Question

Is \(x / 8>y / 12 ?\) (1) \(y=0\) (2) \(x>1\) A. 1 alone, not 2 alone B. 2 alone, not 1 alone C. 1 and 2 together (need both) D. 1 alone or 2 alone E. 1 and 2 together are not sufficient

Short answer

A. 1 alone, not 2 alone

Step-by-step solution

Analyze Statement (1)

Consider statement (1): \[ y = 0 \] Substitute into the inequality: \[ \frac{x}{8} > \frac{0}{12} \] This simplifies to: \[ \frac{x}{8} > 0 \] Since \( \frac{x}{8} \) is always positive when \( x \) is positive and always zero when \( x \) is zero, if \( x eq 0 \), this statement alone is sufficient to determine the inequality.

Analyze Statement (2)

Consider statement (2): \[ x > 1 \] This statement does not provide any information about \( y \). Thus, by itself, it is not sufficient to determine whether \( \frac{x}{8} > \frac{y}{12} \).

Combine Statements (1) and (2)

Combine statement (1) and statement (2): \[ y = 0 \] \[ x > 1 \] With \( y = 0 \) and \( x > 1 \), we substitute into the inequality: \[ \frac{x}{8} > \frac{0}{12} \] This simplifies to: \[ \frac{x}{8} > 0 \] Since \( x > 1 \), it is always positive, confirming the inequality.

Key concepts

inequalities in math

Inequalities in math are used to compare the relative size of two values.
For example, in the inequality \( \frac{x}{8} > \frac{y}{12} \), we are comparing two fractions. To solve, you need to understand which fraction is larger.
When dealing with inequalities, remember some key rules:

• If you multiply or divide both sides of an inequality by a positive number, the inequality direction doesn't change.
• If you multiply or divide both sides by a negative number, the inequality direction reverses.
• Combining inequalities involves combining the conditions or constraints from both sides.

In our problem when we substitute \( y = 0 \) in the inequality, it simplifies to \( \frac{x}{8} > 0 \).
This means we need to investigate when \( \frac{x}{8} \) is positive. It's essential to remember these principles as they form the basis for solving many math problems on the GMAT.

data sufficiency

Data sufficiency questions are unique on the GMAT. Instead of finding a final answer, your task is to determine if there's enough information to answer the question.
To solve these questions effectively, follow these steps:

• Analyze each statement independently and decide if each statement alone is sufficient.
• Combine both statements only if necessary.

For our problem, statement (1) alone was sufficient because substituting \( y = 0 \) simplified our inequality and gave us clear information about \( x \).
However, statement (2) alone was insufficient, as it didn’t provide any information about \( y \).
When combining both statements, it was evident the inequality holds true, confirming sufficiency.
Practicing these steps will help you ace data sufficiency questions on the GMAT.

GMAT problem-solving

GMAT problem-solving tests your ability to handle different mathematical concepts under pressure.
Here’s a quick approach to tackle these types of problems:

• Carefully read the problem and identify what is being asked.
• Break down the problem into manageable parts and analyze each part.
• Use logical reasoning and mathematical principles to find the solution.

Our initial problem asked if \( \frac{x}{8} > \frac{y}{12} \). By breaking it down and analyzing each statement separately, then together, we could easily find the solution.
Being systematic and thorough helps in avoiding errors and arriving at the right conclusions quickly.
Practice various types of problems to improve your speed and accuracy in problem-solving.

algebraic expressions

Algebraic expressions are combinations of variables, numbers, and operators.
Mastering these is essential for solving many GMAT problems.
Here are some tips for working with algebraic expressions:

• Understand the basic operations: addition, subtraction, multiplication, and division.
• Know how to simplify expressions by combining like terms.
• Use substitution to solve for variables.

In our problem, we had an inequality involving fractions: \( \frac{x}{8} \) and \( \frac{y}{12} \). Upon substituting \( y = 0 \), it simplified to \( \frac{x}{8} > 0 \).
Recognizing how to manipulate and simplify algebraic expressions is crucial.
Practice these skills to become proficient in handling algebraic problems on the GMAT.