Maximum # of students who go to school

[Max]

A class with 36 students, 1/3 of the boys and 1/4 of the girls walk to school. What is the greatest possible number of students in the class who go to school?

Answers: A9,B10,C11,D12,E13

My development:
Boys = x
Girls= 36-x
Total= 36

Equation:

1/3x + 1/4 (36 - x) = Greatest possible number

However I can´t solve this equation well.

Tks. in advance for your help.

Max

(taken from Power Prep)

[Nagm]

Equation will look like this:
A = (X/3) + (36-X)/4
= 9 + X/12

X/12 must be an integer. So X = 12K where K=1,2,3,4...............
K=1, A = 10
K=2, A = 11
K=3, A = 12

X can not be greater than 36 = Total number of students in class
So A = 12 is the answer

Or short cut
Say you have all the boys in the class.
so A = 36/3 = 12, no girls

[Max]

Pls. explain how you equal to 9 + X/12

[Nagm]

Equation will look like this:
A = (X/3) + (36-X)/4
= (X/3) + 9 - (X)/4
= 9 +(4X-3X)/4*3
= 9 + X/12

[rfernandez]

I like Nagm's second, more intuitive approach. With problems like these, it's often helpful to think in the most extreme of cases. Nice job.

Rey

[NC2012]

Equation will look like this:
A = (X/3) + (36-X)/4
= 9 + X/12

X/12 must be an integer. So X = 12K where K=1,2,3,4...............
K=1, A = 10
K=2, A = 11
K=3, A = 12

X can not be greater than 36 = Total number of students in class
So A = 12 is the answer

Or short cut
Say you have all the boys in the class.
so A = 36/3 = 12, no girls

I have a doubt.. Is it ok to assume a class comprising of only boys or only girls, when the question mentions "1/3 of the boys and 1/4 of the girls walk to school" ?

[tim]

you're not likely to see such a situation on the GMAT because they're much more careful about their wording, but the exact wording of this problem does not technically prevent a situation where all the students are the same gender..

[NC2012]

Thanks Tim.

[tim]

my pleasure..