x - 20 ) = 5 y : 9 y 5 x - 20 = 5 y 7 x - 20 = 9 y 140 - 100 = 45 y - 35 y 40 = 10 y y = 4 5 x - 20 = 20 x = 8 the two numbers are 5 x and 7 x which are 40 and 56 . the answer is b ."
Answer: b
Python program:
a = 9 * 4
b = 5 * 20
c = a - b
d = c * 2
e = 3 / 0
f = d * e
g = 9 * 20
h = 5 * 20
i = g - h
j = i * 5
k = f - j
Problem: a train 500 m long can cross an electric pole in 10 sec and then find the speed of the train ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "length = speed * time speed = l / t s = 500 / 10 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : e"
Answer: e
Python program:
a = 500 / 1000
b = 10 / 3600
c = a / b
Problem: a retailer sold 2 houses at each $ 15000 . on 1 st house he got 20 % profit and on 2 nd house he loss 5 % then find his net profit or loss ?
Options: a ) 10 % , b ) 9 % , c ) 14 % , d ) 15 % , e ) 12 %
Rationale: "a = 20 % b = - 5 % profit % = 20 - 5 + ( - 100 / 100 ) = 14 % answer is c"
Answer: c
Python program:
a = 5 / 100
b = 1 - a
c = b * 2
d = 5 / 100
e = c - d
f = e * 5
Problem: ages of two persons differ by 16 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 16,32 , d ) 18,34 , e ) 19,32
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 16 ) = > 3 ( x - 6 ) = ( x + 16 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 10 = > x = 14 . so other person age is x + 16 = 30 answer : option b"
Answer: b
Python program:
a = 6 * 6
b = a + 16 
c = b - 6
d = 6 - 1
e = c / d
f = e - 1
Problem: the sum of two consecutive numbers is 452 . the greatest among these three number is :
Options: a ) 226 , b ) 228 , c ) 229 , d ) 230 , e ) 200
Rationale: "let the numbers be x , x + 1 then , x + ( x + 1 ) = 452 2 x = 450 x = 225 greatest number , ( x + 1 ) = 226 answer : a"
Answer: a
Python program:
a = 452 + 1 
b = a / 2
Problem: a car travels uphill at 30 km / hr and downhill at 90 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 39 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 90 = 5 / 9 ; avg speed = 150 / ( 10 / 3 + 5 / 9 ) = 39 kmph answer : b"
Answer: b
Python program:
a = 100 + 50 
b = 100 / 30
c = 50 / 90
d = b + c 
e = a / d
Problem: six 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 7776 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 = 46656 ways . hence the probability is 6 / 46656 = 1 / 7776 answer : b"
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: a present value of a machine is $ 700 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 567
Rationale: "p = $ 700 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 700 * 9 / 10 * 9 / 10 = $ 567 answer is e"
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = b ** 2
d = 700 * c
Problem: if xy denotes x is raised to the power y , find the last two digits of 19413843 + 19614181
Options: a ) 67 , b ) 97 , c ) 55 , d ) 32 , e ) 62
Rationale: "1721 ^ 3856 unit digit = 1 ^ 2 = 1 10 th digit = 5 * 6 = 30 = 0 means last two digit = 1 and 1982 ^ 4181 unit digit = 1 10 th digit = 8 * 2 = 16 mean last two digit = 61 hence , 61 + 1 = 62"
Answer: e
Python program:
a = 100 ** 2
b = reminder - (
c = b - 100
d = c + 10 
e = d - 10
f = 100 ** 2
g = 19413843 / f
h = math.floor(g)
i = e - reminder
Problem: two trains 200 m and 180 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 72 sec , b ) 132 sec , c ) 192 sec , d ) 273.6 sec , e ) none
Rationale: "solution relative speed = ( 45 - 40 ) kmph = 5 kmph = ( 5 x 5 / 18 ) m / sec = ( 25 / 18 ) m / sec time taken = ( 380 x 18 / 25 ) sec = 273.6 sec . answer d"
Answer: d
Python program:
a = 200 + 180 
b = a / 1000
c = 45 - 40
d = b / c
e = 3600 * d
Problem: at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "in 24 liters , red = 5 / 8 * 24 = 15 and blue = 9 so , 15 / ( 9 + x ) = 3 / 5 or , x = 16 ( answer d )"
Answer: d
Python program:
a = 5 + 3 
b = 5 / a
c = 24 * b
d = 5 + 3 
e = 3 / d
f = c / e
g = 5 + 3 
h = 5 / g
i = f * h
j = 5 + 3 
k = 5 / j
l = 24 * k
m = 24 - l
n = i - m
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 33 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 22 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: 262.85 ( 33 ) + 3 , 104.35 x = 1 , 399.45 ( 33 + x ) solve the equation . 262.85 ( 33 ) + 3 , 104.35 x = 1 , 399.45 ( 33 + x ) 8 , 674.05 + 3 , 104.35 x = 46181.85 + 1 , 369.45 x 8 , 674.05 + 1 , 704.9 x = 46181.85 1 , 704.9 x = 37 , 507.8 x = 22 answer is b .
Answer: b
Python program:
a = 33 * 1399
b = 33 * 262
c = a - b
d = 3104 - 35
e = c / d
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 7800 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 7800 ] – [ 3 1 / 3 % of rs . 7800 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 7800 = 1 / 6 % of rs . 7800 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 7800 ] = rs . 13 . answer is b ."
Answer: b
Python program:
a = 1 / 2
b = a + 3 
c = 1 / 3
d = c + 3 
e = b - d
f = e * 7800
g = f / 100
Problem: a train 200 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 12 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 200 m at ( 50 / 3 ) m / sec = ( 200 x 3 / 50 ) sec = 12 sec . answer d"
Answer: d
Python program:
a = 68 + 8 
b = a * const_0_2778
c = 200 / b
Problem: evaluate : 40 - 12 ÷ 6 × 2 =
Options: a ) a ) 24 , b ) b ) 36 , c ) c ) 48 , d ) d ) 60 , e ) e ) 72
Rationale: "according to order of operations , 12 ÷ 6 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 6 × 2 = 2 × 2 = 4 hence 40 - 12 ÷ 6 × 2 = 40 - 4 = 36 correct answer is b ) 36"
Answer: b
Python program:
a = 12 * 6
b = a * 2
c = 40 - b
Problem: in town x , 96 percent of the population are employed , and 24 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 75 % , e ) 52 %
Rationale: "total employed people 96 % , out of which 24 are employed males , hence 72 % are employed females . ( employed females ) / ( total employed people ) = 72 / 96 = 3 / 4 = 75 % answer : d ."
Answer: d
Python program:
a = 96 - 24
b = a / 96
c = b * 100
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 4 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 16
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 4 ( pir ^ 2 ) pir ^ 2 = 8 pir r = 8 answer : d"
Answer: d
Python program:
a = 4 ** 2
b = math.sqrt(a)
c = 2 * b
Problem: in an entrance exam , 3 marks is awarded for every correct answer and ( - 1 ) for every wrong answer . if a student gets 38 marks after attempting all questions , find the number of questions answered correctly if the total questions were 70 .
Options: a ) 38 , b ) 40 , c ) 27 , d ) 43 , e ) 56
Rationale: explanation : let x be the number of questions answered correctly . hence , number of questions whose answer were wrong = ( 70 – x ) 3 * x + ( 70 – x ) * ( - 1 ) = 38 4 x = 38 + 70 = 108 x = 27 answer c
Answer: c
Python program:
a = 3 * 70
b = a - 38
c = 3 + 1 
d = b / c
e = 70 - d
Problem: a meal cost $ 35.50 adn there was no tax . if the tip was more than 5 pc but less than 8 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 38 , e ) 36 - 37
Rationale: 5 % ( 35.5 ) = 1.775 8 % ( 35.5 ) = 2.84 total amount could have been 35.5 + 1.775 and 35.5 + 2.84 = > could have been between 37.275 and 38.34 = > approximately between 37 and 38 answer is b . d
Answer: d
Python program:
a = 35 * 5
b = a / 100
c = b + 35
Problem: r is the set of positive odd integers less than 10 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none
b ) two
c ) four
d ) five
e ) seven
Rationale: squares < 10 { 1 , 4,9 } s = { 1,9 } r = { 1,3 , . . . . . 10 } hence b .
Answer: b
Python program:
a = 10 - 4
b = a - 4
Problem: in a certain kindergarten , every child has got either a dog or a cat or both . 18 children have got dogs only and 6 children have got both dogs and cats . if there are 30 children in the kindergarten , how many of them have cats ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: a : only cats b : both cats and dogs c : only dogs as per question , a + b + c = 30 c = 18 b = 6 , so a = 6 . hence , a + b = 12 . answer is b
Answer: b
Python program:
a = 30 - 18
Problem: if 45 % of z is 90 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 150
Rationale: ( 45 / 100 ) z = ( 90 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 90 / 100 ) * ( 3 / 4 ) x i . e . z = ( 90 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.5 ) x = ( 150 / 100 ) x i . e . z is 150 % of x answer : option e
Answer: e
Python program:
a = 75 / 100
b = 45 / 100
c = 90 / 100
d = b / c
e = a / d
f = e * 100
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fifth of his earnings to charity . if the worker ' s charitable contributions totaled one - seventh of his earnings for the entire year , what is the value of n ?
Options: a ) 31 / 4 , b ) 33 / 4 , c ) 29 / 4 , d ) 27 / 4 , e ) 25 / 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 5 = 1 / 7 ( 11 x + nx ) ; 11 / 10 + n / 5 = 1 / 7 ( 11 + n ) 11 + 2 n / 10 = 11 + n / 7 = > 77 + 14 n = 110 + 10 n = > 4 n = 33 n = 33 / 4 answer : b"
Answer: b
Python program:
a = 12 - 1
b = 12 - 3
c = 1/(b)
d = 1/(10)
e = c - d
f = a * e
g = 1 + 4 
h = 1/(g)
i = 12 - 3
j = 1/(i)
k = h - j
l = f / k
Problem: a lady builds 7 cm length , 18 cm width , and 3 cm height box using 9 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 42
b ) 45
c ) 47
d ) 49
e ) 56
Rationale: number of cubes required = volume of box / volume of cube = 7 * 18 * 3 / 9 = 42 cubes answer : a
Answer: a
Python program:
a = 7 * 18
b = a * 3
c = b / 9
Problem: solve the quickfire maths brain teaser â ˆ š 49 % = ?
Options: a ) 30 % , b ) 40 % , c ) 70 % , d ) 19 % , e ) 29 %
Rationale: "â ˆ š 49 % = > â ˆ š 49 / â ˆ š 100 = > 7 / 10 = > 70 / 100 = > 70 % c"
Answer: c
Python program:
a = 1 + 49 
b = 100 / a
Problem: the compound ratio of 1 : 4 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 3 : 10 , e ) 1 : 4
Rationale: "1 / 4 * 3 / 2 * 4 / 5 = 3 / 10 = 3 : 10 answer : d"
Answer: d
Python program:
a = 1 * 3
b = 4 * 2
c = a / b
d = 3 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 6 € ( 4 € 5 ) =
Options: a ) 480 , b ) 120 , c ) 160 , d ) 240 , e ) 360
Rationale: working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 6 € 40 = 2 * 6 * 40 = 480 hence , answer is a
Answer: a
Python program:
a = 2 * 6
b = 2 * 4
c = b * 5
d = a * c
Problem: a is a working partner and b is a sleeping partner in a business . a puts in 50,000 and b 60,000 . a gets 12.5 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the share of a in profit of 8800 .
Options: a ) 3500 , b ) 4600 , c ) 5400 , d ) 4800 , e ) none of these
Rationale: the amount a gets for managing = 12.5 % of rs . 8800 = 1100 remaining profit = 8800 – 1100 = 7700 this is to be divided in the ratio 5 : 6 . share of a = 5 / 11 of 7700 = 3500 ⇒ total share of a = 3500 + 1100 = 4600 . answer b
Answer: b
Python program:
a = 12 * 5
b = a / 100
c = 8800 - b
d = 2 + 3 
e = c * d
f = 2 + 3 
g = 2 + 4 
h = f + g 
i = e / h
j = 12 * 5
k = j / 100
l = i + k
Problem: the number x of cars sold each week varies with the price y in dollars according to the equation x = 800000 – 50 y . what would be the total weekly revenue , in dollars , from the sale of cars priced at $ 12000 ?
Options: a ) 50,000 , b ) 750,000 , c ) 850,000 , d ) 7 , 500,000 , e ) 2,400 , 000,000
Rationale: number of cars sold = x = 800000 - 50 y y = 12000 x = 800000 - 600000 = 200000 revenue from 50000 cars = 12000 * 200000 = 2400000000 answer e
Answer: e
Python program:
a = 50 * 12000
b = 800000 - a
c = b * 12000
d = c / 1000
e = d / 1000
f = e / 3
g = f + 50
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 20 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2700 , d ) 10800 , e ) 3600
Rationale: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 20 ã — 4 ã — 270 â ‡ ” x = 20 x 4 x 270 / 6 = 3600 . answer e"
Answer: e
Python program:
a = 270 / 6
b = a * 4
c = b * 20
Problem: the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 111 cm . what was the actual average height of the students in the class ?
Options: a ) 174 cm , b ) 173 cm , c ) 172 cm , d ) 171 cm , e ) 170 cm
Rationale: "the total height was 40 cm too much . the average height should be reduced by 40 cm / 20 = 2 cm the answer is b ."
Answer: b
Python program:
a = 20 * 175
b = 151 - 111
c = a - b
d = c / 20
Problem: john was thrice as old as tom 6 years ago . john will be 2 times as old as tom in 4 years . how old is tom today ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 4 = 2 ( t + 4 ) ( 3 t - 12 ) + 4 = 2 t + 8 t = 16 the answer is c .
Answer: c
Python program:
a = 6 * 2
b = 4 * 2
c = a + b 
d = c - 4
Problem: mary and mike enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 800 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 2000 , b ) $ 6000 , c ) $ 4000 , d ) $ 1333 , e ) $ 3000
Rationale: explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 7 : 3 . i . e . , 70 % of 2 x would go to mary and 30 % of 2 x would go to mike . hence , mary would get ( 70 - 30 ) % of 2 x more than mike or 40 % of 2 x = $ 800 i . e . , ( 40 / 100 ) * 2 x = 800 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . the correct choice is ( e )
Answer: e
Python program:
a = 700 / 1000
b = 300 / 1000
c = a - b
d = 1 / 3
e = 1 - d
f = c * e
g = 800 / f
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds w in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out w : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Python program:
a = 25 + 25 
b = a / 2
c = 10 + b
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much t does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) t = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Python program:
a = 3 / 96
b = a / 2
c = 1 + b 
d = c ** 4
e = 10000 * d
Problem: in an intercollegiate competition that lasted for 3 days , 115 students took part on day 1 , 80 on day 2 and 100 on day 3 . if 50 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 40 took part on all three days , how many students took part only on day 3 ?
Options: a ) 20 , b ) 35 , c ) 40 , d ) 55 , e ) 60
Rationale: "day 1 & 2 = 50 ; only day 1 & 2 ( 50 - 40 ) = 10 , day 2 & 3 = 70 ; only day 2 & 3 ( 70 - 40 ) = 30 , only day 3 = 100 - ( 10 + 30 + 40 ) = 20 answer : a"
Answer: a
Python program:
a = 40 + 50 
b = 50 + 70 
c = b + 40 
d = 80 - c
e = 40 + d 
f = e / 2
g = a + f 
h = 115 - g
Problem: a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 401 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ?
Options: a ) 44001 , b ) 44000 , c ) 40400 , d ) 40401 , e ) can not be determined
Rationale: "explanatory answer the shape of the area used for growing cauliflower has remained a square in both the years . let the side of the square area used for growing cauliflower this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cauliflower last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cauliflower grown has increased by 401 , the area would have increased by 401 sq ft because each cauliflower takes 1 sq ft space . hence , x 2 - y 2 = 401 ( x + y ) ( x - y ) = 401 . 401 is a prime number and hence it will have only two factors . i . e . , 401 and 1 . therefore , 401 can be expressed as product of 2 numbers in only way = 401 * 1 i . e . , ( x + y ) ( x - y ) = 401 * 1 so , ( x + y ) should be 401 and ( x - y ) should be 1 . solving the two equations we get x = 201 and y = 200 . therefore , number of cauliflower produced this year = x 2 = 2012 = 40401 alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , b and c . as 44001,44000 and 40400 are not the square of any number . check choice d : if this year ' s produce is 40401 , last year ' s produce would have been 40401 - 401 = 40000 40000 is the square of 200 . so , 40401 is the answer . choice d ."
Answer: d
Python program:
a = 401 - 1
b = a / 2
c = b ** 2
d = c + 401
Problem: if 5 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 30 , c ) 36 , d ) 40 , e ) 60
Rationale: let the capacity of the tank = c ( 3 / 4 ) c + 5 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 5 = > ( 3 / 20 ) c = 5 = > c = ( 5 * 20 ) / 3 = 33.33 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 5 = 24.99 + 5 = 29.99 = 30 answer b
Answer: b
Python program:
a = 9 / 10
b = 3 / 4
c = a - b
d = 5 / c
e = 3 / 4
f = d * e
g = f + 5
Problem: a retailer buys 120 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 210 , b ) 215 , c ) 212 , d ) 230 , e ) 320
Rationale: "let the market price of each pen be $ 1 then , cost price of 120 pens = $ 36 selling price of 120 pens = 99 % of $ 120 = $ 118.80 profit % = ( ( 82.80 * 100 ) / 36 ) % = 230 % answer d"
Answer: d
Python program:
a = 1 / 100
b = 1 - a
c = 36 / 120
d = b - c
e = 36 / 120
f = d / e
g = 100 * f
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 68 %
Options: a ) 14.11 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 68 / 100 = 50.40 so x = 14.11 answer : a"
Answer: a
Python program:
a = 100 / 68
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
Problem: a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 1.60 , what total number of pens and pencils did the customer purchase ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y . there are six possible numbers of pencils that fit that requirement : 1 pen : $ 0.35 and 5 pencils for $ 0.25 each . that ' s 1 pens and 5 pencils for a total of 6 pens and pencils . choice ( a ) is correct ."
Answer: a
Python program:
a = 0 + 35 
b = 1 / 60
c = b * 2