Problem Solving

There are 24 students in a certain class, including boys and girls. If 1/2 of the boys and 1/3 of the girls had taken a course in biology, at most how many students had taken a course in biology?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15

OA is b

Given the constraints, here is how I tackled the problem.

24 Children – since we are dealing with people, all numbers should be integers.

We want to maximize the number while ensuring a few things…

The total # of men is an even number AND the total number of women is a factor of 3. Given the # men has to be even, we know the number of women also need to be even.

So, the first number we can find for women is 6 (a factor of 3 and even), which leaves 18 men. The answer is calculated by taking ½ of the men = 9 and 1/3 of the women = 2 equaling 11 (Answer B)

I would love to see this solved algebraically by one of our quantitative wizards!

Thanks - T

my ans - 11

the number of boys and girls has to be multiple of 6.so the combinations possible are (12,12) ; (6,18) ; (18,6) and the last combination gives maximum number ie 9 and 2.

Yes, my answer is also 11