Bunuel wrote:

In the triangle above, x and y are integers. If 30 < y < 40, what is one possible value of x?

(A) 95

(B) 100

(C) 105

(D) 110

(D) 115

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Working from answer choices sometimes sparks the right thought.

Subtract the answer choice (x) from 180, and then divide by 2.

I didn't write all the algebra down but you could.*:

Start with C) 105

180 - 105 = 95, which, divided by 2, does not yield an integer, which y must be. All answers with odd numbers are out.

That leaves B and D. It takes seconds to calculate if you don't happen to see that if 2y cannot be greater than 80, x cannot be smaller than 100. B gives

2y = 80. y = 40. Not permissible.

By POE, if you're brave, choose D and move on. Or

Answer D) 110: (180 - 110) = 70, y = 35. Correct

ANSWER D

*x + 2y = 180

2y = 180 - x

y = \(\frac{180 - x}{2}\)

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"