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Rates and Ratios

Rates are just ratios.  Here are a four problems exploring rates.  Remember: no calculator! 1) Someone on a skateboard is traveling 12 miles per hour.  How many feet does she travel in 10 seconds?  (1 mile = 5280 feet) 60 88 120 176 264 2) At 12:00 noon, a machine, operating at a fixed rate, […]

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Practice Problems on Powers and Roots

Here are ten reasonably challenging problems on powers and roots.  Solutions follow the problems.   Remember, no calculator! Statement #1: x < 1 Statement #2: x > –1 4 8 14 28 42 5) If A is an integer, what is the value of A? 11 30 45 75 225   Powers & roots This is […]

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GMAT Practice Questions with Fractions and Decimals

Here are ten problems on fractions and decimals, some of which are quite challenging.  Remember, no calculator! 0.1 1 10 100 1000 6)  Suppose you have access to a large vat of distilled water, several gallons large.  You have two precise measuring pipettes, one to measure exactly 1/3 of an ounce and one to measure […]

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GMAT Math: The Uses and Abuses of Formulas

First, a few practice problems: 1) In the figure above, AC = BC = 8, angle C = 90°, and the circular arc has its center at point C.   Find the area of the shaded region. 2)  Employees at a company will vote for an executive team of five people from eight qualified candidates.  The […]

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Backsolving on GMAT Math

First of all, try these challenging GMAT Problem Solving practice problems without a calculator. 2 3 4 5 6 2) In the month of August, Pentheus Corporation made $200,000 in profit.  Pentheus made 6% of that profit on the second Wednesday of August.   If the profits that day were approximately 14.5% of the revenue for […]

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GMAT Quant: Arithmetic with Inequalities

Here are four GMAT Data Sufficiency questions involving inequalities. Full solutions will come at the end of this article.   The arithmetic of equations: a review First of all, let’s review what should be more familiar — the arithmetic of equations.   Suppose A = B and P = Q.  The soundbyte is: you can combine […]

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GMAT Quantitative: Ratio and Proportions

First, a bank of eight practice problems 1) A certain zoo has mammal and reptiles and birds, and no other animals.  The ratio of mammals to reptiles to birds is 11: 8:5.  How many birds are in the zoo? Statement (1): there are twelve more mammals in the zoo than there are reptiles Statement (2): […]

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GMAT Quant: Mathematical Grouping Symbols

Many folks remember Order of Operations by means of the mnemonic PEMDAS.  Just for review, PEMDAS is a quick way to remember the following order of mathematical prioritization: Priority #1: P = Parentheses Priority #2: E = Exponents Priority #3: MD = Multiplication & Division Priority #4: AS = Addition and Subtraction A few things […]

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GMAT Math: How to Divide by a Square Root

A lot of students, especially those away from math for a long time, get lost when trying to divide by a square root. First, consider these three practice questions. 1.  In the equation above, x = 2. Triangle ABC is an equilateral triangle with an altitude of 6.  What is its area? 3.  In the […]

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Mathematical Thinking on the GMAT

What does the GMAT Quantitative section test?  Math, of course.  As tautological as that may seem, there is a very subtle point here.  What exactly is math?   Mathematics Strange as it may seem, there is no generally accepted formal definition of the word mathematics.  Most of the dictionary definitions, for example, cover the more […]

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