Need help with sets please

Initial statement gives us the following formulas:

OnlyP + OnlyQ + Both (P+Q) = 150
P + Q - Both (P + Q) = 150

These are easier seen when drawn out as venn diagrams. Imagine two circles P & Q that overlap. You can plot a point inside P only, inside P and Q together, and inside Q only. You could also, in theory, plot a point outside either circle. But, the stem has provided us with the total inside (at 150).

(1) This statement tells us that 60 people attend meeting P only. Plug that into our first equation:
60 + OnlyQ + Both (P+Q) = 150
We're left with two variables, so we cannot determine how many attended each meeting. Insufficient.

(2) This statement tells us that 90 people attended meeting Q. This includes both OnlyQ and those that attended both P and Q.
Using our 2nd equation, P + 90 - Both (P+Q) = 150. Again, we have two variables. Insufficient.

(1) + (2) Together?
Essentially, Statement (2) is giving us a value we already knew from Statement (1).
(1) 60 + OnlyQ + Both (P+Q) = 150
So, OnlyQ + Both (P+Q) = 90
Statement (2) tells us the exact same information. We still cannot distinguish the distinct variables... just the two together. Insufficient.

E.

Statement 2 does not say 90 attended Q only. I got 90 = q + (p&q)

heshamelaziry wrote:Statement 2 does not say 90 attended Q only. I got 90 = q + (p&q)

E is the answer . Check my approach in the attachment.