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Circle problems on the GMAT

Here are eight practice problems involving circles.  The difficulty of these problems ranges from medium to very challenging. 1) In the diagram above, O is the center of the circle and angle AOB = 144º.  What is the area of the circle? Statement #1: The area of sector AOB is 40% of the area of […]

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GMAT Tuesdays with Kevin: Challenge Question — Tour through Geometry

  Hello! This week, I’m solving a tough challenge question that you might have seen on our blog if you visit often! This challenge question draws on a whole host of geometry concepts and formulas, so it’s a great test for how much of geometry you really know. And just in case the board isn’t […]

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GMAT Geometry Practice Problems

1) A triangle could possibly intersect a circle at the following number of points: I. 3 II. 4 III. 5 I only I & II only I & III only II & III only I, II, III 2) Each circle in the diagram above has a radius of r = 6.  What is the total […]

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GMAT Tuesdays with Kevin: GMAT Quant Challenge Question

Hello! Today, I talk through how to solve this tricky-looking geometry question. If you have any questions for us or suggestions for future video topics, let us know in the comments below. Enjoy!

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Angles and Parallel Lines on the GMAT

First, a couple of relatively easy practice problems. 1) In the diagram above, what is the measure of angle y? Statement #1: x = 30° Statement #2: line AB is parallel to line CD 2) In the diagram above, line m and line n are parallel.  Given that angle a = 40° and angle c […]

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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, […]

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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? 7 […]

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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 […]

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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 […]

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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 […]

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