Data Sufficiency

BTGmoderatorDC wrote:All attendees at a university gathering are faculty or alumni of the university. Are any of the attendees both faculty and alumni?

(1) 3/5 of the attendees are members of the university faculty

(2) 40% of the attendees are not members of the university faculty

OA E

Source: Veritas Prep

There are a total of T attendees; out of which, there are F ONLY faculty members, A ONLY alumni and B both faculty members and alumni.

Thus, we have

T = F + A + B ---(1)

We have to get the value of B.

Let's take each statement one by one.

(1) 3/5 of the attendees are members of the university faculty.

=> F + B = 3/5 of T = 3T/5. Can't get the value of B. Insufficient

(2) 40% of the attendees are not members of the university faculty.

=> A = 40% of T = 2/5 of T = 2T/5. Can't get the value of B. Insufficient

(1) and (2) together

From (1) and (2), we get

Plugging-in the value of F + B = 3T/5 and A = 2T/5 in the equation T = F + A + B, we get T = 3T/5 + 2T/5 => T = T. Can't get the valaue of B. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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