Question

If \(x+3 y=2 x-y\), then \(x-2 y\) is: (A) 0 (B) 1 (C) \(1 / 2\) (D) \(2 / 3\) (E) Cannot be determined

Short answer

2y

Step-by-step solution

- Rearrange the Equation

Start by rearranging the given equation, moving all terms involving variables to one side: \( x + 3y = 2x - y \). Subtract \( x \) and subtract \( 2x \) from both sides to get: \( x - 2x + 3y + y = 0 \)

- Simplify the Equation

Combine like terms to simplify the equation: \( -x + 4y = 0 \). Now, solve for \( x \): \( x = 4y \)

- Substitute the Value of x

Substitute \( x = 4y \) into the expression \( x - 2y \): \( x - 2y = 4y - 2y \)

- Simplify the Expression

Finally, simplify the expression: \( x - 2y = 2y \)

Key concepts

Understanding Algebra Equations

Algebra equations are mathematical statements that show the equality of two expressions with variables. Solving these equations involves finding the value(s) of the variable(s) that make the equation true. For the given exercise, we start with the equation: \(x + 3y = 2x - y\).
To solve this, we rearrange and combine like terms, ultimately aiming for an equation where the variable x can be isolated, making it easier to substitute and solve for y later on.

Variable Manipulation Techniques

Manipulating variables involves algebraic operations to isolate one variable in terms of others. It's a critical skill for solving equations. In our example, we start by rearranging the given equation: \(x + 3y = 2x - y\).
First, subtract x and 2x from both sides to move all variable terms to the same side:\(x - 2x + 3y + y = 0\).
You’re left with: \(-x + 4y = 0\).
This process helps us simplify the equation, making it easier to isolate one variable.

Simplification Techniques

Simplification is reducing an equation or expression to its simplest form. Combining like terms and reducing coefficients are common techniques. In this exercise, after rearranging the terms, we get:\(-x + 4y = 0\).Next, we solve for x by isolating it:\(x = 4y\).
Substitute this value back into the expression we need to find, which is \(x - 2y\): \(x - 2y = 4y - 2y\), simplifying it further to get:\(2y\).
Simplification helps us see that the value of \(x - 2y\) in terms of y is simply a factor times y.

Effective GMAT Math Preparation

Preparing for GMAT math involves mastering basic concepts and practicing a variety of problem types. Focus on:

• Understanding the fundamentals of algebra equations and manipulations.
• Practicing simplification techniques.
• Working on a wide range of problems to build confidence.
• Using time wisely, ensuring you can rearrange, simplify, and solve equations quickly.

In our example, these skills help us smoothly transition from identifying the equation, through manipulation, to simplification, ensuring a correct and speedy solution. By repeatedly practicing these steps, you can enhance your problem-solving efficiency.