PIE Issues!

Here's a problem. I know the answer through intuition, but wanted to know if the principle of inclusion-exclusion would work. I can't figure out how to use the PIE equations.

Students receive a BA degree only after passing all their tests and submitting all their papers. Out of 300 students, 250 passaged all their tests and 215 submitted all their papers. How many students received a BA degree? A. atleast215 B. no more than 185 C. exactly 215 D. at least 165

So the answer is D.

But I tried to use PIE, and I got stymied. So U = Set A + Set B + (Complement of A & B) - (Intersection of A&B).

I know U and A and B, but I got confused on the rest. Any help?

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$