GMAT By The Numbers: Geometry

Now that you’ve learned how to approach geometry questions on the GMAT, let’s add one more dimension to your understanding of how they work.

Take a moment to try this question. Following is performance data from thousands of people who have studied with Kaplan over the decades. Through analyzing this data, we will show you how to approach questions like this one most effectively and how to avoid similarly tempting wrong answer choice types on Test Day.

A triangle with interior angles measuring a, b, and c degrees is drawn.  An exterior angle measuring d degrees is drawn adjacent to angle c, and angle c and d form a straight line.
  1. In the figure above, what is the value of b?
    1. a + c + d = 225
    2. d – a = 55
    1. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
    2. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
    3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    4. EACH statement ALONE is sufficient.
    5. Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation

The key to most GMAT geometry problems is to analyze the given figure before you worry too much about how you’re going to solve. In this problem, you’re given a triangle and a straight line, both of which have angles that add to 180°. Hence, you can create two equations:

a + b + c = 180 and d + c = 180

Since both (a + b + c) and (d + c) equal 180, you can set them equal to each other. And since you’re solving for b, you’ll want to first simplify the equation to isolate b:

To solve for b, you need only find a value for d – a. Having thus analyzed the question stem, you see that Statement (2) gives you exactly what you need and is sufficient and that Statement (1) does not and is insufficient. Hence, (B) is correct.

The question statistics reveal what the test maker already knows—that the vast majority of test takers don’t do much up-front analysis, thereby making their task much harder and causing them to miss what could be straightforward solutions. Make sure to analyze figures before you solve, and you’ll make GMAT geometry much easier.

More GMAT by the Numbers . . .

To see more questions with answer choice statistics, be sure to review the full-length CATs in your online resources.