euclaise/mathqa_programs huggingface dataset:
Problem: a class has a ratio of 3 : 6 : 7 of children with red hair , blonde hair and black hair respectively . if the class has 9 kids with red hair , how many kids are there with black hair ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 21 , e ) 63
Rationale: "since there is a 3 : 7 ratio between red haired children and black - haired children , if there are 9 children with red hair , then there must be 3 times the amount of black - haired children . therefore , are 21 children with black hair . answer : d )"
Answer: d
Python program:
a = 7 + 6 
b = a + 3 
c = b * 3
Problem: a walks at 10 kmph and 5 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 50 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 5 hours . x / 10 - x / 20 = 5 x = 100 km answer is a"
Answer: a
Python program:
a = 5 * 20
Problem: evaluate : 28 % of 400 + 45 % of 250
Options: a ) 220.3 , b ) 224.5 , c ) 190.3 , d ) 150 , e ) none of these
Rationale: explanation : 28 % of 400 + 45 % of 250 = ( 28 / 100 * 400 + 45 / 100 * 250 ) = ( 112 + 112.5 ) = 224.5 answer b
Answer: b
Python program:
a = 400 * 28
b = a / 100
c = 45 * 250
d = c / 100
e = b + d
Problem: a rope of which a calf is tied is increased from 10 m to 20 m , how much additional grassy ground shall it graze ?
Options: a ) 540 , b ) 128 , c ) 100 , d ) 942 , e ) 942.86
Rationale: "π ( 202 – 102 ) = 942.86 answer : e"
Answer: e
Python program:
a = 20 ** 2
b = 10 ** 2
c = a - b
d = 10 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is :
Options: a ) 1 / 26 , b ) 1 / 52 , c ) 2 / 62 , d ) 2 / 26 , e ) 3 / 26
Rationale: "here , n ( s ) = 52 . let e = event of getting a queen of club or a king of heart . then , n ( e ) = 2 . p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer should be a"
Answer: a
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: a man can row 8 kmph in still water . when the river is running at 1.8 kmph , it takes him 2 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 8.2 km , b ) 6.7 km , c ) 7.6 km , d ) 7.4 km , e ) 6.3 km
Rationale: "m = 8 s = 1.8 ds = 9.8 us = 6.2 x / 9.8 + x / 6.2 = 1 x = 3.8 d = 2.88 * 2 = 7.6 answer : c"
Answer: c
Python program:
a = 8 + 1 
b = 8 - 1
c = a * b
d = 8 + 1 
e = 8 - 1
f = d + e 
g = c / f
h = g * 2
Problem: a cube of side 5 cm is painted on all its side . if it is sliced into 1 cubic centimer cubes , how many 1 cubic centimeter cubes will have exactly one of their sides painted ?
Options: a ) 9
b ) 61
c ) 98
d ) 54
e ) 64
Rationale: explanatory answer when a 5 cc cube is sliced into 1 cc cubes , we will get 5 * 5 * 5 = 125 cubes of 1 cubic centimeter . in each side of the larger cube , the smaller cubes on the edges will have more than one of their sides painted . therefore , the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted . in each face of the larger cube , there will be 5 * 5 = 25 cubes . of these , the cubes on the outer rows will be on the edge . 16 such cubes exist on each face . if we count out the two outer rows on either side of a face of the cube , we will be left with 3 * 3 = 9 cubes which are not on the edge in each face of the cube . therefore , there will be 9 cubes of 1 - cc volume per face that will have exactly one of their sides painted . in total , there will be 9 * 6 = 54 such cubes . choice d is the correct answer .
Answer: d
Python program:
a = surface_cube / (
b = a + 3
Problem: a person buys an article at $ 800 . at what price should he sell the article so as to make a profit of 12 % ?
Options: a ) 896 , b ) 890 , c ) 990 , d ) 789 , e ) 740
Rationale: "a 896 cost price = $ 800 profit = 12 % of 800 = $ 96 selling price = cost price + profit = 800 + 96 = 896"
Answer: c
Python program:
a = 12 / 100
b = 800 * a
c = 800 + b
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 25 !
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "we should find the highest power of 3 in 25 ! : 25 / 3 + 25 / 3 ^ 2 = 8 + 2 = 10 ( take only the quotient into account ) . . so the highest power of 3 in 25 ! is 10 . answer : b ."
Answer: b
Python program:
a = 25 / 3
b = math.floor(a)
c = 3 ** 2
d = 25 / c
e = math.floor(d)
f = b + e
Problem: jane makes toy bears . when she works with an assistant , she makes 44 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 ) 60 % , 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 57.6 bears per 36 hours a week or 1.6 bears / hr ( [ 40 bears * 1.44 ] / [ 40 hrs * . 90 ] ) . [ ( 1.6 - 1 ) / 1 ] * 100 % = 60 % answer : b"
Answer: b
Python program:
a = 100 - 44
b = a - 10
c = 10 / b
d = c * 100
Problem: two trains are moving in the same direction at 108 kmph and 36 kmph . the faster train crosses the slower train in 17 seconds . find the length of the faster train in meters .
Options: a ) 270 m , b ) 340 m , c ) 310 m , d ) 350 m , e ) 327 m
Rationale: relative speed = ( 108 - 36 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in 17 sec = 17 * 20 = 340 m . the length of the faster train = 340 m . answer : b
Answer: b
Python program:
a = 108 - 36
b = a / const_3_6
c = b * 17
Problem: how many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 55
Rationale: "solution speed of train relative to man = ( 63 - 3 ) km / hr = 60 km / hr = ( 60 x 5 / 18 ) m / sec = 50 / 3 m / sec time taken to pass the man = ( 500 x 3 / 50 ) sec = 30 sec answer b"
Answer: b
Python program:
a = 63 - 3
b = const_0_2778 * a
c = 500 / b
Problem: if 5 < x < 8 < y < 13 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x = 5.1 and y = 12.1 greatest possible difference = 12.1 - 5.1 = 7 answer e"
Answer: e
Python program:
a = 13 - 5
b = a - 1
Problem: in a garden , 26 trees are planted at equal distances along a yard 500 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 20 , b ) 8 , c ) 12 , d ) 14 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 500 / 25 = 20 i . e . , distance between two consecutive trees = 20 answer is a ."
Answer: a
Python program:
a = 26 - 1
b = 500 / a
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 2200 in all from both of them as interest . the rate of interest per annum is :
Options: a ) 5 % , b ) 10 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let the rate of interest per annum be r % simple interest for rs . 5000 for 2 years at rate r % per annum + simple interest for rs . 3000 for 4 years at rate r % per annum = rs . 2200 ⇒ 5000 × r × 2 / 100 + 3000 × r × 4 / 100 = 2200 ⇒ 100 r + 120 r = 2200 ⇒ 220 r = 2200 ⇒ r = 10 i . e , rate = 10 % . answer : option b"
Answer: b
Python program:
a = 5000 * 2
b = 3000 * 4
c = a + b 
d = 2200 / c
e = d * 100
Problem: 12 + 6 = 792 10 + 2 = 110 1 + 9 = 9 2 + 7 = 16 11 + 4 = ? ? solve it ?
Options: a ) 100 , b ) 120 , c ) 190 , d ) 160 , e ) 154
Rationale: x + y = x [ y + ( x - 1 ) ] = x ^ 2 + xy - x 12 + 6 = 12 [ 6 + ( 12 - 1 ) ] = 792 10 + 2 = 10 [ 2 + ( 10 - 1 ) ] = 110 1 + 9 = 1 [ 9 + ( 1 - 1 ) ] = 9 2 + 7 = 2 [ 7 + ( 2 - 1 ) ] = 16 11 + 4 = 11 [ 4 + ( 11 - 1 ) ] = 154 answer : e
Answer: e
Python program:
a = 11 + 4 
b = a * 10
c = b + 4
Problem: at a certain high school , the senior class is 3 times the size of the junior class . if 1 / 3 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 5 / 16 , d ) 1 / 4 , e ) 7 / 16
Rationale: start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 300 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 3 ) * 300 = 100 and ( 3 / 4 ) * 100 = 75 . 100 + 75 = 175 . there are a total of 400 students in the junior class and senior class combined ( 100 + 300 = 300 ) , and there are 175 total students in japanese , so 175 students in japanese / 400 total students equals 7 / 16 of the students in both classes that study japanese . answer : e
Answer: e
Python program:
a = 3 / 4
b = 1 + a 
c = 3 + 1 
d = b / c
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference ?
Options: a ) 9 feet , b ) 12 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 12 / 4 = 3 total feet squirrel travels = 3 * 3 = 9 feet answer : a"
Answer: a
Python program:
a = 12 / 4
b = a * 3
Problem: evaluate 2 + 22 + 222 + 2.22
Options: a ) 269.72 , b ) 268.22 , c ) 248.21 , d ) 248.22 , e ) 268.21
Rationale: "2 + 22 + 222 + 2.22 = 248.22 option d"
Answer: d
Python program:
a = 22 / 2
b = 2 / a
Problem: the least number which when increased by 7 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 857 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 7 = 864 - 7 = 857 . answer a"
Answer: a
Python program:
a = math.lcm(24, 32)
b = math.lcm(a, 36)
c = math.lcm(b, 54)
d = c - 7
Problem: what is the area of a square field whose diagonal of length 12 m ?
Options: a ) 288 , b ) 72 , c ) 200 , d ) 112 , e ) 178
Rationale: "d 2 / 2 = ( 12 * 12 ) / 2 = 72 answer : b"
Answer: b
Python program:
a = square_area / (
Problem: at a contest with 3,500 participants , 1 / 2 of the people are aged 18 to 22 . next year , the number of people aged 18 to 22 will increase by 1 / 7 . after this change , what percentage of the total 3,500 people will the 18 - to 22 - year - olds represent ?
Options: a ) 33 % , b ) 40 % , c ) 55 % , d ) 57.14 % , e ) 66.14 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 3,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 7 , we are multiplying it by 1 + 1 / 7 = 8 / 7 , so the answer here must be ( 1 / 2 ) * ( 8 / 7 ) = 4 / 7 = 57.14 % . answer : d"
Answer: d
Python program:
a = 3 / 500
b = 1 / 7
c = 1 + b 
d = a * c
e = d / 3
f = e * 100
Problem: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes jerry can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Python program:
a = 1 / 2
b = 2 + a 
c = 15 / b
d = 3 / 4
e = d + 2 
f = 16 / e
g = math.floor(f)
h = min(c)
i = 1 / 3
j = i + 1 
k = 8 / j
l = min(h)
Problem: daniel went to a shop and bought things worth rs . 25 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19.7 , b ) 20 , c ) 21.3 , d ) 21.5 , e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 a"
Answer: a
Python program:
a = 30 / 100
b = 25 - a
c = 30 / 6
d = b - c
Problem: the sum of the present age of henry and jill is 40 . what is their present ages if 11 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 23 , d ) and 29 , e ) of these
Rationale: "let the age of jill 11 years ago be x , age of henry be 2 x x + 11 + 2 x + 11 = 40 x = 6 present ages will be 17 and 23 answer : c"
Answer: c
Python program:
a = 40 + 11 
b = a / 3
c = 40 - b
Problem: if log 2 = 0.3010 and log 3 = 0.4771 , the value of log 5 512 is :
Options: a ) 2.87 , b ) 2.965 , c ) 3.876 , d ) 3.9 , e ) 4.526
Rationale: "log 5 512 = log 512 / log 5 = log 2 ^ 9 / log ( 10 / 2 ) = 9 log 2 / log 10 - log 2 = ( 9 * 0.3010 ) / 1 - 0.3010 = 2.709 / 0.699 = 2709 / 699 = 3.876 answer c"
Answer: c
Python program:
a = 0 / 3010
b = 0 * 3010
Problem: a is half good a work man as b and together they finish a job in 18 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 27 , d ) 36 , e ) 48
Rationale: "c 27 wc = 1 : 2 2 x + x = 1 / 18 = > x = 1 / 54 2 x = 1 / 27 = > 27 days"
Answer: c
Python program:
a = 3 / 2
b = 18 * a
Problem: the radius and height of a right circular cone are in the ratio 3 : 4 . if its volume is 96 ∏ cm ³ , what is its slant height ?
Options: a ) 8 cm
b ) 10 cm
c ) 12 cm
d ) 14 cm
e ) none
Rationale: sol . let the radius and the height of the cone be 3 x and 4 x respectively . then , 1 / 3 * ∏ * ( 3 x ) ² * 4 x = 96 ∏ ⇔ 36 x ³ = ( 96 * 3 ) ⇔ x ³ = [ 96 * 3 / 36 ] = 8 ⇔ x = 2 & ther 4 ; radius = 6 cm , height = 8 cm . slant height = √ 6 ² + 8 ² cm = √ 100 cm = 10 cm . answer b
Answer: b
Python program:
a = 96 / 3
b = a / math.pi
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 84 . how much was lent at 5 % ?
Options: a ) 299 , b ) 466 , c ) 578 , d ) 600 , e ) 677
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 84 5 x / 100 + 90 – 6 x / 100 = 84 x / 100 = 6 = > x = 600 answer : d"
Answer: d
Python program:
a = 5 + 6 
b = a * 100
Problem: an engine moves at the speed of 60 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 4 coaches are attached speed decreases to 48 kmph . what will be the speed of train when 36 coaches are attached .
Options: a ) 24 , b ) 28 , c ) 20 , d ) 32 , e ) 40
Rationale: "1 . no . of coaches = 4 sqr root = 2 speed decreases by 12 12 = k * 2 k = 6 no . of coaches = 36 swr root = 6 decrease = 6 * 6 = 36 new speed = 60 - 36 = 24 a"
Answer: a
Python program:
a = math.sqrt(36)
b = 60 - 48
c = math.sqrt(4)
d = b / c
e = a * d
f = 60 - e
Problem: you and your friend spent a total of $ 15 for lunch . your friend spent $ 5 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 10
Rationale: "my lunch = l , my friends lunch = l + 5 ( l ) + ( l + 5 ) = 15 l + l + 5 - 5 = 15 - 5 2 l = 10 l = 5 my friends lunch l + 5 = 5 + 5 = $ 10 , the answer is e"
Answer: e
Python program:
a = 15 - 5
b = a / 2
c = b + 5
Problem: the rear – most end of a 66 foot truck exits a 330 foot tunnel exactly 6 seconds after the front – most end of the truck entered the tunnel . if the truck traveled the entire tunnel at a uniform speed , what is the speed of the truck in miles per hour ( 1 mile = 5,280 feet ) ?
Options: a ) 225 , b ) 90 , c ) 45 , d ) 37.5 , e ) 27
Rationale: total length will be 330 + 66 = 396 time = 6 secs speed = 396 / 6 = 66 feet / sec conversion to miles per hour = 66 * 3600 / 5280 = 45 . answer c
Answer: c
Python program:
a = 330 + 66 
b = a / 6
c = b * 3600
d = 4 + 1 
e = d * 1000
f = 3 * 100
g = 2 * 10
h = f - g
i = e + h 
j = c / i
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 800 × 20.625 ) = 16500 . answer d"
Answer: d
Python program:
a = 5 * 5
b = 800 * a
Problem: 2 men and 2 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 4 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: the list should be wmwmw . hence , from women 2 ! and men 2 ! , we get ( 2 ! ) ( 2 ! ) = 4 . therefore , the correct answer is a .
Answer: a
Python program:
a = math.factorial(2)
b = math.factorial(2)
c = a * b
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts six hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )"
Answer: d
Python program:
a = 40 - 30
Problem: how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 70 m long and 16 1 / 2 m board ?
Options: a ) 99 , b ) 18 , c ) 16 , d ) 10 , e ) 231
Rationale: "70 * 33 / 2 = 5 / 2 * 2 * x = > x = 231 answer : e"
Answer: e
Python program:
a = 1 / 2
b = 16 + a 
c = 70 * b
d = 1 / 2
e = 2 + d 
f = e * 2
g = c / f
Problem: what is the rate percent when the simple interest on rs . 1200 amount to rs . 160 in 4 years ?
Options: a ) 3.3 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 1200 * 4 * r ) / 100 r = 3.3 % answer : a"
Answer: a
Python program:
a = 100 * 160
b = 1200 * 4
c = a / b
Problem: the simple form of the ratio 2 / 3 : 2 / 5 is ?
Options: a ) 5 : 0 , b ) 5 : 3 , c ) 5 : 1 , d ) 5 : 2 , e ) 5 : 7
Rationale: "2 / 3 : 2 / 5 = 10 : 6 = 5 : 3 answer : d"
Answer: d
Python program:
a = 2 / 5
Problem: on a map , 1 inch represents 28 miles . how many inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "28 miles represented by 1 inch 1 mile represented by ( 1 / 28 ) inch 383.6 miles represented by ( 1 / 28 ) * 383.6 approximately = 14 we should use estimation here as the answer options are not close . ( 28 * 10 = 280 and 28 * 20 = 560 , hence we select the only option between 10 and 20 ) answer c"
Answer: c
Python program:
a = 383 / 6
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.5 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.5 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.5 ) < = > k = 0.3 / 0.6 = 1 / 2 . required ratio = 1 / 2 : 1 = 1 : 2 . answer : a"
Answer: a
Python program:
a = 15 - 8
b = 16 - 4
c = a / b
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 3 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 8 , b ) 16 , c ) 21 , d ) 22 , e ) 27
Rationale: i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 3 ) x solve for r , r = 11 11 - 3 = 8 mpg a
Answer: a
Python program:
a = 462 - 336
b = a / 3
c = 336 / b
Problem: how many multiples of 5 are less than 5000 , and also multiples of 50 ?
Options: a ) 100 , b ) 208 , c ) 625 , d ) 832 , e ) 833
Rationale: the lcm of 5 and 50 is 50 . divide 5000 / 50 = 100 . xxx . so a is your answer .
Answer: a
Python program:
a = 50 - 5000
b = a / 5
c = b + 1
Problem: solution for 3.15 + . 014 + . 458
Options: a ) 3.622 , b ) 3.911 , c ) 4.938 , d ) 2.986 , e ) 2.999
Rationale: "3.15 + . 014 + . 458 = 0 0 = 0 - 3.15 - 0.014 - 0.458 0 = - 3.622 answer : a"
Answer: a
Python program:
a = 14 / 1000
b = 3 + 15 
c = 458 / 1000
d = b + c
Problem: a , b and c are entered into a partnership . a invested rs . 6500 for 6 months , b invested rs . 8400 for 5 months and c invested for rs . 10000 for 3 months . a is a working partner and gets 5 % of the total profit for the same . find the share of c in a total profit of rs . 7400 .
Options: a ) 2997 , b ) 1900 , c ) 2887 , d ) 2898 , e ) 27912
Rationale: "65 * 6 : 84 * 5 : 100 * 3 26 : 28 : 20 c share = 74000 * 95 / 100 = 7030 * 20 / 74 = > 1900 . answer : b"
Answer: b
Python program:
a = 5 * 7400
b = a / 100
c = 7400 - b
d = 10000 * 3
e = c * d
f = 6500 * 6
g = 8400 * 5
h = f + g 
i = 10000 * 3
j = h + i 
k = e / j
Problem: 3 , 7,12 , 18,25 . . . . . . . . . . . . . . 9 th terms
Options: a ) 43 , b ) 53 , c ) 63 , d ) 65 , e ) 78
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 42 + 10 = 52 52 + 11 = 63 answer : c"
Answer: c
Python program:
a = negate - (
Problem: if 60 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 33 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "60 % of ( x - y ) = 30 % of ( x + y ) ( 60 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 6 ( x - y ) = 3 ( x + y ) 3 x = 9 y x = 3 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 3 y ) x 100 ) = 33 % answer is a ."
Answer: a
Python program:
a = 60 - 30
b = 60 + 30 
c = a / b
d = c * 100
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 10 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 5 , b ) 4.5 , c ) 6 , d ) 7 , e ) 8
Rationale: work done by a & b in a day = x & y respectively . when a starts : no . of days when a works = 6 no . of days when b works = 4 → 6 x + 4 y = 1 when b starts : no . of days when b works = 5 no . of days when a works = 5 → 5 x + 5 y = 1 solving the above two equations for xy x = 1 / 10 y = 1 / 10 → total work done by ab in a day = 1 / 10 + 1 / 10 = 2 / 10 = 1 / 5 → no . of days to complete the work when both work together = 5 answer : a
Answer: a
Python program:
a = 10 - 1
b = 1/(a)
c = 10 + 2 
d = 1/(c)
e = b + d 
f = 1/(e)