euclaise/mathqa_programs huggingface dataset:
Problem: my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 140 years . can you tell me my age in years ?
Options: a ) 80 , b ) 90 , c ) 85 , d ) 84 , e ) 89
Rationale: let the age of the man = x years so according to the given condition age of my grandson = x / 12 years and age of my son = x 30 / 52 = 15 x / 26 and x + ( x / 12 ) + ( 15 x / 26 ) = 140 or ( 156 x + 13 x + 90 x ) / 156 = 140 or 259 x = 156 * 140 or x = 156 * 140 / 259 = 84 answer : d
Answer: d
Python program:
a = 10 + 10 
b = 140 / a
c = b * 12
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 15,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 120,000
Rationale: answer equals e in 48 years . i thought by 50 th year it would reach 120,000 . options should have been separated more widely for clarity .
Answer: e
Python program:
a = 2 + 3 
b = a * 1000
c = b * 12
d = c / 2
Problem: there are 361 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 57 , d ) 171 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 361 = 209 answer : a"
Answer: a
Python program:
a = 11 - 8
b = 8 * a
c = b * 11
Problem: 20 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33.33 , b ) 34.01 , c ) 26.32 , d ) 28.33 , e ) 19.21
Rationale: "explanation : let the two parts be ( 20 - x ) and x . then , 10 ( 20 - x ) + 22 x = 780 = > 12 x = 580 = > x = 48.33 . bigger part = ( 20 - x ) = 28.33 . answer : d ) 28.3"
Answer: d
Python program:
a = 20 * 10
b = 780 - a
c = 22 - 10
d = b / c
e = 20 - d
Problem: a chartered bank offers a 5 - year escalator guaranteed investment certificate . in successive years it pays annual interest rates of 4 % , 4.5 % , 5 % , 5.5 % , and 6 % , respectively , compounded at the end of each year . the bank also offers regular 5 - year gics paying a fixed rate of 5 % compounded annually . calculate and compare the maturity values of $ 1000 invested in each type of gic . ( note that 5 % is the average of the 5 successive one - year rates paid on the escalator gic . )
Options: a ) 1276.28 , b ) 1276.22 , c ) 1276.29 , d ) 1276.21 , e ) 1276.23
Rationale: explanation : fv = $ 1000 ( 1.04 ) ( 1.045 ) ( 1.05 ) ( 1.055 ) ( 1.06 ) = $ 1276.14 the maturity value of the regular gic is fv = $ = $ 1276.28 answer : a ) 1276.28
Answer: a
Python program:
a = 5 / 100
b = a + 1 
c = b ** 5
d = c * 1000
Problem: how many seconds will a 1200 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 26 sec , b ) 65 sec , c ) 55 sec , d ) 19 sec , e ) 72 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 1200 * 3 / 50 = 72 sec . answer : e"
Answer: e
Python program:
a = 63 - 3
b = a * const_0_2778
c = 1200 / b
Problem: the ratio of two quantities is 3 to 4 . if each of the quantities is increased 4 and 3 respectively , what is the ratio of these two new quantities ?
Options: a ) 3 / 4 , b ) 8 / 9 , c ) 18 / 19 , d ) 23 / 24 , e ) it can not be determined from the information given
Rationale: "3 / 4 = 3 x / 4 x we need to find out ( 3 x + 4 ) / ( 4 x + 3 ) off course we can not solve this to arrive at any rational number hence e ."
Answer: e
Python program:
a = 3 + 4 
b = 4 + 4 
c = a / b
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.30 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 865.8 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.3 = 865.8 answer : c"
Answer: c
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
Problem: 25 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 8 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 10 days
Rationale: "1 women ' s 1 day work = 1 / 175 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 175 + 10 / 140 ) = 1 / 10 5 women and 10 children will complete the work in 10 days . answer : e"
Answer: e
Python program:
a = 25 * 7
b = 5 / a
c = 25 * 14
d = 25 / c
e = b + d 
f = 1/(e)
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 300 kmph , b ) 360 kmph , c ) 600 kmph , d ) 720 kmph , e ) none
Rationale: "explanation : distance = ( 240 x 5 ) = 1200 km . speed = distance / time speed = 1200 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 1200 x 3 / 5 km / hr = 720 km / hr . answer : option d"
Answer: d
Python program:
a = 240 * 5
b = 2 / 3
c = 1 + b 
d = a / c
e = d / 2
Problem: in arun ' s company 60 % of the employees earn less than $ 50000 a year , 60 % of the employees earn more than $ 40000 a year , 11 % of the employees earn $ 43000 a year and 5 % of the employees earn $ 49000 a year . what is the median salary for the company ?
Options: a ) 43.0 , b ) 45.5 , c ) 46.0 , d ) 49.0 , e ) 50.0
Rationale: in arun ' s company 60 % of the employees earn less than $ 50,000 a year , 50 and 51 employee will be each 43 k . hence median = ( 43 k + 43 k ) / 2
Answer: a
Python program:
a = 2 * 43000
b = a / 2
c = b / 100
d = c / 10
Problem: 50 square stone slabs of equal size were needed to cover a floor area of 72 sq . m . find the length of each stone slab ?
Options: a ) 120 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 72 / 50 m 2 = 1.44 m 2 length of each slab √ 1.44 = 1.2 m = 120 cm"
Answer: a
Python program:
a = 72 / 50
b = math.sqrt(a)
c = b * 100
Problem: a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 90 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 36 % , c ) 30 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 190 , so from 2003 to 2005 it increased by ( 190 - 140 ) / 140 = 50 / 140 = ~ 29 % . answer : b"
Answer: b
Python program:
a = 90 / 100
b = 1 + a 
c = 40 / 100
d = 1 + c 
e = b - d
f = 40 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: a train 300 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 19 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 300 m at 50 / 3 m / sec = 300 * 3 / 50 sec = 18 sec answer : d ."
Answer: d
Python program:
a = 68 - 8
b = a * const_0_2778
c = 300 / b
Problem: at the store opening , larry ' s grocery had 50 lemons and 60 oranges . by closing , the store at 20 lemons and 40 oranges left . by approximately what percent did the ratio of lemons to orange decrease from opening to closing .
Options: a ) 50.0 % , b ) 40.0 % , c ) 30.0 % , d ) 20.0 % , e ) 10.0 %
Rationale: opening : lemons / oranges = 50 / 60 = 100 / 120 closing : lemons / oranges = 20 / 40 = 60 / 120 aside : it ' s useful to write both ratios with the same denominator . this allows us to ignore the denominator and focus solely on the numerators . so , our ratio went from 100 / 120 to 60 / 120 ignoring the denominators , we went from 100 to 60 the percent change = 100 ( difference in values ) / ( original value ) = ( 100 ) ( 100 - 60 ) / 100 = ( 100 ) ( 40 ) / 100 ) = 40 answer : b
Answer: b
Python program:
a = 50 / 60
b = 20 / 40
c = a - b
d = 50 / 60
e = c / d
f = e * 100
Problem: what is the 27 th digit to the right of the decimal point in the decimal form of 5 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "5 / 11 = 0.45454545 . . . the odd numbered positions in the decimal expansion are all 4 . the answer is b ."
Answer: b
Python program:
a = 5 / 11
Problem: if x is a positive integer with fewer than 3 digits , what is the probability that z x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability z that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Python program:
a = 100 / 4
b = a * 2
c = 100 / 5
d = c * 2
e = b + d 
f = e - 4
g = 100 - 1
h = f / g
Problem: the cash realised on selling a 14 % stock is rs . 108.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 108 , d ) 156 , e ) 240
Rationale: "explanation : cash realised = rs . ( 108.25 - 0.25 ) = rs . 108 . answer : c"
Answer: c
Python program:
a = 1 / 4
b = 108 - 25
Problem: if y is 40 % greater than x , than x is what % less than y ?
Options: a ) 24.4 % , b ) 28.6 % , c ) 32.3 % , d ) 36.5 % , e ) 40.9 %
Rationale: "y = 1.4 x x = y / 1.4 = 10 y / 14 = 5 y / 7 x is 2 / 7 less which is 28.6 % less than y . the answer is b ."
Answer: b
Python program:
a = 40 + 100 
b = 40 / a
c = b * 100
Problem: a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 16 heads and 41 legs . how many cats does the ship host ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 7 , e ) 8
Rationale: sa ' s + co + ca + cats = 16 . sa ' s + 1 + 1 + cats = 16 or sa ' s + cats = 14 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 41 sa ' s * 2 + cats * 4 = 38 or sa ' s + cats * 2 = 19 or 14 - cats + cat * 2 = 19 then cats = 5 a
Answer: a
Python program:
a = 41 - 1
b = 16 - 1
c = b * 2
d = a - c
e = 16 - 1
f = e * 4
g = 16 - 1
h = g * 2
i = f - h
j = d / i
k = 16 - 1
l = j * k
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.85 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 420 $ , c ) 582 $ , d ) 650 $ , e ) 780 $
Rationale: 12 * 1.75 + 0.85 * 12 * 55 = 582 hence - c
Answer: c
Python program:
a = 0 * 85
b = a * 12
Problem: what sum of money will produce rs . 75 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 337 , b ) 500 , c ) 266 , d ) 288 , e ) 536
Rationale: "75 = ( p * 4 * 7 / 2 ) / 100 p = 536 answer : e"
Answer: e
Python program:
a = 1 / 2
b = 3 + a 
c = 4 * b
d = c / 100
e = 75 / d
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 16000 , then find his savings ?
Options: a ) 3600 , b ) 3607 , c ) 3200 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 16000 = > x = 3200 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3200 . answer : c"
Answer: c
Python program:
a = 4 / 5
b = a * 16000
c = 16000 - b
Problem: a certain fraction has the same ratio to 1 / 33 , as 3 / 4 does to 7 / 11 . what is this certain fraction ?
Options: a ) 1 / 14 , b ) 1 / 18 , c ) 1 / 21 , d ) 1 / 25 , e ) 1 / 28
Rationale: "x / ( 1 / 33 ) = ( 3 / 4 ) / ( 7 / 11 ) x = 3 * 11 * 1 / 33 * 4 * 7 = 1 / 28 the answer is e ."
Answer: e
Python program:
a = 1 / 33
Problem: a certain car increased its average speed by 5 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 38 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 4.0
Rationale: "in the third time interval the average speed of the car was 38 + 5 + 5 = 30 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 48 * 1 / 12 = 4 miles . answer : e ."
Answer: e
Python program:
a = 38 + 5 
b = a + 5 
c = 5 / const_60
d = b * c
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 1 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 1 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 1 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 1 / 7 x 1 / 5 = 1 / 35 answer : a"
Answer: a
Python program:
a = 1 / 7
b = 1 / 5
c = a * b
Problem: if a and b are distinct positive integers . the units digit of a ^ 2 is equal to the units digit of a , and the units digit of b ^ 2 is equal to the units digit of b . if the units digit of a · b is equal to neither the units digit of a nor the units digit of b , then what is the units digit of a · b ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: there are four digits which when squared give the same units digits : 0 , 1 , 5 , 6 0 ^ 2 = 0 1 ^ 2 = 1 5 ^ 2 = 25 6 ^ 2 = 36 so a and b must take 2 of these values . they are positive integers so 0 is not possible . if one of the digits is 1 , when the other is multiplied by 1 , you will get the same digit . 1 * 5 = 5 so 1 is out of the picture . then you have only two digits left 5 and 6 . so out of a and b , one must be 5 and the other 6 . 5 * 6 = 30 so units digit of their product = 0 answer ( a )
Answer: a
Python program:
a = 2 * 3
b = 2 + 3 
c = a * b
Problem: what is the next number : 3 , 27 , 627 , __
Options: a ) 8847 , b ) 9837 , c ) 11,497 , d ) 15,627 , e ) 19,307
Rationale: "5 ^ 0 + 2 = 3 5 ^ 2 + 2 = 27 5 ^ 4 + 2 = 627 5 ^ 6 + 2 = 15,627 the answer is d ."
Answer: d
Python program:
a = 627 * 10
b = a - 100
c = b - 3
d = c - 3
Problem: if the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 2 , what is the ratio of apples to cucumbers ?
Options: a ) 6 : 5 , b ) 1 : 4 , c ) 4 : 3 , d ) 2 : 3 , e ) 5 : 4
Rationale: "the ratio of bananas to cucumbers is 1 to 2 which equals 2 to 4 . the ratio of apples to bananas to cucumbers is 5 to 2 to 4 . the ratio of apples to cucumbers is 5 to 4 . the answer is e ."
Answer: e
Python program:
a = 5 / 2
b = a / 2
Problem: what is the least integer greater than 1 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( 1 ) + ( 0.5 ) = 1.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from 1 to 1.5 ) . next , the question asks for the least integer that is greater than 1.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of 1.5 is 2 . final answer : e"
Answer: e
Python program:
a = 1 + 1 
b = a * 2
Problem: when 242 is divided by a certain divisor the remainder obtained is 6 . when 698 is divided by the same divisor the remainder obtained is 13 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 23 , e ) none of these
Rationale: "let that divisor be x since remainder is 6 or 13 it means divisor is greater than 13 . now 242 - 6 = 236 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 13 = 685 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 236 + 685 ) + 6 + 13 = x ( k + l ) + 19 when we divide this number by x then remainder will be equal to remainder of ( 19 divided by x ) = 5 hence x = 19 - 5 = 14 hence b"
Answer: b
Python program:
a = 6 + 13 
b = a - 5
Problem: in a river flowing at 2 km / hr , a boat travels 56 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 21 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 56 km total time taken = time taken downstream + time taken upstream = ( 56 / 8 ) + ( 56 / 4 ) = 21 hr . answer : option d"
Answer: d
Python program:
a = 6 - 2
b = 56 / a
c = 6 + 2 
d = 56 / c
e = b + d
Problem: a certain rectangular crate measures 8 feet by 12 feet by 14 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 6 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . so to maximize the above eqn , radius may be of 9 , 10,12 one of the base area ( 8 x 12 , 14 x 12 or 8 x 14 ) r is maximum for base 14 x 12 and 12 can be maximum value so r = 10 / 2 = 6 a"
Answer: a
Python program:
a = 12 / 2
b = volume_cylinder / (
c = math.pi * 8
d = math.sqrt(b)
Problem: there are 640 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 375 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 640 . hence 3 x + 5 x = 640 solve for x 8 x = 640 x = 80 number of boys 3 x = 3 × 80 = 240 number of girls 5 x = 5 × 80 = 400 e"
Answer: e
Python program:
a = 640 / 5
b = a * 3
Problem: a ratio between two numbers is 5 : 4 and their l . c . m . is 80 . the first number is
Options: a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 5 x and 4 x . then , their l . c . m . is 20 x . ∴ 20 x = 80 ⇔ x = 4 . hence , the first number is 20 . answer c"
Answer: c
Python program:
a = 5 * 4
b = 80 / a
c = b * 5
Problem: if the simple interest on a sum of money for 3 years at 7 % per annum is rs . 570 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 610.83 , b ) rs . 810.83 , c ) rs . 617 , d ) rs . 618 , e ) rs . 610.83
Rationale: "sum = ( 570 * 100 ) / ( 7 * 3 ) = rs . 2 , 714.29 amount = [ 2 , 714.29 * ( 1 + 7 / 100 ) 3 ] = rs . 3 , 325.12 c . i . = ( 3 , 325.12 - 2 , 714.29 ) = rs . 610.83 . answer : e"
Answer: e
Python program:
a = 7 / 100
b = a * 2
c = 570 / b
d = c * 7
e = d / 100
f = 7 / 100
g = f * 3
h = 570 / g
i = e + h 
j = 7 / 100
k = j * 3
l = 570 / k
m = l * 7
n = m / 100
o = 7 / 100
p = o * 3
q = 570 / p
r = n + q 
s = r * 7
t = s / 100
u = i + t 
v = 7 / 100
w = v * 3
x = 570 / w
y = u - x
Problem: what is the least number that should be added to 1055 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1055 / 23 ) gives a remainder 20 so we need to add 3 . the answer is c ."
Answer: c
Python program:
a = 1055 / 23
b = math.floor(a)
c = 1 + b 
d = 1055 / 23
e = c - d
f = e * 23
Problem: an entry in an unshaded square is obtained by adding the entries connected to it from the row above ( 11 is one such number ) . write the value of n ?
Options: a ) 10
b ) 11
c ) 12
d ) 9
e ) 8
Rationale: see the values row wise 5 6 n 7 11 6 + n 7 + n 11 + 6 + n 6 + n + 7 + n 60 hence 11 + 6 + n + 6 + n + 7 + n = 60 n = 10 answer : a
Answer: a
Python program:
a = 11 * 3
b = a - 3
c = b / 3
Problem: in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 65 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 10 , c ) 15 , d ) 20 , e ) 30
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 65 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 65 x 1 ( a = 6 , b = 5 respectively we have = 30 ) . this is the greatest possible value of b x a . imo e ."
Answer: e
Python program:
a = 3 + 4 
b = 2 + 3 
c = a * b
Problem: a computer factory produces 3024 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 3024 / ( 28 * 24 * 2 ) = 2.25 answer a"
Answer: a
Python program:
a = 3024 / 28
b = 28 - 4
c = b * 2
d = a / c
Problem: a man has rs . 400 in the denominations of one - rupee notes , 5 - rupee notes and 10 rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 90 , e ) 95
Rationale: let number of notes of each denomination be x . then x + 5 x + 10 x = 400 16 x = 400 x = 25 . hence , total number of notes = 3 x = 75 answer : option c
Answer: c
Python program:
a = 1 + 5 
b = a + 10 
c = 400 / b
d = c * 3
Problem: in a sports club with 30 members , 17 play badminton and 17 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 17 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 17 - x ) + x + 2 = 30 36 - 2 x + x = 30 36 - x = 30 x = 6 so 6 members play both badminton and tennis . b"
Answer: b
Python program:
a = 17 + 17 
b = a + 2 
c = b - 30
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5000 = ?
Options: a ) 392 , b ) 229 , c ) 753 , d ) 750 , e ) 540
Rationale: "d 750 ? = 5000 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 750"
Answer: d
Python program:
a = 3 / 4
b = 1 / 2
c = a * b
d = 2 / 5
e = c * d
f = e * 5000
Problem: if x / y = 2 / z , then 5 x ^ 2 =
Options: a ) y / z , b ) 20 y ² / z ² , c ) y ² z ² , d ) 5 y ² / z ² , e ) yz
Rationale: "this question is most easily solved by isolating y in the equation and substituting into the expression 5 x ² : x / y = 2 / z x = 2 y / z if we substitute 2 y / z into the expression for x , we get : 5 ( 2 y / z ) ² = 5 ( 4 y ² / z ² ) = 20 y ² / z ² . the correct answer is choice ( b )"
Answer: b
Python program:
a = 2 + 5 
b = 2 - 5
c = a / b