euclaise/mathqa_programs huggingface dataset:
Problem: in the set of positive integers from 1 to 80 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 260 , e ) 270
Rationale: "reduce to 1 - 80 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 are valid multiples . add them - - > 320 c"
Answer: c
Python program:
a = 3 * 5
b = 80 * a
c = b / 5
Problem: dan ' s age after 18 years will be 8 times his age 3 years ago . what is the present age of dan ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let dan ' s present age be x . x + 18 = 8 ( x - 3 ) 7 x = 42 x = 6 the answer is b ."
Answer: b
Python program:
a = 3 * 8
b = 18 + a 
c = 8 - 1
d = b / c
Problem: the wages earned by robin is 44 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 30.55 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 144 and $ 160 respectively . charles earns $ 44 more than robin who earns $ 144 . therefore , charles ' wage is 44 / 144 * 100 = 30.55 % . the correct choice is ( d )"
Answer: d
Python program:
a = 100 + 60 
b = 100 + 44 
c = a - b
d = 100 + 44 
e = c / d
f = e * 100
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 67.5 % percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "67.5 % is 12.5 % - points below 80 % and 12.5 % - points above 55 % . so the ratio of solution p to solution q is 1 : 1 . mixture p is 1 / 2 = 50 % of the volume of mixture pq . the answer is c ."
Answer: c
Python program:
a = 67 / 5
b = 55 / 100
c = a - b
d = 67 / 5
e = 55 / 100
f = d - e
g = 80 / 100
h = 67 / 5
i = g - h
j = f + i 
k = c / j
l = k * 100
Problem: the average age of a family of 6 members is 40 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 33 , b ) 18 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 40 = 240 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 240 - 42 = 198 therefore , avg age at the birth of youngest member = 198 / 6 = 33 . answer : a"
Answer: a
Python program:
a = 6 * 40
b = a - 7
c = b / 4
d = c - 7
Problem: a man rows his boat 80 km downstream and 38 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 9 , c ) 7 , d ) 8 , e ) 2
Rationale: "speed downstream = d / t = 80 / ( 3 ) = 27 kmph speed upstream = d / t = 38 / ( 3 ) = 9 kmph the speed of the stream = ( 27 - 9 ) / 2 = 9 kmph answer : b"
Answer: b
Python program:
a = 80 / 3
b = 38 / 3
c = a - b
d = c / 2
Problem: if x ⁄ 2 + 5 ⁄ 4 = 5 ⁄ 4 , what is the value of x ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: x ⁄ 2 + 5 ⁄ 4 = 5 ⁄ 4 let ' s multiply both sides by 4 . 2 x + 5 = 5 2 x = 0 x = 0 the answer is c .
Answer: c
Python program:
a = 5 / 4
Problem: at what rate percent per annum will a sum of money double in 7 years .
Options: a ) 12.5 % , b ) 13.5 % , c ) 14.2 % , d ) 14.5 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 8 ) ] % = 14.2 % per annum . answer : c"
Answer: c
Python program:
a = 100 / 7
Problem: sum of the squares of 3 no . ' s is 99 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 19 , d ) 28 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 99 + 2 * 131 a + b + c = √ 361 = 19 c"
Answer: c
Python program:
a = 131 * 2
b = a + 99 
c = math.sqrt(b)
Problem: a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 2 per sq m ?
Options: a ) 2288 , b ) 2779 , c ) 2779 , d ) 3900 , e ) 2600
Rationale: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 2 = rs . 2600 answer : e"
Answer: e
Python program:
a = 80 + 60 
b = a - 10
c = b * 10
d = c * 2
Problem: the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 150 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 154 , c ) 156 , d ) 144 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 150 . so , total number of ducks and frogs in the pond , = 2 * 150 = 300 . therefore , number of frogs , = ( 300 * 39 ) / 76 = 154 . answer : option b"
Answer: b
Python program:
a = 37 + 39 
b = a + 2 
c = b / 2
d = 150 / c
e = 39 * d
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 14000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 470400 , e ) none of these
Rationale: "b ' s monthly income = 14000 * 112 / 100 = rs . 15680 b ' s monthly income = 2 parts - - - - > rs . 15680 a ' s monthly income = 5 parts = 5 / 2 * 15680 = rs . 39200 a ' s annual income = rs . 39200 * 12 = rs . 470400 answer : d"
Answer: d
Python program:
a = 12 / 100
b = 1 + a 
c = 14000 * b
d = 5 / 2
e = c * d
f = e * 12
Problem: in the rectangular coordinate system , points ( 2 , 0 ) and ( – 2 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "the answer is a it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 2"
Answer: a
Python program:
a = 2 ** 2
b = math.sqrt(a)
Problem: if ram and gohul can do a job in 10 days and 15 days independently , how many days would they take to complete the same job working simultaneously ?
Options: a ) 10 , b ) 5 , c ) 8 , d ) 6 , e ) 13
Rationale: if total work is x . ram working rate = x / 10 per day . working rate of gohul = x / 15 per day . rate of work = ( x / 10 ) + ( x + 15 ) = 30 x / 5 x = 6 days the answer is option d
Answer: d
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1/(c)
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 4 ) , k = ( – 2 , 2 ) , l = ( 6 , 8 ) , and m = ( 6 , – 4 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 6 lm = 12 kl = using distance formula 10 jm = using distance formula 8 sum of all is 36 b"
Answer: b
Python program:
a = 2 + 4 
b = 10 + a 
c = 2 + 6 
d = b + c 
e = 8 + 4 
f = d + e
Problem: a box contains 7 purple , 5 blue and 11 yellow balls . what is the minimum number of tries required to get one blue and one yellow ball ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: 11 yellow + 7 purple + after that we have only one option that is to be blue so answer is 19 answer : d
Answer: d
Python program:
a = 7 + 11 
b = a + 1
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 361 is required to paint the floor at the rate of rs . 3.00001 / sq m , what would be the length of the floor ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 361 / 3 = 120.33 sq m l b = 120.33 i . e . , l * l / 3 = 120.33 l ^ 2 = 361 = > l = 19 . b"
Answer: b
Python program:
a = 361 / 3
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: 3 men and 3 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 ) 12 , b ) 15 , c ) 18 , d ) 36 , e ) 24
Rationale: the list should be wmwmw . hence , from women 3 ! and men 3 ! , we get ( 3 ! ) ( 3 ! ) = 36 . therefore , the correct answer is d .
Answer: d
Python program:
a = math.factorial(3)
b = math.factorial(3)
c = a * b
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 24
b ) 26
c ) 28
d ) 30
e ) 32
Rationale: area of first rectangle is 12 * 15 = 180 hence area of second would be 6 x = 180 x x = 30 answer is d
Answer: d
Python program:
a = rectangle_area / (
Problem: the calendar of the year 2080 can be used again in the year ?
Options: a ) 2105 , b ) 1955 , c ) 1945 , d ) 1935 , e ) 2108
Rationale: "explanation : given year 2080 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2080 + 28 = 2108 answer : e"
Answer: e
Python program:
a = 4 * 4
b = a - 2
c = b * 2
d = c + 2080
Problem: sum of 42 odd numbers is ?
Options: a ) 1764 , b ) 1774 , c ) 1784 , d ) 1794 , e ) 1754
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 42 odd numbers = 42 ^ 2 = 1764 answer : a"
Answer: a
Python program:
a = 42 * 2
b = 42 / 2
c = a * b
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 5,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.11 %
Rationale: the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 5,500 = 4,500 gallons and sodium chloride is 500 gallons ( 5 % of initial solution of 10,000 gallons ) then sodium chloride is 500 / 4,500 * 100 = ~ 11.11 % of the remaining solution of 4,500 gallons . answer : e .
Answer: e
Python program:
a = 100 * 100
b = 5 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: 4 , 25,49 , 121,169 , 289,361 ,
Options: a ) 149 , b ) 169 , c ) 189 , d ) 529 , e ) 219
Rationale: "23 ^ 2 = 529 because follow sequence of square of the prime numbers answer : d"
Answer: d
Python program:
a = negate - (
Problem: the distance from steve ' s house to work is 20 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 20 km = > speed = 10 kmph b"
Answer: b
Python program:
a = 20 / 2
b = 20 + a 
c = b / 6
d = c * 2
Problem: a and b can do a piece of work in 4 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 4 days , b ) 21 days , c ) 13 days , d ) 12 days , e ) 3 days
Rationale: "c = 1 / 3 – 1 / 4 = 1 / 12 = > 12 days answer : d"
Answer: d
Python program:
a = 3 / 4
b = 3 - a
c = 1/(b)
Problem: in a garden , there are 10 rows and 16 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 32 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 16 plants . there are 15 gapes between the two corner trees ( 15 x 2 ) metres and 1 metre on each side is left . therefore length = ( 30 + 2 ) m = 32 m . answer : a"
Answer: a
Python program:
a = 16 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: on a certain date , pat invested $ 9,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 36,000 , in how many years total will the total value of the investment plus interest increase to $ 72,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "36,000 = 9,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 72,000 = 9,000 ( 1 + x ) ^ n 8 = ( 1 + x ) ^ n 2 ^ 3 = ( 1 + x ) ^ n ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
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 / 10
i = g ** h
j = math.log(i)
k = d / j
Problem: 30 pens and 75 pencils were purchased for 510 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) can not be determined , e ) none of the above
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 510 – 150 ) = 360 ∴ average price of a pen = 360 ⁄ 60 = 12 answer c"
Answer: c
Python program:
a = 75 * 2
b = 510 - a
c = b / 30
Problem: a rectangular carpet has an area of 60 sq . m . if its diagonal and longer side together equal 5 times the shorter side , the length of the carpet is :
Options: a ) 5 m
b ) 12 m
c ) 13 m
d ) 14.5 m
e ) 15.5 m
Rationale: let , length = x meters and breadth = y meters then xy = 60 and ( x 2 + y 2 ) + x = 5 therefore , x = 60 and ( x 2 + y 2 ) = ( 5 y - x ) 2 or xy = 60 and 24 y 2 - 10 xy = 0 . therefore , 24 y 2 - 10 * 60 = 0 or y 2 = 25 or = 5 . therefore , x = ( 60 / 5 ) m = 12 m . so , length of the carpet = 12 m answer : b
Answer: b
Python program:
a = 60 * 10
b = 5 ** 2
c = b - 1
d = a / c
e = math.sqrt(d)
f = 60 / e
Problem: a train is 357 meter long is running at a speed of 42 km / hour . in what time will it pass a bridge of 137 meter length ?
Options: a ) 44 , b ) 42.343 , c ) 50 , d ) 39.252 , e ) 27.851
Rationale: "speed = 42 km / hr = 42 * ( 5 / 18 ) m / sec = 35 / 3 m / sec total distance = 357 + 137 = 494 meter time = distance / speed = 494 * ( 3 / 35 ) = 42.343 seconds . answer : b"
Answer: b
Python program:
a = 357 + 137 
b = 42 * 1000
c = b / 3600
d = a / c
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 34 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 18 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 34 pints will require 9 / 17 * 34 = 18 points . . second way . . get both red and white paints in same denominator . . . 3 / 4 + 2 / 3 = ( 9 / 12 ) + ( 8 / 12 ) pints . . from here we get the ratio of red : white = 9 : 8 . . so in 34 pints red will be 9 / ( 9 + 8 ) * 34 = 18 . . answer : c"
Answer: c
Python program:
a = 3 * 2
b = 4 * 3
c = a / b
d = 34 * c
Problem: the value of ( 0.137 + 0.098 ) ² - ( 0.137 - 0.098 ) ² / 0.137 × 0.098 is
Options: a ) 0.039 , b ) 0.235 , c ) 0.25 , d ) 4 , e ) 5
Rationale: solution given expression = ( a + b ) ² - ( a - b ) ² / ab = 4 ab / ab = 4 . answer d
Answer: d
Python program:
a = 0 + 137 
b = a ** 2
c = 0 - 137
d = c ** 2
e = b - d
f = 0 * 137
g = e / f
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6900 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7391
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6900 * 6 ) - 34009 ] = rs . ( 41400 - 34009 ) = rs . 7391 . answer : e"
Answer: e
Python program:
a = 5 + 1 
b = a * 6900
c = 6435 + 6927 
d = c + 6855 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 457 ?
Options: a ) 26.4 % , b ) 21 % , c ) 20 % , d ) 19 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 457 , discount = 621 - 457 = 164 discount % = 164 / 621 * 100 = 26.4 % answer : a"
Answer: a
Python program:
a = 100 + 15 
b = a / 100
c = 540 * b
d = c - 457
e = d * 100
f = 100 + 15 
g = f / 100
h = 540 * g
i = e / h
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 8 cubic feet . if a small block has half the width , half the depth , and half the length of a normal block , what is the volume of cheese in a small block in cubic feet ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 2
Rationale: "volume of cube = lbh = 8 new cube l , b , h are decreases of . 5 l , . 5 b , . 5 h new volume of cube = . 5 l * . 5 b * . 5 h = . 125 * lbh = . 125 * 8 = 1 answer : a"
Answer: a
Python program:
a = 2 * 2
b = a * 2
c = b * 8
Problem: boy sells a book for rs . 450 he gets a loss of 10 % , to gain 10 % , at price he should sell ?
Options: a ) rs . 400 , b ) rs . 450 , c ) rs . 550 , d ) rs . 600 , e ) rs . 650
Rationale: "find selling price to gain 10 % . now , we are asked to find selling price to gain 10 % profit . hint : selling price = ( 100 + gain % ) × c . p . 100 selling price = ( 100 + 10 ) × 500 100 selling price = ( 110 ) × 500 100 therefore , selling price = rs . 550 c"
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 450 / b
d = 10 / 100
e = 1 - d
f = 450 / e
g = 10 / 100
h = f * g
i = c + h
Problem: how many seconds does sandy take to cover a distance of 700 meters , if sandy runs at a speed of 18 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "18 km / hr = 18000 m / 3600 s = 5 m / s time = 700 / 5 = 140 seconds the answer is c ."
Answer: c
Python program:
a = 18 * const_0_2778
b = 700 / a
Problem: 5358 x 51 = ?
Options: a ) 272258 , b ) 272358 , c ) 273258 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 1 ) = 5358 x 50 + 5358 x 1 = 267900 + 5358 = 273258 . c )"
Answer: c
Python program:
a = 5358 / 51
b = a * 100
Problem: a company purchased raw material worth 1 / 4 of it capital , 1 / 10 of the remaining is spent on machinery . how much fraction of the capital was left with the company after its expenditures on raw material and machinery ?
Options: a ) 1 / 5 , b ) 2 / 8 , c ) 5 / 9 , d ) 27 / 40 , e ) 15 / 30
Rationale: the amount spent by the company on raw material is 1 / 4 , so remaining is 3 / 4 . 1 / 10 of the remaining is spent on machinery , 1 / 10 * 3 / 4 = 3 / 40 total amount spent on raw material and machinery is 1 / 4 + 3 / 40 to make the denominator common we use 40 , so 1 / 4 is 10 / 40 10 / 40 + 3 / 40 = 13 / 40 is spent on raw material and machinery remaining 27 / 40 is left with the company answer is d
Answer: d
Python program:
a = 1 / 4
b = 1 - a
c = 1 / 4
d = 1 - c
e = d / 10
f = b - e
Problem: if x = y = 2 z and xyz = 256 then what is the value of x ?
Options: a ) 12 , b ) 8 , c ) 16 , d ) 6 , e ) 2
Rationale: given that x = y = z . so , x = y , x = 2 z , y = 2 z . given xyz = 256 = > ( 2 z ) * ( 2 z ) * z = 256 = > 4 z ^ 3 = 256 = > z = 4 then x = 2 z = 2 ( 4 ) = 8 answer : b
Answer: b
Python program:
a = 256 * 2
b = 1 / 3
c = a ** b
Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 5184 , what is the area of the side face of the box ?
Options: a ) 123 , b ) 167 , c ) 178 , d ) 199 , e ) 288
Rationale: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 5184 l * 1.5 l * 2 l = 5184 l = 12 side face area = l * d = l * 2 l = 12 * 2 * 12 = 288 e is the answer"
Answer: e
Python program:
a = 5184 ** 2
b = 3 * a
c = 1 / 3
d = b ** c
e = d / 1
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed r of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = r ans = c"
Answer: c
Python program:
a = 24 * 4
b = a / 3
c = b - 24
d = 35 - 25
e = d + 50 
f = 35 - 25
g = e / f
h = c * g
Problem: if a ã — b = 2 a - 3 b + ab , then 4 ã — 5 + 5 ã — 4 is equal to :
Options: a ) 31 , b ) 32 , c ) 43 , d ) 45 , e ) 26
Rationale: "explanation : 4 ã — 5 + 5 ã — 4 = ( 2 ã — 4 - 3 ã — 5 + 4 ã — 5 ) + ( 2 ã — 5 - 3 ã — 4 + 5 ã — 4 ) = ( 8 - 15 + 20 + 10 - 12 + 20 ) = 31 . answer : a"
Answer: a
Python program:
a = 5 * 4
b = 3 * 2
c = a - b
d = 4 * 2
e = c + d 
f = 2 * 2
g = 3 * 4
h = f - g
i = 2 * 4
j = h + i 
k = e + j
Problem: my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 100 years . can you tell my grandson age in years ?
Options: a ) 50 years , b ) 20 years , c ) 5 years , d ) 10 years , e ) 90 years
Rationale: let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 120 years , g + s + m = 100 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows : g + 365 g / 52 + 12 g = 100 or 52 g + 365 g + 624 g = 5,200 or g = 5,200 / 1,041 = 5 years answer : c
Answer: c
Python program:
a = 10 + 10 
b = 100 / a
c = b * 12
Problem: what is the difference between the place values of two sevens in the numeral 54179759 ?
Options: a ) 699990 , b ) 99990 , c ) 99980 , d ) 69300 , e ) none of these
Rationale: explanation : required difference = 70000 - 700 = 69300 answer is d
Answer: d
Python program:
a = 3 + 4 
b = a * 10
c = b * 1000
d = 3 + 4 
e = d * 10
f = c - e
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 34 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 22.67 litres , c ) 11 litres , d ) 07 litres , e ) 38.67 litres
Rationale: "262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) solve the equation . 262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) 8936.9 + 3 , 104.35 x = 47 , 581.3 + 1 , 399.45 x 8936.9 + 1 , 704.9 x = 47 , 581.3 1 , 704.9 x = 38 , 644.40 x ≈ 22.67 answer is b ."
Answer: b
Python program:
a = 34 * 1399
b = 34 * 262
c = a - b
d = 3104 - 35
e = c / d