euclaise/mathqa_programs huggingface dataset:
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 r 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 r : ( 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: what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 4 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 4 , hence the sum in the brackets will be even multiple of 4 ( the sum of 9 even numbers is even ) . which yields remainder of 0 upon division by 4 . answer : e"
Answer: e
Python program:
a = 8 ** 1
b = 8 ** 1
c = a - b
d = c / 8
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 8112 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 91.00 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 7600 ⇔ 12 x 2 = 8112 ⇔ x 2 = 676 ⇔ x = 26 so , length = 78 m and breadth = 104 m . perimeter = [ 2 ( 78 + 104 ) ] m = 364 m . ∴ cost of fencing = rs . ( 0.25 × 364 ) = rs . 91 . answer d"
Answer: d
Python program:
a = 3 * 4
b = 8112 / a
c = math.sqrt(b)
d = 3 * c
e = 3 * 4
f = 8112 / e
g = math.sqrt(f)
h = 4 * g
i = rectangle_perimeter * (
j = i / 25
Problem: a sum was put at simple interest at a certain rate for 5 years had it been put at 6 % higher rate , it would have fetched 90 more . find the sum .
Options: a ) 90 , b ) 100 , c ) 200 , d ) 300 , e ) 400
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 90 = p × 5 x 6 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 90 × 100 / 5 x 6 = 300 answer d"
Answer: d
Python program:
a = 6 / 100
b = a * 5
c = 90 / b
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 5 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 15 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 20 ) * ( x - 5 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 20 ) + ( x / 30 ) - ( 5 / 20 ) = 1 5 x / 60 = 5 / 4 x = 60 / 4 x = 15 therefore , the answer is d : 15 ."
Answer: d
Python program:
a = 1 / 30
b = a * 5
c = 1 - b
d = 1 / 20
e = 1 / 30
f = d + e 
g = c / f
h = g + 5
Problem: if 30 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 10 : 9 , d ) 7 : 3 , e ) none of these
Rationale: "explanation : let 30 % of a = 1 / 3 b then , 30 a / 100 = 1 b / 3 = > 3 a / 10 = b / 3 = > a : b = 10 : 9 answer : c"
Answer: c
Python program:
a = 1 / 4
b = 30 / 100
c = a / b
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 32000 ?
Options: a ) 81000 , b ) 33888 , c ) 77678 , d ) 200988 , e ) 40500
Rationale: "32000 * 9 / 8 * 9 / 8 = 40500 answer : e"
Answer: e
Python program:
a = 1 / 8
b = a * 32000
c = 32000 + b 
d = 1 / 8
e = 1 / 8
f = e * 32000
g = 32000 + f 
h = d * g
i = c + h
Problem: out of 450 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 150 , e ) none of these
Rationale: "explanation : students who play cricket , n ( a ) = 325 students who play football , n ( b ) = 175 total students who play either or both games , = n ( a ∪ b ) = 450 − 50 = 400 required number , n ( a ∩ b ) = n ( a ) + n ( b ) − n ( a ∪ b ) = 325 + 175 − 400 = 100 option b"
Answer: b
Python program:
a = 175 + 325 
b = 450 - 50
c = a - b
Problem: a number is doubled and 7 is added . if resultant is trebled , it becomes 99 . what is that number
Options: a ) 8 , b ) 10 , c ) 14 , d ) 13 , e ) 16
Rationale: "explanation : = > 3 ( 2 x + 7 ) = 99 = > 2 x + 7 = 33 = > x = 13 option d"
Answer: d
Python program:
a = 3 * 7
b = 99 - a
c = 3 * 2
d = b / c
Problem: a bag holds 3 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be green ?
Options: a ) 1 / 10 , b ) 1 / 6 , c ) 3 / 10 , d ) 1 / 5 , e ) 1 / 2
Rationale: "given : 3 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 3 red and 3 green marbles after one green has been picked , we need to pick 1 green from a total of 2 greenand 3 red marbles . p ( both green ) = ( 3 / 6 ) * ( 2 / 5 ) = 1 / 5 option d"
Answer: d
Python program:
a = math.comb(3, 3)
b = 2 + 0 
c = math.comb(b, 2)
d = a / c
Problem: in a 200 m race , a covers the distance in 45 seconds and b in 60 second . in this race a beats b by :
Options: a ) 20 m , b ) 50 m , c ) 45 m , d ) 60 m , e ) none of these
Rationale: "solution distance covered by b in 15 sec . = ( 200 / 60 x 15 ) m = 50 m . ∴ a beats b by 50 metres . answer b"
Answer: b
Python program:
a = 200 / 60
b = 60 - 45
c = a * b
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 8 x + 4 = 0 ?
Options: a ) 15 , b ) 14 , c ) 13 , d ) 12 , e ) 11
Rationale: "a / b + b / a = ( a 2 ] / ab a + b = + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab - 8 / 1 = - 8 ab = 4 / 1 = 4 hence a / b + b / a = [ ( - 8 ) 2 - 2 ( 4 ) ] / 4 = 56 / 4 = 14 . answer : b"
Answer: b
Python program:
a = negate ** (
b = a / 2
c = b - 4
Problem: 20 ^ 10 / 120 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 10 / 3 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "20 ^ 10 / 120 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 10 / 3 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 20 ^ 10 / 120 ^ 5 = ( 20 ^ 10 ) / ( 6 ^ 5 ) ( 20 ^ 5 ) = ( 20 ^ 5 ) / ( 6 ^ 5 ) = ( 2 ^ 5 ) ( 10 ^ 5 ) / ( 2 ^ 5 ) ( 3 ^ 5 ) = ( 10 / 3 ) ^ 5 . thus , c is the answer ."
Answer: c
Python program:
a = 20 ** 10
b = 20 ** 5
c = a / b
Problem: darren bought 5 packs of white t - shirts and 3 packs of blue t - shirts for his basketball team . the white t - shirts come in packs of 6 , and the blue t - shirts come in packs of 9 . how many t - shirts did darren buy in all ?
Options: a ) 77 , b ) 57 , c ) 34 , d ) 65 , e ) 21
Rationale: step 1 : find the number of white t - shirts . 5 × 6 = 30 step 2 : find the number of blue t - shirts . 3 × 9 = 27 step 3 : find the total number of t - shirts . 30 + 27 = 57 darren bought 57 t - shirts . answer is b .
Answer: b
Python program:
a = 5 * 6
b = 3 * 9
c = a + b
Problem: car a is 10 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 2.25 , c ) 2.75 , d ) 2.5 , e ) 3.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 10 miles and drive 8 miles ahead so to drive 18 miles it ' ll need 18 / 8 = 2.25 hours . answer : b"
Answer: b
Python program:
a = 10 + 8 
b = 58 - 50
c = a / b
Problem: in a 400 m race , a covers the distance in 60 seconds and b in 100 second . in this race a beats b by :
Options: a ) 20 m , b ) 125 m , c ) 120 m , d ) 160 m , e ) none of these
Rationale: "solution distance covered by b in 40 sec . = ( 400 / 100 x 40 ) m = 160 m . ∴ a beats b by 160 metres . answer d"
Answer: d
Python program:
a = 400 / 100
b = 100 - 60
c = a * b
Problem: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 20 % tip , what is the most their food can cost ?
Options: a ) 39.55 $ , b ) 40.63 $ , c ) 38.63 $ , d ) 37.88 $ , e ) 35.15 $
Rationale: let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.20 * 1.07 x = 50 x = 37.88 hence , the correct option is c
Answer: c
Python program:
a = 7 + 20 
b = a / 100
c = b + 1 
d = 50 / c
Problem: the h . c . f . of two numbers is 11 and their l . c . m . is 693 . if one of the number is 77 , find the other ?
Options: a ) 88 , b ) 99 , c ) 76 , d ) 55 , e ) 66
Rationale: "other number = 11 * 693 / 77 = 99 answer is b"
Answer: b
Python program:
a = 11 * 77
Problem: p , q and r can do a work in 6 , 9 and 12 days respectively . they completed the work and got rs . 195 . what is the share of p ?
Options: a ) 80 , b ) 70 , c ) 85 , d ) 90 , e ) 95
Rationale: "the ratio of their working rates = 1 / 6 : 1 / 9 : 1 / 12 = 6 : 4 : 3 . since , they work together , the share of p = 6 / 13 * 195 = rs . 90 answer : d"
Answer: d
Python program:
a = 100 * 100
b = 195 * 9
c = 9 * 12
d = c / 6
e = d + 9 
f = e + 12 
g = b / f
h = a + g
Problem: machine a and machine b are each used to manufacture 220 sprockets . it takes machine a 10 hours longer to produce 220 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "machine b : takes x hours to produce 220 sprockets machine a : takes ( x + 10 ) hours to produce 220 sprockets machine b : in 1 hour , b makes 220 / x sprockets machine a : in 1 hour , a makes 220 / ( x + 10 ) sprockets equating : 1.1 ( 220 / ( x + 10 ) ) = 220 / x 242 / ( x + 10 ) = 220 / x 242 x = 220 x + 2200 22 x = 2200 x = 100 a makes 220 / ( 110 ) = 2 sprockets per hour answer : a"
Answer: a
Python program:
a = 10 * 220
b = 100 + 10 
c = b / 100
d = a * c
e = 100 + 10 
f = e / 100
g = 220 * f
h = g - 220
i = d / h
j = 220 / i
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 30 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 130 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 130 - 90 ) / 90 * 100 = 30 % answer : d ."
Answer: d
Python program:
a = 100 + 30 
b = 100 - 10
c = a - b
d = c * 100
e = 100 - 10
f = d / e
Problem: a cricket bat is sold for $ 900 , making a profit of $ 300 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 40 %
Rationale: "300 / ( 900 - 300 ) = 50 % . answer : d"
Answer: d
Python program:
a = 900 - 300
b = 300 / a
c = b * 100
Problem: each of the integers from 1 to 15 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
Options: a ) 9 , b ) 12 , c ) 11 , d ) 10 , e ) 3
Rationale: "out of the 15 integers : 8 are odd and 7 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 8 odd numbers first 2 . 9 th number will be the first even number so we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 9 . ( a )"
Answer: a
Python program:
a = 15 / 2
b = a + 1
Problem: a student chose a number , multiplied it by 7 , then subtracted 150 from the result and got 130 . what was the number he chose ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "let x be the number he chose , then 7 ⋅ x − 150 = 130 7 x = 280 x = 40 correct answer a"
Answer: a
Python program:
a = 130 + 150 
b = a / 7
Problem: average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 550 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 550 x 3 rs . = 1290 rs . correct option : e"
Answer: e
Python program:
a = 735 * 4
b = 4 - 1
c = 550 * b
d = a - c
Problem: evaluate : ( 1 - 1 / 10 ) ( 1 - 1 / 11 ) ( 1 - 1 / 12 ) . . . ( 1 - 1 / 99 ) ( 1 - 1 / 100 )
Options: a ) 5 / 100 , b ) 6 / 100 , c ) 7 / 100 , d ) 8 / 100 , e ) 9 / 100
Rationale: ( 1 - 1 / 10 ) ( 1 - 1 / 11 ) ( 1 - 1 / 12 ) . . . ( 1 - 1 / 99 ) ( 1 - 1 / 100 ) = ( 9 / 10 ) ( 10 / 11 ) ( 11 / 12 ) . . . ( 98 / 99 ) ( 99 / 100 ) = 9 / 100 : simplify correct answer e
Answer: e
Python program:
a = 10 - 1
b = a / 100
Problem: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of w ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . w * 23 + 39 = 25 * ( w + 1 ) w = 7 ans . ( a )"
Answer: a
Python program:
a = 39 - 15
b = 2 + 1 
c = a / b
d = c - 1
Problem: 210 college students were asked in a survey if they preferred windows or mac brand computers . 90 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 60 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: "210 = 90 ( mac ) + x ( window ) + 60 ( both ) = > x = 60 answer : d"
Answer: d
Python program:
a = 210 - 60
b = a - 90
c = 210 - 60
d = c - 90
e = d / 3
f = b - e
Problem: 210 school students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .
Answer: b
Python program:
a = 90 + 60 
b = a + 10 
c = b + 10 
d = 210 - c
Problem: speed of a boat in standing water is 11 kmph and speed of the stream is 2.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 21.12 hours , b ) 20.12 hours , c ) 19.12 hours , d ) 18.12 hours , e ) 17.12 hours
Rationale: "speed upstream = 8.5 kmph speed downstream = 13.5 kmph total time taken = 105 / 8.5 + 105 / 13.5 = 20.12 hours answer is b"
Answer: b
Python program:
a = 11 + 2 
b = 11 - 2
c = a + b 
d = c * 105
e = 11 + 2 
f = 105 / e
g = 11 - 2
h = 105 / g
i = f + h 
j = 11 + 2 
k = 11 - 2
l = j + k 
m = i - l
n = m * const_60
o = d + n
Problem: a train 650 m long is running at a speed of 81 km / hr . in what time will it pass a bridge 340 m long ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "speed = 81 * 5 / 18 = 45 / 2 m / sec total distance covered = 650 + 340 = 990 m required time = 990 * 2 / 45 = 44 sec answer : c"
Answer: c
Python program:
a = 81 - 340
b = a * const_0_2778
c = 650 / b
Problem: what is the probability that carol and bernie will get selected for a job they both applied for in a company , given that their chances of getting selected is 4 / 5 and 3 / 5 respectively ?
Options: a ) 8 / 25 , b ) 11 / 24 , c ) 12 / 25 , d ) 12 / 25 , e ) 12 / 23
Rationale: explanation : p ( carol ) = 4 / 5 p ( bernie ) = 3 / 5 e = { carol and bernie both get selected } p ( e ) = p ( carol ) * p ( bernie ) = 4 / 5 * 3 / 5 = 12 / 25 answer : d
Answer: d
Python program:
a = 4 / 5
b = 3 / 5
c = a * b
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 5 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: "5 b = 7 c and so b = 7 c / 5 7 a = 2 b and so a = 2 b / 7 = 2 c / 5 a + b = 2 c / 5 + 7 c / 5 = 9 c / 5 b + c = 7 c / 5 + c = 12 c / 5 the ratio of a + b : b + c = 9 : 12 = 3 : 4 the answer is c ."
Answer: c
Python program:
a = 7 / 2
b = 1 + a 
c = 7 / 2
d = 5 / 2
e = c + d 
f = b / e
Problem: a certain bag contains 100 balls â € ” 10 white , 30 green , 10 yellow , 47 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 10 + 30 + 10 ) / 100 = 50 / 100 = 0.5 . answer is e"
Answer: e
Python program:
a = 47 + 3 
b = 100 - a
c = b / 100
Problem: how many bricks , each measuring 25 cm x 11 cm x 6 cm , will be needed to build a wall of 8 m x 1 m x 5 cm ?
Options: a ) 5600 , b ) 6000 , c ) 242 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 100 x 5 ) / ( 25 x 11 x 6 ) = 242 . answer : option c"
Answer: c
Python program:
a = 8 * 100
b = 1 * 100
c = a * b
d = c * 5
e = 25 * 11
f = e * 6
g = d / f
Problem: the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m , find out the area of the field .
Options: a ) 37500 , b ) 38000 , c ) 38500 , d ) 39000 , e ) 39500
Rationale: "given that breadth of the rectangular field is 60 % of its length . ⇒ b = 60 l 100 = 3 l 5 perimeter of the field = 800 m ⇒ 2 ( l + b ) = 800 ⇒ 2 ( l + 3 l 5 ) = 800 ⇒ l + 3 l 5 = 400 ⇒ 8 l 5 = 400 ⇒ l 5 = 50 ⇒ l = 5 × 50 = 250 m b = 3 l 5 = 3 × 2505 = 3 × 50 = 150 m area = lb = 250 × 150 = 37500 m 2 answer is a ."
Answer: a
Python program:
a = 800 / 2
b = 60 / 100
c = b + 1 
d = a / c
e = 800 / 2
f = 800 / 2
g = 60 / 100
h = g + 1 
i = f / h
j = e - i
k = d * j
Problem: if the number is divided by 3 , it reduced by 30 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 30 = > 2 x / 3 = 30 = > x = 45 answer : option c"
Answer: c
Python program:
a = 30 * 3
b = 3 - 1
c = a / b
Problem: among 400 students , 51 % study sociology , 46 % study mathematics and 40 % study biology . if 34 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 148 , d ) 172 , e ) 188
Rationale: i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 136 using your analysis : we see that the total number of students who study either maths or sociology = 184 + 204 - 136 = 252 so , in the image we know that the number of students in the zone with the black boundary = 252 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 252 + b + w = 400 or , b + w = 400 - 252 = 148 that is , b = 148 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 148 c
Answer: c
Python program:
a = 400 / 100
b = a * 51
c = 400 / 100
d = c * 46
e = b + d 
f = 400 / 100
g = f * 34
h = e - g
i = 400 - h
Problem: in the third grade of windblown school there are 102 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 102 failed in math = 102 / 3 = 34 failed in literature = 108 / 6 = 17 the least failed in both can be 0 while max can be 17 answer a"
Answer: a
Python program:
a = 102 / 3
b = 102 / 6
c = min(a)
Problem: the principal that amounts to rs . 5913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 5913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 5096 . answer : e"
Answer: e
Python program:
a = 1 / 4
b = 6 + a 
c = b / 100
d = 1 + c 
e = d ** 3
f = 5913 / e
Problem: if 2805 / 2.55 = 1100 , then 280.5 / 25.5 is equal to ?
Options: a ) 1.01 , b ) 1.1 , c ) 0.11 , d ) 11 , e ) none
Rationale: "answer given expression 280.5 / 25.5 = 2805 / 255 = 2805 / ( 2.55 x 100 ) = 1100 / 100 = 11 correct option : d"
Answer: d
Python program:
a = 1100 * 2
b = a / 2805
Problem: a and b complete a work in 50 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.075 days , b ) 0.185 days , c ) 0.065 days , d ) 0.045 days , e ) 0.0775 days
Rationale: "1 / 50 + 1 / 40 = 0.045 days answer : d"
Answer: d
Python program:
a = 1/(50)
b = 1/(40)
c = a + b 
d = 1/(c)