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# Archive | Geometry

## GMAT Math: How do You Find the Height of a Triangle?

Suppose you have a triangle with sides {6,7,8} — how do you find the height? This is a question some GMAT test takers ask.  They know they would need the height to find the area, so they worry: how would I find that height.  The short answer is: fuhgeddaboudit!   Which height? First of all, […]

## GMAT Math: Similar Shapes

Some GMAT students who struggle with geometry find similar shapes confusing. I’ll try to clear that confusion up now. First, though, a couple tricky practice questions involving geometric similarity. 1) In the diagram above, BC is parallel to DE, DE = 20, and AC = CE = 6.  What is the length of AB? (A) […]

## Geometric Probability on the GMAT

In the first three articles in this series on GMAT probability questions, I discussed the AND and OR probability rules,  “at least” probability questions, and probability questions that involve counting.  This post covers relatively rare kind of probability question not covered in the first three posts: geometric probability questions.  First, a few challenging practice GMAT […]

## Slicing up GMAT Circles: Arclength, Sectors, and Pi

Few topics perplex students like circles on the GMAT. “What was the formula for area of a circle, again? I know pi is in there somewhere!” With a few simple insights, though, this entire topic simplifies.  First, let’s look at a problem. How do you find the do calculations for something like this? Given that […]

## Re-thinking Pythagoras: Is a triangle obtuse?

The Pythagorean Theorem is one of the most remarkable theorems in all of mathematics.  It has a treasure trove of ramifications up its sleeve, any one of which could provide you with invaluable help on the GMAT Quantitative section.  For example, consider this practice problem. 1) Consider the following three triangles I. a triangle with […]

## GMAT Math: Midpoints and Parallel vs. Perpendicular lines

First, a few practice questions. 1) Line A has the equation 3x + y = 7.  Which of the following lines is perpendicular to Line A? (A) y = 3x + 4 (B) y = –3x – 6 (C) y = (1/3)x – 1 (D) y = (–1/3)x + 2 (E) y = (–7/3)x – […]

## Pythagorean Triplets to Memorize for the GMAT

Learn the most common solutions to the Pythagorean Theorem There aren’t many numbers you need to memorize for success on the GMAT Quantitative section, but knowing a few key Pythagorean triplets will save you a ton of time.  First, try these GMAT practice question: remember: no calculator! 1) In right triangle ABC, BC = 48 […]

## GMAT Data Sufficiency: Congruence Rules

Learn how to use these formal Geometry rules to your advantage on the GMAT Data Sufficiency section!   A reminder about Data Sufficiency If this question format is new to you, read this post.  If you have done DS questions for a while, it’s still worthwhile to remind yourself of the basics.  You don’t actually […]

## Scale Factors on the GMAT: Percent Increases and Decreases

First, try these practice questions:   1) Every length in a 45°-45°-90° triangle increases by 20%.  By what percent does the area of the triangle increase? (A) 20% (B) 25% (C) 40% (D) 44% (E) 80% 2) At a certain pizza parlor, the diameter of a large pizza is 40% larger than the diameter of […]

## Inscribed and Circumscribed Circles and Polygons on the GMAT

Inscribed and circumscribed One more sophisticated type of geometric diagram involves polygons “inside” circles or circles “inside” polygons.  When a polygon is “inside” a circle, every vertex must lie on the circle: In this diagram, the irregular pentagon ABCDE is inscribed in the circle, and the circle is circumscribed around the pentagon.  We can also […]