euclaise/mathqa_programs huggingface dataset:
Problem: on a certain transatlantic crossing , 25 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 62.5 %
Rationale: "0.25 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.25 p = 0.40 ( rt ) rt / p = 62.5 % answer - e"
Answer: e
Python program:
a = 100 - 60
b = a / 100
c = 25 / b
Problem: two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 40 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 10 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 2
Rationale: "option c 10 + 40 t = 50 t t = 1"
Answer: c
Python program:
a = 50 - 40
b = 10 / a
Problem: the average of 25 results is 19 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 74 , b ) 75 , c ) 103 , d ) 78 , e ) 45
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 19 or , x = 103 . answer : option c"
Answer: c
Python program:
a = 25 * 19
b = 12 * 17
c = a - b
d = 12 * 14
e = c - d
Problem: in town p , 70 percent of the population are employed , and 21 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 46 % , b ) 52 % , c ) 58 % , d ) 64 % , e ) 70 %
Rationale: the percent of the population who are employed females is 70 - 21 = 49 % the percent of employed people who are female is 49 % / 70 % = 70 % . the answer is e .
Answer: e
Python program:
a = 70 - 21
b = a / 70
c = b * 100
Problem: mysoon collects glass ornaments . 10 more than 1 / 6 of the ornaments in her collection are handmade , and 1 / 2 of the handmade ornaments are antiques . if 1 / 3 of the ornaments in her collection are handmade antiques , how many ornaments are in her collection ?
Options: a ) 20 , b ) 60 , c ) 108 , d ) 144 , e ) 180
Rationale: the number of ornaments = a ten more than 1 / 6 of the ornaments in her collection are handmade = > handmade = 10 + a / 6 1 / 2 of the handmade ornaments are antiques = > handmade ornaments = 1 / 2 * ( 10 + a / 6 ) = 5 + a / 12 1 / 3 of the ornaments in her collection are handmade antiques = > handmade ornaments = a / 3 = > 5 + a / 12 = a / 3 = > a = 200 ans : a
Answer: a
Python program:
a = 10 * 3
b = 3 / 6
c = 2 - b
d = a / c
Problem: a train speeds past a pole in 12 seconds and a platform 160 m long in 17 seconds . its length is ?
Options: a ) 384 , b ) 360 , c ) 324 , d ) 390 , e ) 395
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 12 = > y = x / 12 x + 160 / 17 = x / 12 x = 384 m . answer : a"
Answer: a
Python program:
a = 2 - 1
b = 160 * a
Problem: a picnic attracts 240 persons . there are 40 more men than women , and 40 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 110 , d ) 90 , e ) 200
Rationale: "adult + children = 240 let , children = y then , adult = y + 40 i . e . y + ( y + 40 ) = 240 i . e . y = 100 i . e . adult = 100 + 40 = 140 adults include only men and women i . e . men + women = 140 let women , w = x then men , m = x + 40 i . e . x + ( x + 40 ) = 2 x + 40 = 140 i . e . x = 54 i . e . men , m = 54 + 40 = 90 answer : option d"
Answer: d
Python program:
a = 240 - 40
b = a / 2
c = b + 40 
d = c - 40
e = d / 2
f = e + 40
Problem: two vessels contains equal number of mixtures milk and water in the ratio 4 : 1 and 7 : 3 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 2 : 1 , b ) 4 : 1 , c ) 3 : 1 , d ) 2 : 3 , e ) 4 : 3
Rationale: the ratio of milk and water in the new vessel is = ( 4 / 5 + 7 / 10 ) : ( 1 / 5 + 3 / 10 ) = 3 / 2 : 1 / 2 = 3 : 1 answer is c
Answer: c
Python program:
a = 7 + 3 
b = 4 + 1 
c = a / b
d = 4 * c
e = d + 7 
f = 7 + 3 
g = 4 + 1 
h = f / g
i = 1 * h
j = i + 3 
k = e / j
Problem: if x : y is 1 : 2 and y : z is 2 : 5 then x : z is equal to
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 1 : 5 , d ) 4 : 5 , e ) 1 : 3
Rationale: "the two ratios given are having the same number 2 for y in both the ratios . hence - x : y = 1 : 2 y : z = 2 : 5 = > x : z = 1 : 5 answer c"
Answer: c
Python program:
a = 1 / 5
Problem: if | x - 16 | = 2 x , then x = ?
Options: a ) 10 , b ) 15 , c ) - 16 , d ) 16 , e ) 5
Rationale: "| x - 16 | = 2 x . . . ( given ) x ^ 2 - 32 x + 256 = 4 x ^ 2 3 * x ^ 2 + 32 * x - 256 = 0 . . . . ( by solving above eq . we get ) , x = - 16 or 5.33 = = = > ans - c"
Answer: c
Python program:
a = 2 + 16 
b = 2 - 16
c = a - b
Problem: in a 200 meter race a beats b by 35 meters in 7 seconds . a ' s time over the cause is ?
Options: a ) 47 sec , b ) 40 sec , c ) 45 sec , d ) 33 sec , e ) 35 sec
Rationale: b covers 35 m in 7 seconds b take time = ( 200 * 7 ) / 35 = 40 a takes time = 40 - 7 = 33 sec answer : d
Answer: d
Python program:
a = 7 / 35
b = a * 200
c = b - 7
Problem: a life insurance company insured 25,000 young boys , 14,000 young girls and 16,000 young adults . the probability of death within 10 years of a young boy , young girl and a young adult are 0.02 , 0.03 and 0.15 respectively . one insured person dies . what is the probability that the dead person is a young boy ?
Options: a ) 36 / 165 , b ) 25 / 166 , c ) 26 / 165 , d ) 32 / 165 , e ) 33 / 165
Rationale: the number of young boys that will die = 0.02 x 25,000 = 500 the number of young girls that will die = 0.03 x 14,000 = 420 the number of young adults that will die = 0.15 x 16,000 = 2400 the required probability = the number of young boys who will die / the total number of people who will die . = 500 / ( 500 + 420 + 2400 ) = 25 / 166 answer : b
Answer: b
Python program:
a = 5 ** 2
b = 0 * 2
c = 5 ** 2
d = 0 * 2
e = 3 + 4 
f = e * 2
g = 0 * 3
h = d + g 
i = 4 ** 2
j = i * 0
k = h + j 
l = b / k
Problem: triangle a ’ s base is 10 % greater than the base of triangle b , and a ’ s height is 10 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less
b ) 1 % less
c ) equal to each other
d ) 1 % more
e ) 9 % more
Rationale: base of a = 11 / 10 * base of b height of a = 9 / 10 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 11 / 10 * 9 / 10 * area of b = 99 / 100 * area of b area of a is 1 % less than the area of b . answer ( b )
Answer: b
Python program:
a = math.floor(100)
b = math.floor(100)
c = b * 10
d = c / 100
e = a + d 
f = math.floor(100)
g = math.floor(100)
h = g * 10
i = h / 100
j = f - i
k = triangle_area / (
Problem: peter and tom shared the driving on a certain trip . if peter and tom both drove for the same amount of time , but peter only drove 3 / 5 of the total distance , what was the ratio of peter ' s average speed to tom ' s average speed ?
Options: a ) 1 : 5 , b ) 3 : 2 , c ) 1 : 2 , d ) 3 : 5 , e ) 2 : 3
Rationale: "the answer is suppose to be b . 3 : 2 . it ' s from the gmatprep answer : option b"
Answer: b
Python program:
a = 2 / 0
b = 1 - a
c = 3 / 5
d = b / c
Problem: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 2.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 41 / 25 , b ) 15 / 14 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / ( 5 / 2 ) = 84 / 5 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 5 ) / 10 = 84 / 50 = 41 / 25 answer a"
Answer: a
Python program:
a = 42 / 2
b = 42 / 4
c = a / b
Problem: in a store , the total price for 20 shirts is $ 360 and the total price for 45 sweaters is $ 900 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5
Rationale: "the average price of a shirt is : $ 360 / 20 = $ 18 . the average price of a sweater is : $ 900 / 45 = $ 20 . the difference in price is : $ 20 - $ 18 = $ 2 . the answer is b ."
Answer: b
Python program:
a = 900 / 45
b = 360 / 20
c = a - b
Problem: a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 17.5 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 38 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.10 = 132 increase in 1993 from 1991 = 132 - 100 = 32 answer : d"
Answer: d
Python program:
a = 100 + 20 
b = 100 + 10 
c = b / 100
d = a * c
e = d - 100
Problem: the average expenditure of a labourer for 8 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 80 , b ) 85 , c ) 75 , d ) 95 , e ) 100
Rationale: "income of 8 months = ( 8 × 85 ) – debt = 680 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 950 average monthly income = 950 ÷ 10 = 95 answer d"
Answer: d
Python program:
a = 85 * 8
b = 60 * 4
c = a + b 
d = c + 30 
e = 8 + 4 
f = d / e
Problem: in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 140 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 314.45 $
Rationale: "service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 140 / 100 ) = 312 total fuel ( van + truck ) = 507 litre total fuel cost = 507 * 0.6 = 304.2 total cost = fuel + service = 304.2 + 10.25 = 314.45 answer is e"
Answer: e
Python program:
a = 65 * 140
b = a / 100
c = 65 + b 
d = c * 2
e = d * 0
f = 65 * 3
g = f * 0
h = e + g
Problem: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 66 , b ) 84 , c ) 80 , d ) 72 , e ) 68
Rationale: "let the length of the wire be h . radius = 1 / 2 mm = 1 / 20 cm . then , ( 22 / 7 ) x ( 1 / 20 ) x ( 1 / 20 ) x h = 66 . h = ( 66 x 20 x 20 x 7 ) / 22 = 8400 cm = 84 m . answer b"
Answer: b
Python program:
a = 1 / 2
b = a ** 2
c = b * math.pi
d = 66 / c
Problem: if the cost price of 58 articles is equal to the selling price of 50 articles , then what is the percent profit ?
Options: a ) 12 % , b ) 16 % , c ) 20 % , d ) 24 % , e ) 28 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 50 y = 58 x y = 1.16 x the answer is b ."
Answer: b
Python program:
a = 100 * 50
b = a / 58
c = 100 - b
d = 100 * 50
e = d / 58
f = c / e
g = 100 * f
Problem: a person is traveling at 20 km / hr and reached his destiny in 8 hr then find the distance ?
Options: a ) 180 km , b ) 200 km , c ) 160 km , d ) 220 km , e ) 240 km
Rationale: "t = 8 hrs d = t * s = 20 * 8 = 160 km answer is c"
Answer: c
Python program:
a = 20 * 8
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?
Options: a ) 3,108 , b ) 3,100 , c ) 3,108 , d ) 3,124 , e ) 3,250
Rationale: "to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 22.95 * 13 = 298.35 $ amount remaining = 300 - 298.35 = 1.65 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 13 = 3250 answer e"
Answer: e
Python program:
a = 300 / 22
b = a * 250
Problem: a train 400 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 87 kmph , b ) 28 kmph , c ) 72 kmph , d ) 18 kmph , e ) 29 kmph
Rationale: "length = speed * time speed = l / t s = 400 / 20 s = 20 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 72 kmph answer : c"
Answer: c
Python program:
a = 400 / 1000
b = 20 / 3600
c = a / b
Problem: two diesel trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 30 sec , c ) 40 sec , d ) 20 s , e ) 50 sec
Rationale: d relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 sec .
Answer: d
Python program:
a = 120 + 280 
b = 42 + 30 
c = b * 1000
d = c / 3600
e = a / d
Problem: two trains start simultaneously from opposite ends of a 180 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 180 - km trip in 5 hours . train y , travelling at a constant rate , completes the 180 - km trip in 4 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 72 , b ) 74 , c ) 76 , d ) 78 , e ) 80
Rationale: if the two trains cover a total distance d , then train x travels ( 4 / 9 ) * d while train y travels ( 5 / 9 ) * d . if the trains travel 180 km to the meeting point , then train x travels ( 4 / 9 ) * 180 = 80 km . the answer is e .
Answer: e
Python program:
a = 180 / 5
b = 180 / 5
c = 180 / 4
d = b + c 
e = 180 / d
f = a * e
Problem: maria bought 10 notebooks and 5 pens costing 2 dollars each . how much did maria pay ?
Options: a ) $ 10 , b ) $ 20 , c ) $ 30 , d ) $ 40 , e ) $ 50
Rationale: 2 × ( 10 + 5 ) = 2 × 10 + 2 × 5 = 20 + 10 = 30 dollars correct answer is c ) $ 30
Answer: c
Python program:
a = 10 + 5 
b = a * 2
Problem: a jogger running at 9 km / hr along side a railway track is 280 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 40 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 280 + 120 = 400 m . time taken = 400 / 10 = 40 sec . answer : e"
Answer: e
Python program:
a = 280 + 120 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 55 ?
Options: a ) s . 3944 , b ) s . 3948 , c ) s . 3942 , d ) s . 3965 , e ) s . 3740
Rationale: "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 55 = rs . 3740 . answer : e"
Answer: e
Python program:
a = math.sqrt(289)
b = square_perimeter * (
Problem: in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 9 years older than b , the present age of b is
Options: a ) 16 years , b ) 88 years , c ) 39 years , d ) 66 years , e ) 77 years
Rationale: "let b ' s age = x years . then , as age = ( x + 9 ) years . ( x + 9 + 10 ) = 2 ( x — 10 ) hence x = 39 . present age of b = 39 years answer : c"
Answer: c
Python program:
a = 2 * 10
b = 9 + 10 
c = a + b
Problem: how many times hour hand covers full circle in a day ?
Options: a ) 3 times , b ) 2 times , c ) 4 times , d ) 5 times , e ) once
Rationale: 2 times answer : b
Answer: b
Python program:
a = 3 * 4
b = a * 2
c = 3 * 4
d = b / c
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 3 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 7 , b ) 11 , c ) 12 , d ) 14 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 3 ^ 2 - 2 = 7 . thus , the answer is a ."
Answer: a
Python program:
a = 2 ** 2
b = a - 2
Problem: how many integers between 400 and 1000 are there such that their unit digit is odd ?
Options: a ) 250 , b ) 150 , c ) 300 , d ) 400 , e ) 450
Rationale: there are 600 numbers from 401 to 1000 ( inclusive ) . half of the numbers are odd , so there are 300 odd numbers . the answer is c .
Answer: c
Python program:
a = 1000 - 400
b = a / 2
Problem: a company pays 15.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 31 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 15.5 * 50 ) / 100 = rs . 7.75 rs . 25 is income on an investment of rs . 100 rs . 7.75 is income on an investment of rs . ( 7.75 * 100 ) / 25 = rs . 31 answer : b"
Answer: b
Python program:
a = 15 * 5
b = a / 100
c = b * 100
d = c / 25
Problem: the average of first 6 prime numbers is ?
Options: a ) 10.11 , b ) 11.11 , c ) 12.11 , d ) 6.83 , e ) 14.11
Rationale: "sum of 6 prime no . = 41 average = 41 / 6 = 6.83 answer : d"
Answer: d
Python program:
a = 6 + 1
Problem: jaya ranks 5 th in a class of 53 . what is her rank from the bottom in the class ?
Options: a ) 49 th , b ) 48 th , c ) 47 th , d ) 50 th , e ) none of these
Rationale: there are 4 students above her . when takan from bottom there are 4 students below her rank . so her rank wud be 53 - 4 i . e . 49 th . answer : a
Answer: a
Python program:
a = 53 - 5
b = a + 1
Problem: if the weight of 10 meters long rod is 23.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 14.04 kg . , d ) 18.0 kg , e ) none
Rationale: "answer ∵ weight of 10 m long rod = 23.4 kg ∴ weight of 1 m long rod = 23.4 / 10 kg ∴ weight of 6 m long rod = 23.4 x 6 / 10 = 14.04 kg option : c"
Answer: c
Python program:
a = 6 * 23
b = a / 10
Problem: a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 30000 rs , what is the value of buzness ?
Options: a ) 75000 , b ) 160000 , c ) 170000 , d ) 60000 , e ) 70000
Rationale: if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 30000 - > x = 60000 answer : d
Answer: d
Python program:
a = 2 / 3
b = 3 / 4
c = a * b
d = 30000 / c
Problem: the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > x or x < 0 ?
Options: a ) 5 / 8 , b ) 4 / 5 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: "the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points to the left of the y - axis satisfy the condition that x < 0 . the union of these two areas is 5 / 8 of the circle . the answer is a ."
Answer: a
Python program:
a = 2 * 4
b = 3 / a
Problem: at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 15 . if the price per share of stock k was $ 16 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 6.67 % , e ) 23.6 %
Rationale: "opening = 15 closing = 16 rise in price = 1 so , percent increase = 1 / 15 * 100 = 6.67 answer : d"
Answer: d
Python program:
a = 16 / 15
b = a - 1
c = b * 100
Problem: of the 70 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 70 - 50 - ( 40 - 35 ) = 70 - 55 = 15 answer b"
Answer: b
Python program:
a = 50 - 35
b = 40 - 35
c = a + b 
d = c + 35 
e = 70 - d
Problem: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 57000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 129000 = 24 / 43 . 24 / 43 is a little above 24 / 48 = 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Python program:
a = 30 / 100
b = a * 57000
c = 40 / 100
d = c * 72000
e = b + d 
f = 72000 + 57000 
g = e / f
h = g * 100
Problem: if a - b = 3 and a 2 + b 2 = 29 , then find the value of ab
Options: a ) 7 , b ) 8.5 , c ) 10 , d ) 12 , e ) 14
Rationale: explanation : 2 ab = ( a 2 + b 2 ) − ( a − b ) 2 = > 2 ab = 29 - 9 = 20 = > ab = 10 option c
Answer: c
Python program:
a = 3 ** 2
b = 29 - a
c = b / 2
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.30 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 663
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 1.30 = $ 663 answer e"
Answer: e
Python program:
a = 1000 * 1000
b = 3 * 6
c = 20 * 20
d = c * 15
e = b / d
f = e * 1
Problem: a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 50 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 4 hours ?
Options: a ) 40 % , b ) 35 % , c ) 30 % , d ) 25 % , e ) 20 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.5 ( 6 ) = 3 gallons at the start , the amount of water is 0.5 ( 6 ) = 3 gallons after 4 hours , the amount of water is 3 - 0.5 ( 4 ) = 1 gallon the concentration of water is 1 / ( 3 + 1 ) = 1 / 4 = 25 % the answer is d ."
Answer: d
Python program:
a = 100 - 50
b = 4 * a
c = b / 100
d = 0 * 5
e = c - d
f = 0 * 5
g = 4 - f
h = e / g
i = h * 100
Problem: he ratio between the sale price and the cost price of an article is 4 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 3 : 7 , c ) 3 : 8 , d ) 2 : 1 , e ) 8 : 3
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 4 x . then , gain = rs . 3 x required ratio = 3 x : 7 x = 3 : 7 . answer : b"
Answer: b
Python program:
a = 3 / 0
b = 1 - a
c = 1/(b)