### GRE Geometry: The Impossible Task

In one of my recent classes, I told the students “You’ll never know how to answer a geometry question.” The reaction was fairly predictable: “Why would you say that?!? That’s so discouraging!!”

Of course, I certainly was **NOT** trying to discourage them. I used that statement to illustrate that geometry questions are often a type of quantitative question that can feel *immensely* frustrating! You know what shape you have, you know what quantity the question wants, but you have no idea how to solve for that quantity.

This is what I meant when I said you’ll never know how to answer these questions. That “leap” to the correct answer is impossible. You can’t get to the answer in one step, but that’s all right: you’re not supposed to!

(An important aside: if you’ve read my post regarding calculation v. principle on the GRE, you should be aware that I am discussing the calculation heavy geometry questions in this post.)

The efficient, effective approach to a calculation-based geometry question is NOT to try and jump to the final answer, but instead to simply move to the next “piece”. For example, let’s say a geometry question gives me an isosceles triangle with two angles equaling *x*. I don’t know what *x* is, and I don’t know how to use it to find the answer to the question. But I **DO** know that the third angle is 180-2*x*.

That’s the game. Find the next little piece. And the piece after that. And the piece after that. Let’s see an example.

The correct response to this problem is “Bu-whah??? I know nothing about the large circle!”

But you do know the area of the smaller circle. What piece will that give you? Ok, you say, area gives me the radius. A = pi*r^2, so pi = pi*r^2, so r^2 = 1, so r = 1. Done, and let’s put that in the diagram.

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### The Math Beast Challenge Problem of the Week – December 5th, 2011

Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.

Quantity A

abc

Quantity B

h(a^{2}+b^{2})