euclaise/mathqa_programs huggingface dataset:
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 35 liters of forest green to change it to verdant green ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 35 / 3 , e ) 10 / 3
Rationale: "35 liter of forset green have 20 liter of blue and 15 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 20 / ( 15 + x ) = ¾ 45 + 3 x = 80 = > x = 35 / 3 answer : d"
Answer: d
Python program:
a = 4 / 3
b = a * 4
c = b - 3
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 12 x + 3 = 0 ?
Options: a ) 6 , b ) 7 , c ) 23 , d ) 17 , e ) 42
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 12 / 1 = - 12 ab = 3 / 1 = 3 hence a / b + b / a = [ ( - 12 ) 2 - 2 ( 3 ) ] / 3 = 126 / 3 = 42 . e )"
Answer: e
Python program:
a = negate ** (
b = a / 2
c = b - 3
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 60 days to complete the same work . then q alone can do it in
Options: a ) 20 , b ) 24 , c ) 25 , d ) 27 , e ) 30
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 60 work done by p , q and r in 1 day = 1 / 10 + 1 / 60 = 7 / 60 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 7 / 60 = > work done by p in 1 day = 7 / 120 = > work done by q and r in 1 day = 7 / 120 hence work done by q in 1 day = 7 / 120 â € “ 1 / 60 = 1 / 24 so q alone can do the work in 24 days answer is b ."
Answer: b
Python program:
a = 1 / 10
b = 1 / 60
c = a + b 
d = c / 2
e = 1 / 60
f = d - e
g = 1 / f
Problem: the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: "given that , a + b = 12 + b + c ⇒ a - c = 12 therefore , c is younger than a by 12 years answer is c ."
Answer: c
Python program:
a = 12 * 1
Problem: there are 1000 students in a school and among them 25 % of them attends chess class . 50 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 125 , d ) 50 , e ) 20
Rationale: "25 % of 1000 gives 250 . so 250 attends chess and 50 % of 250 gives 125 so 125 enrolled for swimming answer : c"
Answer: c
Python program:
a = 25 * 1000
b = a / 100
c = b * 50
d = c / 100
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 60 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 125 , b ) 95 , c ) 80 , d ) 61.8 , e ) 50
Rationale: answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 60 minutes after it was poured is : f = 120 ( 2 ^ - 60 / 10 ) + 60 f = 120 * 1 / 64 + 60 f = 15 / 8 + 60 f = 495 / 8 = 61.8 d
Answer: d
Python program:
a = 60 / 10
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: the edges of three iron cubes are 6 cm ; 8 cm ; 10 cm respectively . a new cube was made by melting them . find the edge of the new cube ?
Options: a ) 17
b ) 19
c ) 16
d ) 12
e ) 14
Rationale: 63 + 83 + 103 = a 3 = > a = 12 answer : d
Answer: d
Python program:
a = 100 + 3 
b = 8 * 10
c = b + 3 
d = a + c 
e = 10 * 6
f = e + 3 
g = d + f 
h = 2 * 10
i = 1 + h 
j = i - const_0_25
k = g / j
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 , b ) 76.5 , c ) 85 , d ) 80 , e ) none of these
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : c"
Answer: c
Python program:
a = 8 * 2
b = a + 65
Problem: if a and b get profits of rs . 5,000 and rs . 2,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 5 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: "ratio = 5000 / 2000 = 5 : 2 answer : c"
Answer: c
Python program:
a = 3 * 2
b = a * 100
c = b * 100
d = 3 * 2
e = d * 100
f = e * 100
g = 2 + 3 
h = g * 2
i = f / h
j = c / i
Problem: someone on a skateboard is traveling 5 miles per hour . how many feet does she travel in 45 seconds ? ( 1 mile = 5280 feet )
Options: a ) 380 ft , b ) 400 ft , c ) 410.05 ft , d ) 329.85 ft , e ) 420.85 ft
Rationale: "per second = > 5 * 5280 ft / 60 * 60 = 7.33 ft 45 seconds = > 7.33 * 45 = 329.85 ft answer : d"
Answer: d
Python program:
a = 5 * 5280
b = a / 3600
c = 45 * b
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 70 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 14,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 250 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 132 , b ) 138 , c ) 144 , d ) 128 , e ) 116
Rationale: "$ 14500 is a fixed cost each component is $ 74 ( $ 70 to produce , $ 4 to ship ) manufacturer will be producing and selling 250 components so therefore the equation to find price would be 250 * p = 14500 + ( 250 * 70 ) + ( 250 * 4 ) p = ( 14500 + 17500 + 1000 ) / 250 p = 132 answer : a"
Answer: a
Python program:
a = 4 * 4
b = a * 1000
c = 4 * 100
d = b + c 
e = 70 + 4 
f = e * 250
g = d + f 
h = g / 250
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 20 seconds . the ratio of their speeds is ?
Options: a ) 3 / 7 , b ) 3 / 2 , c ) 3 / 5 , d ) 3 / 1 , e ) 3 / 3
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 20 = = > 27 x + 17 y = 20 x + 20 y = = > 7 x = 3 y = = > x / y = 3 / 7 . answer : a"
Answer: a
Python program:
a = 27 - 20
b = 20 - 17
c = a / b
Problem: a bucket contains 2 mixtures a and b in the ratio 7 : 5 . if 9 liters of the mixture is replaced by 9 liters of liquid b , then the ratio of the two liquids becomes 7 : 9 . how much of the liquid a was there in the bucket ?
Options: a ) 15 liters , b ) 21 liters , c ) 12 liters , d ) 18 liters , e ) 25 liters
Rationale: 1 st ratio = 7 : 5 2 nd ratio = 7 : 9 difference of cross products ratio = 7 * 9 - 7 * 5 = 28 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 9 / 7 + 5 ) + ( 9 * 7 / 28 ) = 3 quantity of a = 7 * 3 = 21 liters answer is b
Answer: b
Python program:
a = 7 + 5 
b = 7 / a
c = b * 9
d = 9 * c
e = 7 + 5 
f = 5 / e
g = f * 9
h = 9 - g
i = 7 * h
j = d + i 
k = 9 * 7
l = 5 * 7
m = k - l
n = j / m
o = n * 7
Problem: jane makes toy bears . when she works with an assistant , she makes 53 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 70 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears / hr ( [ 40 bears * 1.53 ] / [ 40 hrs * . 90 ] ) . [ ( 1.7 - 1 ) / 1 ] * 100 % = 70 % answer : b"
Answer: b
Python program:
a = 100 - 53
b = a - 10
c = 10 / b
d = c * 100
Problem: two numbers are in the ratio of 1 : 2 . if 5 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 5 ) / ( y + 5 ) = 3 / 5 = > x = 10 and y = 20 answer : a"
Answer: a
Python program:
a = 1 * 5
Problem: if 60 % of 3 / 5 of a number is 72 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 75 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 60 % of 3 / 5 of x = 72 60 / 100 * 3 / 5 * x = 72 x = ( 72 * 25 / 9 ) = 200 required number = 200 . correct option : e"
Answer: e
Python program:
a = 60 / 100
b = 3 / 5
c = a * b
d = 72 / c
Problem: the cost to park a car in a certain parking garage is $ 12.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 2.69 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 12 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 12 + 7 * 1.75 = 24.25 thus the average parking price = 24.25 / 9 = 2.69 $ b is the correct answer ."
Answer: b
Python program:
a = 9 - 2
b = 1 * 75
c = 12 + 0 
d = c / 9
Problem: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability t this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability t of cgd / ( cg ) - > 3 / 19 answer d"
Answer: d
Python program:
a = 1 / 8
b = 2 / 3
c = a / b
d = 1 / 8
e = 2 / 3
f = d / e
g = f + 1 
h = c / g
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 6 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 20 min , b ) 22 min , c ) 15 min , d ) 18 min , e ) 24 min
Rationale: "let t = usual time = distance / usual speed t + 6 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 24 the answer is e ."
Answer: e
Python program:
a = 5 / 4
b = a - 1
c = 6 / b
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity t of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Python program:
a = 48 / const_60
b = 4 + 1 
c = a * b
d = const_60 * c
e = 50 * d
Problem: convert 500 miles to km ?
Options: a ) 600 km , b ) 700 km , c ) 800 km , d ) 900 km , e ) 1000 km
Rationale: "800 km 500 * 1.6 = 800 answer : c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 500
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 4 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 7 , c ) 15 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 4 breaks = . 3 / 4 = . 07 hrs = 7 m so answer is b ) 10 mins"
Answer: b
Python program:
a = 4 * 10
b = 2 * a
c = 3 / 2
d = 4 * 10
e = c * d
f = b - e
g = f / 4
Problem: each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 25 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs , then how manysmallercans are required to fulfill its weekly needs ?
Options: a ) 60 , b ) 70 , c ) 75 , d ) 100 , e ) 120
Rationale: "let x be the number of 25 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 30 ) 10 x = 450 x = 45 therefore , number of 15 ounce cans = 45 + 30 = 75 ans - c"
Answer: c
Python program:
a = 15 + 30
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 . 160 . find the unknown rate of two blankets ?
Options: a ) 420 , b ) 550 , c ) 490 , d ) 450 , e ) 457
Rationale: "10 * 160 = 1600 3 * 100 + 5 * 150 = 1050 1600 – 1050 = 550 answer : b"
Answer: b
Python program:
a = 10 * 160
b = 3 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: a 300 meter long train crosses a platform in 30 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 227 , b ) 266 , c ) 230 , d ) 288 , e ) 200
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 30 = 50 / 3 3 ( x + 300 ) = 1500 è x = 200 m . answer : e"
Answer: e
Python program:
a = 300 / 18
b = a * 30
c = b - 300
Problem: how many different values of positive integer x , for which | x + 6 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer d i opted to put the random value option . i used 0 , 6 , - 6 and the the extreme of 20 and - 20 . . i was able to solve it in 1 : 09 d"
Answer: d
Python program:
a = 6 + 6
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . if the faster train passes the slower train in 36 seconds , what is the length of each train ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 75 , e ) 40
Rationale: "assume the length of each train = x total distance covered for overtaking the slower train = x + x = 2 x relative speed = 46 - 36 = 10 km / hr = ( 10 × 10 ) / 36 = 100 / 36 m / s time = 36 seconds 2 x / ( 100 / 36 ) = 36 = > ( 2 x × 36 ) / 100 = 36 = > x = 50 meter answer is c ."
Answer: c
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 36
e = d / 2
Problem: convert the 9 / 36 m / s into kilometers per hour ?
Options: a ) 0.9 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph
Rationale: "9 / 36 m / s = 9 / 36 * 18 / 5 = 9 / 10 = 0.9 kmph . answer : a"
Answer: a
Python program:
a = 9 / 36
b = const_3_6 * a
Problem: in what time will a train 120 m long cross an electric pole , it its speed be 160 km / hr ?
Options: a ) 2.5 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 160 * 5 / 18 = 44 m / sec time taken = 120 / 44 = 2.7 sec . answer : c"
Answer: c
Python program:
a = 160 * const_0_2778
b = 120 / a
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose two adjacent faces are coloured red ?
Options: a ) 0 , b ) 8 , c ) 16 , d ) 24 , e ) 4
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having two adjacent faces coloured red = ( x - 2 ) x no . of edges = ( 4 - 2 ) x 12 = 24 answer : d"
Answer: d
Python program:
a = 64 / 4
b = a / 2
Problem: a 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 320 m , b ) 350 m , c ) 650 m , d ) none of these , e ) can not be determined
Rationale: "solution speed = ( 300 / 18 ) m / sec = ( 50 / 3 ) m / sec . length of the platform be x metres . then = x + 300 / 39 = 50 / 3 m / sec = 3 ( x + 300 ) = 1950 . = 350 m answer b"
Answer: b
Python program:
a = 18 / 3
b = 300 / a
c = b * 39
d = 3 * 300
e = c - d
f = e / 3
Problem: marketing executives for a certain chewing gum company projected a 30 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 53 % , b ) 57.7 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 130 . actual / projected * 100 = 75 / 130 * 100 = 57.7 % . answer : b ."
Answer: b
Python program:
a = 100 - 25
b = 30 + 100 
c = a / b
d = c * 100
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 190 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 50 sec
Rationale: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 190 = 550 meter time taken to cross the platform = 550 / ( 25 / 2 ) = 550 × 2 / 25 = 44 seconds answer : option c"
Answer: c
Python program:
a = 190 / 1000
b = 360 / 1000
c = a + b 
d = c / 45
e = d * 3600
Problem: find large number from below question the difference of two numbers is 2500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 3345 , b ) 1250 , c ) 1540 , d ) 2997 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 2500 = 6 x + 15 5 x = 2485 x = 497 large number = 497 + 1365 = 2997 d"
Answer: d
Python program:
a = 2500 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: 248 : 3 : : 328 : ?
Options: a ) 7 , b ) 5 , c ) 4 , d ) 6 , e ) none of the above
Rationale: "248 - - - - 24 / 8 . . . 3 328 - - - 32 / 8 . . . 4 answer c"
Answer: c
Python program:
a = 248 / 3
b = 328 * a
Problem: which number should replace both the asterisks in ( * / 18 ) x ( * / 72 ) = 1 ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "let ( y / 18 ) x ( y / 72 ) = 1 y ^ 2 = 18 x 72 = 18 x 18 x 4 y = ( 18 x 2 ) = 36 the answer is c ."
Answer: c
Python program:
a = 72 * 18
b = math.sqrt(a)
Problem: the triplicate ratio of 1 : 5 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 125
Rationale: "1 ^ 3 : 5 ^ 3 = 1 : 125 answer : e"
Answer: e
Python program:
a = 1 ** 5
b = 5 ** 5
c = a / b
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 200 m . then , a wins by :
Options: a ) 60 m , b ) 100 m , c ) 43 m , d ) 20 m , e ) 23 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 200 ) m , i . e . , 300 m . while a covers 3 m , b covers 4 m . while a covers 300 m , b covers 4 x 300 / 3 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 100 m behind . a wins by 100 m . answer : b"
Answer: b
Python program:
a = 500 - 200
b = a * 4
c = b / 3
d = 500 - c
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount q of paint , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture q , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Python program:
a = const_0_25 * 2
b = 2 * 5
c = a + b
Problem: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 9 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 20 , b ) 19 , c ) 18 , d ) 17 , e ) 16
Rationale: "lets q ' s first number be 14 as per question , q contains 9 multiples of 14 , so let q ' s last number be 126 . ( 14 ∗ 9 ) we have , a n = a + ( n − 1 ) d then 126 = 14 + ( n - 1 ) 7 solving for n , we get n = 17 answer : d"
Answer: d
Python program:
a = 9 * 2
b = a - 1
Problem: express a speed of 66 kmph in meters per second ?
Options: a ) 10.33 mps , b ) 17 mps , c ) 97 mps , d ) 17.33 mps , e ) 18.33 mps
Rationale: "66 * 5 / 18 = 18.33 mps answer : e"
Answer: e
Python program:
a = const_0_2778 * 66
Problem: a man buys a cycle for rs . 1600 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1360 , c ) s . 1190 , d ) s . 1202 , e ) s . 1256
Rationale: "s . p . = 85 % of rs . 1600 = rs . 85 / 100 x 1600 = rs . 1360 answer : b"
Answer: b
Python program:
a = 100 - 15
b = a * 1600
c = b / 100
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 8 cm and breadth 6 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 23.56 , b ) 23.59 , c ) 23.55 , d ) 23.53 , e ) 11.0
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 8 + 6 ) = 28 cm parameter of the square = 28 cm i . e . 4 a = 28 a = 7 diameter of the semicircle = 7 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) 7 = 1 / 2 ( 22 / 7 ) ( 7 ) = 11 cm answer : e"
Answer: e
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: a tempo is insured to an extent of 5 / 7 of its original value . if the premium on it at the rate of 3 % amounts to $ 300 , the original value of the tempo is ?
Options: a ) 12500 , b ) 13280 , c ) 17520 , d ) 14000 , e ) 12560
Rationale: "let the original value of the tempo is $ x 3 % of 5 / 7 of x = 300 ( 3 / 100 ) * ( 5 / 7 ) x = 300 x = $ 14000 answer is d"
Answer: d
Python program:
a = 5 / 7
b = a * 3
c = b / 100
d = 300 / c
Problem: last year department store x had a sales total for december that was 3 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 3 / 14 , d ) 4 / 11 , e ) 4 / 5
Rationale: let avg for 11 mos . = 10 therefore , dec = 30 year total = 11 * 10 + 30 = 140 answer = 30 / 140 = 3 / 14 = c
Answer: c
Python program:
a = 12 - 1
b = a + 3 
c = 3 / b