GMAT Tip: What Geometry Questions Really Measure

GMAT Tip: What Geometry Questions Really Measure
You may not use geometry every day, but GMAT measures it to see how creatively you solve problems (Photograph by Getty Images)
Photograph by Getty Images

This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep.

When was the last time you used the Pythagorean Theorem in your job? Unless you’re a math teacher or a pyramid architect, the answer is quite likely “never.” So why does the GMAT test geometry?

While this common question may seem like sour grapes from those who abhor spatial thinking or square roots of three, it’s actually a meaningful exercise in adjusting your mindset to succeed on geometry-based questions. The GMAT doesn’t test geometry because geometric formulas are intrinsically useful in business school; it tests geometry because it lends itself well to the assessment of business-related problem solving.

Simply put, business is all about leveraging assets, and so are geometry questions.

Consider the example:

In triangle PQS, if PQ = 3 and PS = 4, then PR =

(A) 9/4
(B) 12/5
(C) 16/5
(D) 15/4
(E) 20/3

When many attempt to answer this question, their first inclination is to assume that lines SR and RQ are equal—that line PR bisects side SQ. But it doesn’t. The very fact that lines PQ and PS are different lengths should show you that the triangle isn’t symmetrical and therefore won’t be simply cut in half by line PR. The next, more painful response is to try to dive into ugly Pythagorean Theorem calculations, which usually lead to a ton of frustration.

But here’s where the problem-solving/leveraging-assets nature of GMAT geometry can help you a lot. The key to solving this one quickly is actually one of the most basic things you know about triangles:

Area = ½ Base X Height.

Why? Because if you use PQ as the base of the large triangle, then PS is the height (the base and height must be perpendicular), meaning that the area is ½(3)(4) = 6.  But then mentally flip that triangle so that it lies on side SQ, and use SQ as the base. Then, which line is the height? Line PR, the perpendicular line between the base and the opposite angle. And since you know that SQ = 5 (you can get that from the Pythagorean Theorem) and that the area is 6, you now have:

Area = ½ Base X Height

6= ½ (5)(h)

h = 12/5

While the mechanics of this problem do require you to know the Pythagorean Theorem and the area of a triangle, you should see that this problem is much more about creatively leveraging assets (very few people see the area as an asset) than it is about just plain geometry.

Business will reward you for finding efficient and unique ways to pair assets together, and GMAT geometry operates largely the same way. Study geometry to build up your asset bank, but remember that the reason you’re doing it is to focus on the creative application—the real asset you want to demonstrate to business schools.

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