euclaise/mathqa_programs huggingface dataset:
Problem: the perimeter of one square is 44 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 12.1 √ 2 , c ) 23 √ 2 , d ) 12 √ 4 , e ) 13 √ 9
Rationale: "4 a = 44 4 a = 20 a = 11 a = 5 a 2 = 121 a 2 = 25 combined area = a 2 = 146 = > a = 12.1 d = 12.1 √ 2 answer : b"
Answer: b
Python program:
a = 44 / 4
b = a ** 2
c = 20 / 4
d = c ** 2
e = b + d 
f = e * 2
g = math.sqrt(f)
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 19,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 145 % , d ) 150 % , e ) 225 %
Rationale: "we can use approximation to get the answer quickly . like , 19,947 is approx 20000 8902 is approx 8900 so , total increase = 20000 - 8900 = 11100 hence , % increase = 11100 / 8900 = approx . 11 / 9 = 1.22 = approx . 1.25 so , choice is b ."
Answer: b
Python program:
a = 19 - 947
b = a / 8
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 30 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Python program:
a = 30 * 4
b = a / 2
c = 30 + 5 
d = b + c
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 200 square feet and its length is 10 feet longer than its width . if the uniform width between the rug and room is 10 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 1360 , c ) 1000 , d ) 46 , e ) 104
Rationale: "rug ' s area = 200 which is ( x ) x ( 10 + x ) = 200 so x = 10 rug maintains a uniform distance of 10 feet so room has dimension 10 + 20 and 20 + 20 i . e . 30 and 40 area of room 30 x 40 = 1200 area covered is 200 so uncovered area is 1200 - 200 = 1000 ( answer c )"
Answer: c
Python program:
a = 200 / 10
b = a - 2
c = b + 10 
d = 200 / 10
e = 200 / 10
f = e - 2
g = d + f 
h = c * g
i = h - 200
Problem: the sum of money will be double itself in 20 years and simple interest find rate of interest ?
Options: a ) 10 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "t = 20 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 20 x = 5 % answer is b"
Answer: b
Python program:
a = 20 / 100
b = a * 100
Problem: how many positive even integers less than 100 contain digits 3 or 7 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 10 , e ) 20
Rationale: "two digit numbers : 3 at tens place : 30 , 32,34 , 36,38 7 at tens place : 70 , 72,74 , 76,78 if 3 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer d"
Answer: d
Python program:
a = 3 * 2
Problem: if the simple interest on a sum of money for 4 years at 8 % per annum is rs . 560 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 640.86 , b ) rs . 430.86 , c ) rs . 330.86 , d ) rs . 630.86 , e ) rs . 130.86
Rationale: "sum = ( 50 * 100 ) / ( 2 * 5 ) = rs . 1 , 750.00 c . i . on rs . 1 , 750.00 for 4 years at 8 % = rs . 2 , 380.86 . = rs . 2 , 380.86 - 1 , 750.00 = rs . 630.86 answer : d"
Answer: d
Python program:
a = 8 / 100
b = a * 2
c = 560 / b
d = c * 8
e = d / 100
f = 8 / 100
g = f * 4
h = 560 / g
i = e + h 
j = 8 / 100
k = j * 4
l = 560 / k
m = l * 8
n = m / 100
o = 8 / 100
p = o * 4
q = 560 / p
r = n + q 
s = r * 8
t = s / 100
u = i + t 
v = 8 / 100
w = v * 4
x = 560 / w
y = u - x
Problem: bert left the house with n dollars . he spent 1 / 3 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 10.50 left in his pocket . what was the value of n ?
Options: a ) $ 42 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer a if he had 42 , then he spent 13 2 / 3 at hardware store now he was left with 27 1 / 3 $ he spent 7 dollars on cleaning , thus he remained with 20 1 / 3 $ he then spent 1 / 2 of 20 1 / 3 or 10.5 , hence , right option is a ."
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 1/(b)
d = 7 / 2
e = d + 10 
f = c * e
g = f * 2
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 44 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 14
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 44 + q = > q = 14 answer : e"
Answer: e
Python program:
a = 10 * 3
b = 44 - a
Problem: a train 360 m long is running at a speed of 42 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 27 sec , e ) 43 sec
Rationale: "speed = 42 * 5 / 18 = 35 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 35 = 43 sec answer : e"
Answer: e
Python program:
a = 42 - 140
b = a * const_0_2778
c = 360 / b
Problem: pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed t ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this t we get x = 8 . b ."
Answer: b
Python program:
a = 96 / 16
b = 96 / 16
c = 50 / 100
d = 1 + c 
e = b / d
f = e * 4
g = f * 4
h = 96 / 16
i = h ** 2
j = g + i 
k = math.sqrt(j)
l = a + k 
m = l / 2
Problem: a = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set a and one integer from set b . what is the probability q that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: rearrange the first set : a = { 5,4 , 3,2 } b = { 4,5 , 6,7 , 8 } as you can see numbers in each column ( the numbers of the same color ) give the sum of 9 . so there are 4 such pares possible , total # of pairs is 4 * 5 = 20 . q = favorable / total = 4 / 20 = 0.2 . answer : b . or : we can select any number from set a ( 4 / 4 = 1 ) but in this case we must select its matching pair from set b ( the number of the same color ) and since there are only one matching pair of this particular number in b then the probability of this is 1 / 5 . so , overall : q = 1 * 1 / 5 . answer : b .
Answer: b
Python program:
a = 4 / 5
b = 1 / 4
c = a * b
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 99 , c ) 77 , d ) 66 , e ) 32
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 2 / 25 = 40 sec answer : a"
Answer: a
Python program:
a = 45 - 140
b = a * const_0_2778
c = 360 / b
Problem: how many seconds will a 600 m long train take to cross a man walking with a speed of 2 km / hr in the direction of the moving train if the speed of the train is 56 km / hr ?
Options: a ) 30 , b ) 54 , c ) 40 , d ) 36 , e ) 31
Rationale: "speed of train relative to man = 56 - 2 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . time taken to pass the man = 600 * 1 / 15 = 40 sec . answer : c"
Answer: c
Python program:
a = 56 - 2
b = a * const_0_2778
c = 600 / b
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 m 3 , b ) 4580 m 3 , c ) 9000 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 6000 * 2 * 45 ) / 60 = 9000 m 3 answer : option c"
Answer: c
Python program:
a = 2 * 45
b = 6 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: how many times will the digit 3 be written when listing the integers from 1 to 1000 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 3 ) 3000 / 10 = 300 times . answer : c ."
Answer: c
Python program:
a = 1 * 10
b = a * 10
c = b * 3
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 9 cm and breadth 6 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 11.72 , b ) 11.52 , c ) 11.97 , d ) 10.91 , e ) 11.79
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 9 + 6 ) = 30 cm parameter of the square = 30 cm i . e . 4 a = 30 a = 7.5 diameter of the semicircle = 7.5 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 7.5 ) = 1 / 2 ( 22 / 7 ) ( 7.5 ) = 165 / 14 = 11.79 cm to two decimal places answer : e"
Answer: e
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: working alone , mary can pave a driveway in 3 hours and hillary can pave the same driveway in 6 hours . when they work together , mary thrives on teamwork so her rate increases by 10 % , but hillary becomes distracted and her rate decreases by 20 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 3 per hour hillary = 1 / 6 per hour rate when working together : mary = 1 / 3 + ( 1 / 10 * 1 / 3 ) = 3 / 8 per hour hillary = 1 / 6 - ( 1 / 5 * 1 / 6 ) = 2 / 15 per hour together they work 3 / 8 + 2 / 15 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Python program:
a = 1 / 3
b = 10 / 100
c = b + 1 
d = a * c
e = 1 / 6
f = 20 / 100
g = e * f
h = d + g 
i = 1/(h)
Problem: if the remainder is 11 when the integer n is divided by 20 , what is the remainder when 2 n is divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 20 k + 11 2 n = 2 ( 20 k + 11 ) = 4 k * 10 + 22 = 4 k * 10 + 2 * 10 + 2 = 10 j + 2 the answer is c ."
Answer: c
Python program:
a = 11 * 2
b = a - 20
Problem: a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points t that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points t for 12 th player is 100 - 77 = 23 . answer : e ."
Answer: e
Python program:
a = 12 * 7
b = 100 - a
c = b + 7
Problem: a invested $ 400 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find b ' s shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 400 * 12 : 200 * 6 a : b = 4 : 1 b ' s share = 100 * 1 / 5 = $ 20 answer is c"
Answer: c
Python program:
a = 200 / 2
b = 200 / 2
c = 400 + b 
d = a / c
e = 1 - d
f = 100 * e
Problem: plot abcd is as shown in figure , where af = 30 m , ce = 40 m , ed = 50 m , ae = 120 m . find the area of the plot abcd ?
Options: a ) 7207 , b ) 7206 , c ) 7203 , d ) 7200 , e ) 7201
Rationale: "area of plot abcd = area of ade + area of afb + area of bcef = 1 / 2 * 50 * 120 + 1 / 2 * 40 * 30 + 40 * 90 = 3000 + 600 + 3600 = 7200 sq . m answer : d"
Answer: d
Python program:
a = triangle_area + ( 
b = a + triangle_area
Problem: a and b can do a piece of work in 6 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 40 days , b ) 16 days , c ) 6 days , d ) 5 days , e ) 40 days
Rationale: "c 6 days c = 1 / 3 – 1 / 6 = 1 / 6 = > 6 days"
Answer: c
Python program:
a = 3 / 6
b = 3 - a
c = 1/(b)
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 4 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.2 , d ) 5.5 , e ) 6.4
Rationale: "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 4 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 4 = 6.4 desks e is the correct answer ."
Answer: e
Python program:
a = 4 / 2
b = 2 / a
c = b / 2
d = c * 4
e = d * 4
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 50 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 39 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 50 % then output equals 165 to restore new holidy demand output to original 100 . final - initial / final * 100 = 65 / 165 * 100 = 39 % approxiamately . option e is correct ."
Answer: e
Python program:
a = 100 + 10 
b = a / 100
c = 100 + 50 
d = c / 100
e = b * d
f = e - 1
g = 100 + 10 
h = g / 100
i = 100 + 50 
j = i / 100
k = h * j
l = f / k
m = l * 100
Problem: the average of first 10 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17
Rationale: "sum of 10 even numbers = 10 * 11 = 110 average = 110 / 10 = 11 answer : d"
Answer: d
Python program:
a = 10 + 1
Problem: in town p , 60 percent of the population are employed , and 45 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the percent of the population who are employed females is 60 - 45 = 15 % the percent of employed people who are female is 15 % / 60 % = 25 % . the answer is b ."
Answer: b
Python program:
a = 60 - 45
b = a / 60
c = b * 100
Problem: there are 2 sections a and b in a class , consisting of 26 and 34 students respectively . if the average weight of section a is 50 kg and that of section b is 30 kg , find the average of the whole class ?
Options: a ) 35.29 kg , b ) 37.25 kg , c ) 42.45 kg , d ) 38.66 kg , e ) 29.78 kg
Rationale: "total weight of 26 + 34 students = 26 * 50 + 34 * 30 = 2320 average weight of the class is = 2320 / 60 = 38.66 kg answer is d"
Answer: d
Python program:
a = 26 * 50
b = 34 * 30
c = a + b 
d = 26 + 34 
e = c / d
Problem: find the amount on rs . 4000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 4368 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 1671
Rationale: "4000 * 104 / 100 * 105 / 100 = > 4368 answer : a"
Answer: a
Python program:
a = 100 + 4 
b = 4000 * a
c = b / 100
d = 100 + 5 
e = c * d
f = e / 100
Problem: a shopkeeper forced to sell at cost price , uses a 900 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 11.11 % , d ) 12 % , e ) none of these
Rationale: "shopkeeper sells 900 g instead of 1000 g . so , his gain = 1000 - 900 = 100 g . thus , % gain = ( 100 * 100 ) / 900 = 11.11 % . answer : option c"
Answer: c
Python program:
a = 2 * 100
b = 100 / 2
c = a + b 
d = c / 900
e = d * 100
Problem: john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 50 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 50 = 40 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 50 / 100 ) * 100 = ( 0.5 ) * 100 = 50 % . d"
Answer: d
Python program:
a = 100 - 50
Problem: what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 449 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 24
Rationale: "( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 449 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 9,9 ; 5 & 9 are missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 49 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 47 * 01 ) ) ^ 2 = ( 44 * 47 ) ^ 2 = 68 ^ 2 = 24 hence answer is e"
Answer: e
Python program:
a = 100 / 4
b = 2 * 3
c = 1 - 2
d = b * c
e = 1 - 2
f = d * e
g = 1 - 2
h = f * g
i = a + h 
j = i * 4
Problem: divide rs . 1800 among a , b and c so that a receives 2 / 5 as much as b and c together and b receives 1 / 5 as a and c together . a ' s share is ?
Options: a ) 400 , b ) 500 , c ) 375 , d ) 450 , e ) 600
Rationale: a + b + c = 1800 a = 2 / 5 ( b + c ) ; b = 1 / 5 ( a + c ) a / ( b + c ) = 2 / 5 a = 1 / 6 * 3600 = > 600 answer : e
Answer: e
Python program:
a = 1800 / 3
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 4 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 58
Rationale: "et no of sheep and horses are 4 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 4 * 8 ) = 32 answer : c"
Answer: c
Python program:
a = 12880 / 230
b = a / 7
c = b * 4
Problem: a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 154 . find the unknown rate of two blankets ?
Options: a ) 420 , b ) 550 , c ) 490 , d ) 450 , e ) 457
Rationale: "10 * 154 = 1540 3 * 100 + 5 * 150 = 1050 1540 – 1050 = 490 answer : c"
Answer: c
Python program:
a = 10 * 150
b = 3 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: last year , company x paid out a total of $ 1 , 050,000 in salaries to its 21 employees . if no employee earned a salary that is more than 15 % greater than any other employee , what is the lowest possible salary that any one employee earned ?
Options: a ) $ 40,000 , b ) $ 41,667 , c ) $ 42,000 , d ) $ 43,750 , e ) $ 60,000
Rationale: "employee 1 earned $ x ( say ) employee 2 will not earn more than $ 1.15 x therfore , to minimize the salary of any one employee , we need to maximize the salaries of the other 20 employees ( 1.15 x * 20 ) + x = 1 , 050,000 solving for x = $ 43,750 answer d"
Answer: d
Python program:
a = 15 / 100
b = a + 1 
c = 1000 + const_60 
d = c - 10
e = d * 1000
f = b * e
g = 21 - 1
h = 15 / 100
i = h + 1 
j = g * i
k = j + 1 
l = f / k
m = 15 / 100
n = m + 1 
o = l / n
p = o / 100
q = 100 * 2
r = q + 3 
s = p + r
Problem: in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is married ?
Options: a ) 2 / 7 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 70 = 20 males are married if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married . total females = 30 married females = 10 then single females = 30 - 10 = 20 we need to find the fraction of female students who are single i . e single female students / total female student = 10 / 30 = 1 / 3 [ b ]"
Answer: b
Python program:
a = 10 / 30
Problem: the area of a rectangle is 63 sq m . the width is two meters shorter than the length . what is the width ?
Options: a ) 9
b ) 7
c ) - 9
d ) 11
e ) 6
Rationale: a = l x w w = l - 2 l = w + 2 a = ( w + 2 ) x w a = w ^ 2 + 2 x w 63 = w ^ 2 + 2 w 0 = w ^ 2 + 2 w - 63 0 = ( w + 9 ) ( w - 7 ) w = - 9 and w = 7 , width can not be negative so w = 7 answer is b
Answer: b
Python program:
a = 63 * 4
b = 2 ** 2
c = a + b 
d = math.sqrt(c)
e = d - 2
f = e / 2
Problem: a man can row upstream at 25 kmph and downstream at 65 kmph , and then find the speed of the man in still water ?
Options: a ) 45 , b ) 86 , c ) 30 , d ) 78 , e ) 38
Rationale: "us = 25 ds = 65 m = ( 65 + 25 ) / 2 = 45 answer : a"
Answer: a
Python program:
a = 25 + 65 
b = a / 2
Problem: a train crosses a bridge of length 150 m in 7.5 seconds and a lamp post on the bridge in 2.5 seconds . what is the length of the train in metres ?
Options: a ) 37.5 m , b ) 75 m , c ) 25 m , d ) 80 m , e ) 30 m
Rationale: let length of train = l case - 1 : distance = 150 + l ( while crossing the bridge ) time = 7.5 seconds i . e . speed = distance / time = ( 150 + l ) / 7.5 case - 2 : distance = l ( while passing the lamp post ) time = 2.5 seconds i . e . speed = distance / time = ( l ) / 2.5 but since speed has to be same in both cases so ( 150 + l ) / 7.50 = ( l ) / 2.5 i . e . 3 l = l + 150 i . e . 2 l = 150 i . e . l = 75 answer : option b
Answer: b
Python program:
a = 7 - 5
b = 150 / a
c = b * 2
Problem: at a special sale , 12 tickets can be purchased for the price of 3 tickets . if 12 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 12 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 50 % , e ) 75 %
Rationale: "let the price of a ticket be rs . 100 , so 3 tickets cost 300 & 12 tickets cost 1200 12 tickets purchased at price of 3 tickets ie . , for 300 , so amount saved s rs . 900 , % of 5 tickets = ( 900 / 1200 ) * 100 = 75 % answer : e"
Answer: e
Python program:
a = 12 * 12
b = 3 * 12
c = a - b
d = c * 100
e = 12 * 12
f = d / e
Problem: if x > 0 , x / 40 + x / 20 is what percent of x ?
Options: a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 40 + 100 / 20 = 2.5 + 5 = 7.5 7.5 is 75 % of 100 = e"
Answer: e
Python program:
a = 1 / 40
b = 1 / 20
c = a + b 
d = c * 100
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.6 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.6 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.6 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 1 / 2 required ratio = 1 / 1 : 1 = 1 : 2 . answer : a"
Answer: a
Python program:
a = 15 - 8
b = 16 - 6
c = a / b