More formally, these are called “rational expressions” in mathematics — “rational” in the sense of “having do with a ratio”, as the word is used in the phrase “rational numbers“. These rational expression appear in some of the most challenging Quant problems on the GMAT. Here are a few practice questions. (A) –2 (B) –1 […]

# Archive | Algebra

## GMAT Quant: Three Equations, Three Unknowns

First, here are two challenging Quant problems, both involving three equations with three algebraic unknowns. 2a + b + 3c = 6 a – b + 5c = 12 3a + 2b + 2c = 2 1) Given the equations above, what does the product a*b*c equal? (A) 6 (B) -6 (C) 12 (D) -12 […]

## GMAT Math: Strange Symbols

The GMAT sometimes features quant questions with strange symbols. These symbols should not fluster you too much as long as you remember that they do not represent standard mathematical notation. Instead, the symbols pertain only to the problem and are defined by the GMAT (or whatever prep material you happen to be using). Let’s have […]

## GMAT Math: Algebra Equations with Radicals

This is a potentially tricky topic. First, consider these practice questions. 1. Which value(s) of x satisfies the equation above? I. –1 II. 4 III. 9 (A) I (B) III (C) I & II (D) I & III (E) I, II, & III 2. What is the value of y? A full discussion of these […]

## Three Algebra Formulas Essential for the GMAT

First, a few practice problems. 1) The numbers a, b, and c are all positive. If , then what is the value of ? Statement #1: a – b = 3 Statement #2: = 7 2) Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? Statement #1: […]

## 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 […]

## GMAT Math: Can you divide by a variable?

Question #1: In the equation, can you divide both sides by x? Question #2: In the equation (x – 3)(x + 5) = (2x + 1)(x + 5), can you divide both sides by (x + 5)? Question #3: Question #4: Dividing by a variable or by an algebraic expression The short answer is: […]

## GMAT Plugging In Strategy: Always Start with Answer Choice C

Learn this powerful math trick for GMAT Problem Solving questions. First, try these two practice GMAT Quantitative section Problem Solving questions. 1) Bert left the house with N dollars. He spent 1/4 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. […]

## Algebra on the GMAT: How to Factor

Master this fundamental algebraic skill which you will need on test day! First, try these practice problems. 1) (A) (x – 4)(x + 6) (B) (x + 4)(x – 6) (C) (x – 4)(x – 6) (D) (x – 2)(x + 12) (E) (x + 2)(x – 12) 3) If , then |a| + |b| […]

## FOIL on the GMAT: Simplifying and Expanding

First, try this question: 1) (A) (B) (C) (D) (E) If you find this problem relatively easy, probably most of this post will be for you as well. If this problem makes your head spin, you have found exactly the post you need. Monomials and Binomials First, a review of terms. In algebra, any […]