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

This is an EITHER/OR group question.
Every student EITHER dislikes lima beans OR likes lima beans.
Every student EITHER dislikes brussel sprouts OR likes brussels sprouts.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let DL = dislikes limas, LL = likes limas, DB = dislikes brussels sprouts, and LB = likes brussels sprouts.
There are two fractions in the question stem: 2/3 and 3/5.
Since the product of the denominators = 3*5 = 15, let the TOTAL = 15x.
Here's the grid:

_______________DL______LL_______Total

DB:

LB:

Total:___________________________15x

Now let's use the information in the question stem to complete as much of the grid as possible.
Values in the grid have to add up horizontally and vertically.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

2/3 dislike lima beans:
Since (2/3)(15x) = 10x, we get:

_______________DL______LL_______Total

DB:

LB:

Total:__________10x______5x_______15x

Of those who dislike lima beans, 3/5 also dislike brussel sprouts.
Since (3/5)(10x) = 6x, we get:

_______________DL______LL_______Total

DB:____________6x_______________

LB:____________4x_________________

Total:_________10x______5x_______15x

The question stem asks for the number of students who like brussels sprouts but dislike lima beans: 4x.
To determine the value of 4x, we need to know the value of x.
Question rephrased: What is the value of x?

Statement 1: 120 students eat in the cafeteria
Since the total number of students = 15x, we get:
15x = 120
x = 8.
SUFFICIENT.

Statement 2: 40 students like lima beans.
Since the total number of students who like lima beans = 5x, we get:
5x = 40
x = 8.
SUFFICIENT.

The correct answer is D.