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In a certain class consisting of 36 students, some boys and

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In a certain class consisting of 36 students, some boys and [#permalink] New post 20 Nov 2005, 00:44
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In a certain class consisting of 36 students, some boys and some girls, exactly 1/3 of the boys and exactly 1/4 of the girls walk to school. What is the greatest possible number of students in this class who walk to school?

a. 9
b. 10
c. 11
d. 12
e. 13

The explanation in the book is not too clear, I would greatly appreciate it if someone can explain how to work this problem out.
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 [#permalink] New post 20 Nov 2005, 02:04
C. 11

let x be total number of boys, so 36-x gals.
we need to maximize:

x/3 + (36-x)/4 or x/12 + 9

to maximize, x should be maximum.

x should also be divisible by 12
as question says there are "some" gals, we cannot take x=36

so, x = 24
max students walking = 24/12 + 9 = 11
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  [#permalink] 20 Nov 2005, 02:04
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