This page is part of my unofficial solutions manual to the GRE Paper Practice Book (2e), a free resource available on the ETS website. They publish the questions; I explain the answers. If you haven’t worked through the Practice Book, give Section 6 a shot before reading this!

6.1: Two Equilateral Triangles

This isn’t a trick question, exactly, but it’s close. You might think from the problem stem that you’ll be comparing the triangles to each other, since they tell you (in a roundabout way) that triangle T is bigger than triangle X. But the relative sizes of T and X actually end up being irrelevant to the solution — a classic “TMI” (too much information) scenario. More than anything else, this problem is an object lesson in the importance of reading carefully, even when you’re 3 hours into the exam.

Quantity A: Because T is an equilateral triangle, all of its sides are congruent. The ratio of its side lengths (Qty. A) is therefore 1:1 = 1.

Quantity B: Likewise, X is an equilateral triangle, so its sides are all congruent to each other. The ratio of the lengths of any two of those sides (Qty. B) is also 1:1 = 1.

Quantities A and B are equal, so the answer to this Quantitative Comparison is (C), as in “See, they’re the same!”

Math Review Reference

For more on this topic, see the following section of the GRE Math Review:

• 3.3: Triangles (pp. 47-48)