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The Area of an Equilateral Triangle

The Area of an Equilateral Triangle

As promised, we will now connect the 30-60-90 triangle to the equilateral triangle, specifically its area. There is a formula for the area of an equilateral triangle as it relates to the length of its side s, and it is as follows: But more likely than not for the...

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GMAT Divisibility Rules

GMAT Divisibility Rules

Welcome back to our series on number properties. Last time we got familiar with prime factors as the substance of divisibility. In this article, we will extend this understanding by highlighting logical rules that sometimes come into play on GMAT number properties...

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Prime Factors of Perfect Squares

Prime Factors of Perfect Squares

Welcome back to our series on number properties. Now that you know about prime factors, it’s time to learn a special property about the prime factors of perfect squares. Perfect squares are integers that represent the product resulting when some integer is multiplied...

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Exponents on The GMAT/EA: Everything You Need To Know

Exponents on The GMAT/EA: Everything You Need To Know

Understanding Exponents A key piece of algebraic notation on GMAT and Executive Assessment (EA)  quant problems is the exponent. Exponents appear on many kinds of quantitative problems, so fluency with exponents (and radicals) is an indispensable skill for achieving a...

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Large Exponents and The Units Digit

Large Exponents and The Units Digit

Welcome to the final article in our series on exponents. Some GMAT and Executive Assessment (EA) quant problems feature impossibly large numbers like 287459. These are problems that you simply can’t hope to solve without a key piece of knowledge that we call units...

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Exponents: Power of k Problems

Exponents: Power of k Problems

Welcome to the penultimate article in our series on exponents on the GMAT/Executive Assessment (EA). Today we explore a problem category in which exponents are used to notating the highest power of an integer by which a larger integer is divisible. GMAT/EA problems...

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Zeros and Nonzeros

Zeros and Nonzeros

Welcome back to our series on exponents. Last time we used powers of 10 to express “almost integer” numbers. Today we will use powers of 10 to handle problems that ask us to count zeros or nonzero digits. These problems can be baffling if you haven’t learned about...

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“Almost an Integer” Problems

“Almost an Integer” Problems

Unless you do math as a career or a hobby, you probably prefer integers to non-integers. Whole numbers are easier for us to conceptualize. But a certain class of GMAT/Executive Assessment (EA) problems involves numbers that are almost integers. Generally, this nearest...

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Powers of 10 and Scientific Notation

Powers of 10 and Scientific Notation

Many GMAT and Executive Assessment (EA) exponents problems involve the use of 10 as a base. Since all the math we do is in a base 10 system, multiplying or dividing by powers of 10 simply moves the decimal point of a number. This enables us to notate very large and...

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Bases Between -1 and 1

Bases Between -1 and 1

Many GMAT and Executive Assessment (EA) exponent problems - especially data sufficiency ones - require you to consider fractional bases. By this I mean proper fractions with values between -1 and 1, not improper fractions whose numerators exceed their denominators....

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Negative Exponents and Negative Bases

Negative Exponents and Negative Bases

Welcome back to our series on exponents. Today we will see what happens when we throw negatives into our exponential expressions. We will explore both negative bases and negative exponents. First, the bases. The rule to remember for negative bases is that odd powers...

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Undoing Exponents: Radicals and Roots

Undoing Exponents: Radicals and Roots

As you will definitively have to deal with radicals on the GMAT and Executive Assessment (EA), we've put together an article for you to master the topic. Addition is “undone” by subtraction, multiplication is “undone” by division, and the powers notated by exponents...

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