If \(x /(y+2)=3, x /(y+4)=2\), then \(x+y\) is: A. 12 B. 14 C. 40 D. 24 E. 16

Algebraic equations form the foundation of solving many mathematical problems. They consist of variables, constants, and arithmetic operations. In the given exercise, we have two algebraic equations that involve the variable \(x\) and \(y\). These equations are formed by given conditions where the ratios of \(x\) and followed by increases in \(y\) yield specific results. The goal is to find the values of the variables that satisfy both equations. Understanding and manipulating algebraic equations are key skills tested in the GMAT, allowing students to demonstrate their problem-solving abilities and logical thinking. The initial step in such problems is to isolate the variable of interest, helping us understand the relationship between the variables involved.

Solving linear equations involves finding the values of variables that make the equation true. Linear equations take the form \(ax + b = c\), where \(a\), \(b\), and \(c\) are constants. In this problem, we start with two equations involving fractions. By expressing \(x\) in terms of \(y\), we reduce the problem to simpler forms of linear equations: 1) \(x = 3(y + 2)\) and 2) \(x = 2(y + 4)\). Next, we equate the expressions for \(x\) from both equations to find \(y\). This process involves operations like expansion, simplification, and balancing equations:

• Expand: \(3(y + 2) = 3y + 6\), \(2(y + 4) = 2y + 8\)
• Simplify: \( 3y + 6 = 2y + 8\)
• Isolate: \(y = 2\)

By substituting \(y = 2\) back into the expression for \(x\), we get \(x = 12\). Finally, we find \(x + y\) which equals \(14\). Learning these skills ensures a systematic approach to solving GMAT problems.

The Graduate Management Admission Test (GMAT) is a standardized test used for admissions into business school programs worldwide. Its sections include quantitative reasoning, which often tests algebraic proficiency, as seen in this problem. The test evaluates your ability to think critically, recognize patterns, and solve problems efficiently. Mastering algebra and linear equations is essential because these are frequently encountered topics in the quantitative section. It is important to practice problems like these to become comfortable with interpreting, setting up, and solving equations, all of which are crucial for achieving a high score on the GMAT. Tips for success include:

• Practice regularly with timed exercises
• Focus on understanding fundamental concepts
• Review mistakes to avoid repeating them

By mastering algebraic and linear equations, you build a strong foundation for tackling a wide range of problems on the GMAT.