One of the key things to remember with circles is that once you know one piece of information, you know everything about the circle itself. Additional angles and lengths inside are not always so simple, but it is possible to convert circumferences to areas, to radii and diameters without intermediate steps. This will save you time in Data Sufficiency questions.

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Last week, we tackled two GMATPrep® questions; if you missed that article, go read it before continuing with this one. Make sure you try the two sample problems and take the time to master the concepts before you try the super-hard question below.

Okay, this sample problem is from our own archives. Set your timer for 2 minutes…. and… GO!

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In Part I of this series, I talked about approaching wordy GMAT questions as a businessperson would--by carefully reading these questions the first time around in order to absorb all information. The following GMAT problem has inspired me to expand this approach questions to include the actual process of decision-making:

A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches, of the strip?

I. 1
II. 3
III. 4

a. I only
b. II only
c. I and II only
d. I and III only
e. I, II, and III

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To start off, let’s quickly review the essentials. These are formulas/concepts you must know:

1. a² + b² = c², but only when a right triangle. If you don’t know it’s a right triangle, Pythagorean theorem does not apply!
2. Common special right triangles include 3-4-5, 5-12-13, 8-15-17, 7-24-25 (and their multiples.)
3. 45-45-90 triangles are ALWAYS in the ratio 1:1:√2
4. 30-60-90 triangle are ALWAYS in the ratio 1:√3:2
5. Angles and opposite sides are in the same relative size order, but are NOT proportional.

Let’s continue with a standard diagram in which we have an equilateral triangle inscribed in a circle, which is inscribed in a square.

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There are several number properties that GMAT test takers need to know / memorize.  A lot of these seem simple at first glance; however, the GMAT is very good at finding ways to make straightforward concepts difficult.  Additionally, there are number property concepts that are not as straightforward as others.  One of the more difficult concepts is exponent properties.

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In this series, we will cover many types of geometric scenarios encountered on the GMAT. A basic knowledge of simple formulas (area, perimeter, etc.) is essential, but there are numerous shortcuts to geometry questions that will save you time. Today, we’ll explore circles inscribed in squares.

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Even though Data Sufficiency questions test the same math content as Problem Solving questions, most GMAT students find that they can’t use the same strategies on both question types. One of the common errors students make in their approach to Data Sufficiency questions is jumping to the two statements without analyzing the question first and figuring out what information is missing. You wouldn’t start hunting for a jigsaw puzzle piece without first looking at the shape of the hole you’re trying to fill, would you? Most Data Sufficiency questions can be simplified with the Pieces of the Puzzle approach, and some would be nearly impossible to solve without it.

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The answer to yesterday's question.  Try the problem first if you haven't done so already and click more to see if you got the answer right.

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This week, we’re going to tackle two GMATPrep® questions, this time from the quant side of things. My students have been asking (really, complaining!) about maximize / minimize questions lately. A lot of students aren’t sure about the most efficient approach to these kinds of questions. We’ll tackle these two GMATPrep® questions this week in order to learn how to master max/min questions in general, and later this month I’ll give you a super hard one from our own archives – just to see whether you learned the material as well as you thought you did.

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Really?  First they tell us we can’t use a calculator, then they tell us we should average 2 minutes per question, and then they give us this:

67.5% of 812 is 15% of what number?

This may seem impossible to solve in under two minutes without some outside help. In fact, there are many typical time saving tactics to perform “simple” arithmetic without belaboring the process and taking too long. Keep an eye out for common multiples, common fractions and decimals that seem too hard without a shortcut. For this question, we can convert from “English” to “Math” and ignore the percent signs since they cancel each other out.

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The following book review was written by Dana Jinaru.  Dana is currently a finance student in Europe and also serves as a moderator for Beat The GMAT.  On May 13, 2009 she scored a 770 on the GMAT.

Here is Dana’s analysis of the Official Guide for GMAT Quantitative Review, 2^nd Edition.

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Meet the Halls and the Oateses:

Two family reunions are happening at the same hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions?

(A)  2
(B)  5
(C)  10
(D)  16
(E)  22

Answer after the jump.

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The best way to think of inequalities is as equations with slightly less specific information. Instead of providing an exact location, they provide a range of locations, all of which are satisfactory. With “=” instead of“<”, we can solve for the exact number. In an inequality, that number will be used as an endpoint.

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GMAT questions are notorious for seeming harder than they actually are. The writers recognize time is short, and will give you ostensibly time-consuming calculations. One way to mitigate this is by retaining a rockstar aptitude in manipulating fractions, which occur in a large portion of the questions.

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Advanced exponent problems are very common on the GMAT – and very tough. If you're looking for a high score on the math section, this is an area that you need to master. Here are a couple of examples of high-level exponent problems.

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