lima beans and brussel sprouts

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 brussels sprouts but dislike lima beans?

1) 120 students eat in the cafeteria

2) 40 of the students like lima beans

[spoiler]OA:D[/spoiler]

Dont know why am i so confused with this one. Can someone pls help here!!

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by Anurag@Gurome » Tue Aug 28, 2012 3:33 am

koshls wrote: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 brussels sprouts but dislike lima beans?

1) 120 students eat in the cafeteria

2) 40 of the students like lima beans

[spoiler]OA:D[/spoiler]

Dont know why am i so confused with this one. Can someone pls help here!!

Say, number of students who eats in the cafeteria = n
Hence, 2n/3 students dislikes Lima beans.
Hence, (1 - 3/5)*(2n/3) = (2/5)*(2n/3) = 4n/15 students dislikes Lima beans but likes Brussels sprouts.

Statement 1: n = 120 --> Sufficient

Statement 2: (1 - 2/3)*n = 40 --> n = 3*40 = 120 --> Sufficient

The correct answer is D.

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