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Re: In the triangle above, x and y are integers. If 30 < y < 40, what is [#permalink]

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01 Sep 2017, 03:37

The value will be between 35 and 40..and x + 2y =180 We get max value of y as 39 and minimum value as 36..so the equation will be as follows x + 2 X 39= 180 Gives x= 102 Similarly X + 2 X 36= 180 Gives x = 108 It implies X will be between 102~108

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

Since 30 < y < 40, 60 < 2y < 80. Thus, the “minimum” value of x is 180 - 80 = 100 and the “maximum” value of x is 180 - 60 = 120. In other words, 100 < x < 120.

We see that three answer choices, C, D, and E, satisfy this inequality. However, let’s say x = 105; then y = (180 - 105)/2 = 75/2 = 37.5 would not be an integer. The same can be said when x = 115. In other words, if x is odd, then y will not be integer. Thus, x must be even. So x must be 110. In fact, when x = 110, y = (180 - 110)/2 = 70/2 = 35, which is an integer.

Answer: D
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