GMAT Prep DS question 1

[connit]

1. Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike brussels sprouts. How many of the students like brussel sprouts but dislike lima beans?
(1) 120 students eat in the cafeteria
(2) 40 of the students like lima beans.

Ans D. Please help explain why.

Thanks!!!

[2010gmat]

let total students = x

2/3 dislike Lima -- 2/3 X

therefore 1/3 X like Lima

now of those who dislike Lima 3/5 dislike brussel

--> therefore 2/5 must be like Brussel (they either like it or not)

--> 2/5 * 2/3 * X = 4/15 x this is wat we have to find

stmt 1 -- says x = 120 -- suff
stmt - 2 says 1/3 X = 40 again gives value of X = 120

SUff

ans d