euclaise/mathqa_programs huggingface dataset:
Problem: if a * b * c = 195 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these
Rationale: explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 195 / 65 = > a / d = 3 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 1000 = > f / c = 1 / 4 a / d * f / c = 3 * 1 / 4 = 3 / 4 answer : c
Answer: c
Python program:
a = 195 * 250
b = 1000 * 65
c = a / b
Problem: what is the least value of x , so that 2 x 5478 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 1 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 8 = 26 + x least value of x may be ' 1 ' , so that the total 26 + 1 = 27 is divisible by 9 . answer : option d"
Answer: d
Python program:
a = math.lcm(2, 5478)
b = a / 5478
c = b / 4
d = c / 4
Problem: the jogging track in a sports complex is 594 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 4.32 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 594 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 594 m apart , they take ( 100 / 825 * 594 / 1000 ) hrs = ( 594 / 8250 * 60 ) min = 4.32 min . answer : b"
Answer: b
Python program:
a = 594 / 1000
b = 4 + 5 
c = a / b
d = c * const_60
Problem: a can do a job in 45 days and b can do it in 30 days . a and b working together will finish 4 times the amount of work in - - - - - - - days ?
Options: a ) 30 days , b ) 45 days , c ) 80 days , d ) 72 1 / 2 days , e ) 72 days
Rationale: 1 / 45 + 1 / 30 = 5 / 90 = 1 / 18 18 / 1 = 18 * 4 = 72 days answer : e
Answer: e
Python program:
a = 1 / 45
b = 1 / 30
c = a + b 
d = 1/(c)
e = d * 4
Problem: on dividing a number by 357 , we get 37 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 37 = ( 17 * 21 * y ) + ( 17 * 2 ) + 3 = 17 * ( 21 y + 2 ) + 3 . required number = 3 . answer is b"
Answer: b
Python program:
a = 37 ** 2
b = a / 357
c = 37 ** 2
d = c / 357
e = math.floor(d)
f = b - e
g = f * 357
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 55 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 25,560 , d ) $ 21,360 , e ) $ 27,360
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.55 * 12000 = 12000 - 6600 x = 5400 earning becomes 9360 + 3 x = 9360 + 3 * 5400 = 25560 ans : c"
Answer: c
Python program:
a = 100 * 3
b = a + const_60
Problem: a vessel of capacity 45 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 28.8 , b ) 72.9 , c ) 38.3 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 45 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 45 - 9 ) / 45 ] ^ 2 ( 45 ) = 28.8 litres . answer : option a"
Answer: a
Python program:
a = 3 * 3
b = 45 - a
c = 3 * 3
d = 45 - c
e = d / 45
f = 3 * 3
g = e * f
h = b - g
Problem: if circles x and y have the same area and circle x has a circumference of 12 π , half of the radius of circle y is :
Options: a ) 16 , b ) 8 , c ) 3 , d ) 2 , e ) 1
Rationale: "x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 12 * pi x = 6 thus y = 6 y / 2 = 3 ans : c"
Answer: c
Python program:
a = 12 / 2
b = a / 2
Problem: convert the 18 / 42 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.54 kmph . , e ) 1.9 kmph .
Rationale: "18 / 42 m / s = 18 / 42 * 18 / 5 = 1 ( 27 / 50 ) = 1.54 kmph . answer : d"
Answer: d
Python program:
a = 18 / 42
b = const_3_6 * a
Problem: if a man lost 1 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 12 , b ) 14 , c ) 7 , d ) 11 , e ) 10
Rationale: "99 % - - - - 16 144 % - - - - ? 99 / 144 * 16 = 11 answer : d"
Answer: d
Python program:
a = 100 - 1
b = a * 16
c = 100 + 44 
d = b / c
Problem: a certain car uses one gallon of gasoline every 34 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 35 % , e ) 50 %
Rationale: 4 miles on the highway = 4 / 34 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 34 + 4 / 20 = 27 / 85 gallons . 8 miles on the highway = 4 / 17 gallons . the % change = ( 27 / 85 - 4 / 17 ) / ( 4 / 17 ) = 0.35 . answer : d .
Answer: d
Python program:
a = 1 / 20
b = a * 4
c = 1 / 34
d = 4 * c
e = b + d 
f = 1 / 34
g = 8 * f
h = e - g
i = 1 / 34
j = 8 * i
k = h / j
l = k * 100
Problem: in measuring the sides of a rectangle , one side is taken 9 % in excess , and the other 8 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.28 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 12 / 11 ) x ( 23 / 25 ) y = ( 358 / 357 ) ( xy ) error in measurement = ( 358 / 357 ) xy - xy = ( 1 / 357 ) xy error percentage = [ ( 1 / 357 ) xy ( 1 / xy ) 100 ] % = ( 7 / 25 ) % = 0.28 % . answer is e ."
Answer: e
Python program:
a = 9 - 8
b = 9 * 8
c = b / 100
d = a - c
Problem: there is 50 % increase in an amount in 6 years at s . i . what will be the c . i . of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2160 , b ) 3120 , c ) 17988 , d ) 6240 , e ) 5240
Rationale: "let p = rs . 100 . then , s . i . rs . 50 and t = 6 years . r = ( 100 * 50 ) / ( 100 * 6 ) = 10 % p . a . now , p = rs . 12000 , t = 3 years and r = 8.33 % p . a . c . i . = [ 12000 * { ( 1 + 8.33 / 100 ) 3 - 1 } ] = rs . 17988 answer : c"
Answer: c
Python program:
a = 100 * 100
b = 50 / 6
c = 100 * b
d = c * 3
e = a + d 
f = 50 / 6
g = f / 100
h = 1 + g 
i = 50 / 6
j = i / 100
k = 1 + j 
l = h * k
m = 50 / 6
n = m / 100
o = 1 + n 
p = l * o
q = e * p
r = 100 * 100
s = 50 / 6
t = 100 * s
u = t * 3
v = r + u 
w = q - v
Problem: if the cost price is 86 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 16 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 86 profit = $ 14 profit % = 14 / 86 * 100 = 25 / 6 = 16 % approximately answer is c"
Answer: c
Python program:
a = 100 - 86
b = a / 86
c = b * 100
Problem: find the length of the wire required to go 15 times round a square field containing 69696 m ^ 2 .
Options: a ) 1250 , b ) 2489 , c ) 6398 , d ) 15840 , e ) 2487
Rationale: "explanation : a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : d"
Answer: d
Python program:
a = square_perimeter * (
Problem: the average of 5 quantities is 8 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 14 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 8 - 3 x 4 ) / 2 = 14"
Answer: a
Python program:
a = 5 * 8
b = 3 * 4
c = a - b
d = c / 2
Problem: the perimeter of one square is 48 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 ) 5 cm
b ) 13 √ 2 cm
c ) 12 cm
d ) 6 cm
e ) 8 cm
Rationale: explanation : 4 a = 48 4 a = 20 a = 12 a = 5 a ^ 2 = 144 a ^ 2 = 25 combined area = a ^ 2 = 169 = > a = 13 d = 13 √ 2 cm answer : b
Answer: b
Python program:
a = 48 / 4
b = a ** 2
c = 20 / 4
d = c ** 2
e = b + d 
f = e * 2
g = math.sqrt(f)
Problem: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 14 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the class borrowed a total of 40 * 2 = 80 books . the 28 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 14 * 2 = 40 . to maximize the number of books borrowed by 1 student , let ' s assume that 11 students borrowed 3 books and 1 student borrowed the rest . 80 - 40 - 3 * 11 = 7 the maximum number of books borrowed by any student is 7 . the answer is e .
Answer: e
Python program:
a = 40 * 2
b = 12 * 1
c = b + 14 
d = c + 2 
e = 40 - d
f = e - 1
g = f * 3
h = 12 * 1
i = 14 * 2
j = h + i 
k = g + j 
l = a - k
Problem: a picnic attracts 240 persons . there are 30 more men than women , and 30 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 85 , d ) 130 , e ) 200
Rationale: "adult + children = 240 let , children = y then , adult = y + 30 i . e . y + ( y + 30 ) = 210 i . e . y = 115 i . e . adult = 115 + 30 = 145 adults include only men and women i . e . men + women = 145 let women , w = x then men , m = x + 30 i . e . x + ( x + 30 ) = 2 x + 30 = 145 i . e . x = 55 i . e . men , m = 55 + 30 = 85 answer : option c"
Answer: c
Python program:
a = 240 - 30
b = a / 2
c = b + 30 
d = c - 30
e = d / 2
f = e + 30
Problem: find 80 / ? = ? / 20
Options: a ) 40 , b ) 400 , c ) 800 , d ) 1600 , e ) none
Rationale: "answer let 80 / y = y / 20 then , y 2 = 80 x 20 = 1600 ∴ y = √ 1600 = 40 . option : a"
Answer: a
Python program:
a = 80 / 20
Problem: what is the greatest positive integer r such that 3 ^ r is a factor of 9 ^ 10 ?
Options: a ) r = 5 , b ) r = 9 , c ) r = 10 , d ) r = 20 , e ) 30
Rationale: "what is the greatest positive integer r such that 3 ^ r is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Python program:
a = 9 - 10
b = a * 10
Problem: find the average of all the numbers between 40 and 80 which are divisible by 3 .
Options: a ) 15 , b ) 70 , c ) 20 , d ) 60 , e ) none
Rationale: "sol . average = ( 42 + 45 + 48 + 51 + 54 + 57 + 60 + 63 + 66 + 69 + 72 + 75 + 78 / 13 ) = 780 / 5 = 60 . answer d"
Answer: d
Python program:
a = 40 + 4 
b = 80 - 4
c = a + b 
d = c / 2
Problem: a can do a job in 18 days and b can do it in 30 days . in how many days will they finish it together ?
Options: a ) 1 / 9 , b ) 4 / 45 , c ) 2 / 7 , d ) 6 / 3 , e ) 5 / 2
Rationale: explanation : 1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 so , both together will finish the work in 4 / 45 days . answer : b
Answer: b
Python program:
a = 1 / 18
b = 1 / 30
c = a + b
Problem: the mass of 1 cubic meter of a substance is 300 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 1.33
b ) 1.25
c ) 8.0
d ) 12.5
e ) 80.0
Rationale: density is mass divided by volume . so density of the given substance will be mass / volume = 800 kg / 1 m ^ 3 = 300 kg / m ^ 3 or 1 g / 1.33 cm ^ 3 = 0.3 g / cm ^ 3 . next , ask yourself if 300,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 1.33 cubic centimeters . answer is a
Answer: a
Python program:
a = 100 ** 3
b = 300 * 1000
c = a / b
d = c - 2
Problem: in a 300 member association consisting of men and women , exactly 80 % of men and exactly 15 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "solution simple out of 300 80 % are male i . e 240 and 15 % are female i . e 45 , so total homeowner is 295 . now min number homeowner is 45 and max is 240 so question ask us to find least and 46 has least value among all option . so ans is 46 . ans : a"
Answer: a
Python program:
a = 15 / 100
b = a * 80
c = 15 / 100
d = c * 80
e = b * d
f = 300 - 80
g = f / 80
h = e + g
Problem: mark has a rectangular driveway with a line painted diagonally across . the length of the driveway is 5 feet longer than its width . if the total area of the driveway is 36 square feet , what is the length of the painted line ( in feet ) ?
Options: a ) between 9 and 10
b ) between 10 and 11
c ) between 11 and 12
d ) between 12 and 13
e ) between 13 and 14
Rationale: to solve this , we first need to set up an equation for the area of the room . if x is the width , then we have x ( x + 5 ) = 36 . by putting the equation in standard form , we get x ^ 2 + 5 x - 36 = 0 . by using the quadratic formula , we get roots of 4 and - 9 . we know that x is the width , and x + 5 is the length , so by using the roots , we get 4 as the width ( x ) , and 9 as the length ( x + 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 4 ^ 2 + 9 ^ 2 = 16 + 81 = 97 the square root of 97 is less than 10 , since 10 ^ 2 = 100 . going down a number , we can compute 9 ^ 2 = 81 < 97 . therefore , the length of the diagonal must be between 9 and 10 . the correct answer is a .
Answer: a
Python program:
a = 5 ** 2
b = 36 * 4
c = a + b 
d = math.sqrt(c)
e = 5 + d 
f = e / 2
g = f ** 2
h = 5 ** 2
i = 36 * 4
j = h + i 
k = math.sqrt(j)
l = 5 + k 
m = l / 2
n = m - 5
o = n ** 2
p = g + o 
q = math.sqrt(p)
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 41 pages per hour . if tom starts reading a novel at 3 : 20 , and jan begins reading an identical copy of the same book at 4 : 26 , at what time will they be reading the same page ?
Options: a ) 6 : 26 , b ) 6 : 56 , c ) 7 : 26 , d ) 7 : 56 , e ) 8 : 26
Rationale: since tom reads an average of 1 page every 2 minutes , tom will read 33 pages in the first 66 minutes . jan can catch tom at a rate of 11 pages per hour , so it will take 3 hours to catch tom . the answer is c .
Answer: c
Python program:
a = 4 - 3
b = 26 - 20
c = b / const_60
d = a + c 
e = d * 30
f = 41 - 30
g = e / f
h = 4 + g 
i = h / 26
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 355 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 115 , c ) 120 , d ) 130 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 355 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 355 = 3320 - 2840 = 480 i . e . a = 120 and b = 355 - 120 = 235 more seats in balcony than orchestra = b - a = 235 - 120 = 115 answer : option b"
Answer: b
Python program:
a = 12 * 355
b = 3 * 1000
c = 3 * 100
d = b + c 
e = 2 * 10
f = d + e 
g = a - f
h = 12 - 8
i = g / h
j = 12 * 355
k = 3 * 1000
l = 3 * 100
m = k + l 
n = 2 * 10
o = m + n 
p = j - o
q = 12 - 8
r = p / q
s = 355 - r
t = i - s
Problem: a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 6 years ago ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard isr age of david isd age of scott iss now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 6 years ago ? i . e . d - 6 = 14 - 6 = 8 years answer : option a"
Answer: a
Python program:
a = 6 + 8 
b = a - 6
Problem: a type t machine can complete a job in 5 hours and a type b machine can complete the job in 7 hours . how many hours will it take 2 type t machines and 3 type b machines working together and independently to complete the job ?
Options: a ) 1 / 5 , b ) 29 / 35 , c ) 5 / 6 , d ) 35 / 29 , e ) 35 / 12
Rationale: now d should be the answer . t need 5 hours to complete and b needs 7 hours to compete so 2 t + 3 b will complete 2 / 5 + 3 / 7 or 29 / 35 portion of the job in 1 hour so the whole job will take 35 / 29 hours . . . . = d
Answer: d
Python program:
a = 5 / 2
b = 1/(a)
c = 7 / 3
d = 1/(c)
e = b + d 
f = 1/(e)
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 120,000 ?
Options: a ) 15 , b ) 21 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 120 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 120,000 = 3 years total 21 years . answer b"
Answer: b
Python program:
a = 3 * 10
b = 4 + 1 
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1 
g = e / f
h = 1 / 12
i = g ** h
j = math.log(i)
k = d / j
Problem: if the sum of two numbers is 16 and the sum of their squares is 200 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 28
Rationale: "according to the given conditions x + y = 16 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 16 ^ 2 = 200 + 2 xy so xy = 56 / 2 = 28 answer : e"
Answer: e
Python program:
a = 16 ** 2
b = a - 200
c = b / 2
Problem: a and b can do a piece of work in 12 days . with the help of c they finish the work in 6 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 30 , d ) 88 , e ) 12
Rationale: "c = 1 / 6 â € “ 1 / 12 = 1 / 12 = > 12 days answer : e"
Answer: e
Python program:
a = 6 / 12
b = 6 - a
c = 1/(b)
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4000 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 5000 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 4000 5 - - - ? = > 5000 answer : b"
Answer: b
Python program:
a = 12 - 7
b = 7 - 3
c = 4000 / b
d = a * c
Problem: running at the same constant rate , 6 identical machines can produce a total of 390 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2600 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 390 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 390 x = ( 10 x 4 x 390 ) / ( 6 ) x = 2600 . answer : c"
Answer: c
Python program:
a = 390 / 6
b = a * 4
c = b * 10
Problem: a certain pair of used shoes can be repaired for $ 14.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 16 , b ) 10.34 , c ) 12.46 , d ) 11.2 , e ) 14
Rationale: 1 ) cost of repairing = 14.5 ( for one year ) , therefore for 2 years it would be $ 29 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe . i . e ( 32 - 29 ) / ( 29 ) * 100 = 10.34 % . ans is b
Answer: b
Python program:
a = 14 * 5
b = 32 - a
c = 14 * 5
d = b / c
e = 100 * d
Problem: if length of rectangle is increased by 10 % , and breadth is decreased by 10 % . what will it effect on area of rectangle ?
Options: a ) it will have no effect
b ) 1 % increase
c ) 1 % decrease
d ) 2 % increase
e ) 2 % decrease
Rationale: let initial length = l , and breadth = b area = l * b new length = l * 110 % = [ l * 110 / 100 ] = 11 l / 10 , new breadth = 9 b / 10 new area = 11 l / 10 * 9 b / 10 = 99 / 100 lb decrease in area = [ lb - 99 / 100 lb ] = lb / 100 = % decrease = [ lb / 100 * 1 / lb * 100 ] = 1 % answer c
Answer: c
Python program:
a = 10 * 10
b = a / 100
c = b + 10 
d = c - 10
Problem: what is the ratio of 12 minute to 1 hour ?
Options: a ) 1 / 4 , b ) 3 / 4 , c ) 1 / 5 , d ) 2 / 2 , e ) 3 / 1
Rationale: c 1 / 5
Answer: c
Python program:
a = 12 / const_60
Problem: 8 * 8 * 8 * 8 = 2 ^ ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "solution : 2 ^ 3 * 2 ^ 3 * 2 ^ 3 * 2 ^ 3 = 2 ^ ( 3 + 3 + 3 + 3 ) = 2 ^ 12 answer : 12 option : e"
Answer: e
Python program:
a = 8 * 8
Problem: what is the smallest no . which must be added to 53403977 so as to obtain a sum which is divisible by 11 ?
Options: a ) 5 , b ) 4 , c ) 0 , d ) 1 , e ) 2
Rationale: "for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 53403977 , difference = ( 5 + 4 + 3 + 7 ) - ( 3 + 0 + 9 + 7 ) = 19 - 19 = 0 . = > 53403977 is also divisible by 11 c"
Answer: c
Python program:
a = 53403977 * 11
b = a / 53403977
Problem: each child has 8 crayons and 15 apples . if there are 7 children , how many crayons are there in total ?
Options: a ) 22 , b ) 56 , c ) 12 , d ) 36 , e ) 10
Rationale: 8 * 7 = 56 . answer is b .
Answer: b
Python program:
a = 7 * 8
Problem: a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 60 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 81.81 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 60 * 5 = 300 student ' s average = ( 600 + 300 ) / 11 = 81.81 answer d"
Answer: d
Python program:
a = 6 * 100
b = 5 * 60
c = a + b 
d = 6 + 5 
e = c / d
f = math.floor(e)
Problem: a person is traveling at 20 km / hr and reached his destiny in 2.5 hr then find the distance ?
Options: a ) 53 km , b ) 55 km , c ) 52 km , d ) 60 km , e ) 50 km
Rationale: "t = 2.5 hrs = 5 / 2 hrs d = t * s = 20 * 5 / 2 = 50 km answer is e"
Answer: e
Python program:
a = 20 * 2