ExplanationThe figure looks like a right triangle with legs of length 5 + y and 12 – y and hypotenuse of length 13. If y = 0, then the sides of the triangle have lengths 5, 12, and 13. This triangle is in fact a right triangle because \(5^2 + 12^2 = 13^2\). So the angle labeled x° is a right angle; that is, x = 90. In this case, Quantity A is equal to Quantity B.

Now consider another value of y, say y = 1, to see if the triangle is still a right triangle in this case. If y = 1, then the sides of the triangle have lengths 6, 11, and 13. This triangle is not a right triangle because \(6^2 + 11^2\) not equal to \(13^2\). So the angle labeled x° is not a right angle; that is, x ≠ 90. In this

case, Quantity A is not equal to Quantity B.

Because Quantity A is equal to Quantity B in one case and Quantity A is not equal to Quantity B in another case, the correct answer is

Choice D.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test