Question

Which of these two is the greater, \(x\) or \(y\) ? (1) \(x / 3>y\) (2) Both are positive 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

Understand the Problem

We need to determine which of the two variables, \(x\) or \(y\), is greater. There are two given statements: (1) \( \frac{x}{3} > y \) and (2) Both \(x\) and \(y\) are positive.

Analyze Statement 1

Statement 1: \( \frac{x}{3} > y \). Multiplying both sides by 3, we get \(x > 3y\). This tells us that \(x\) is more than three times \(y\), thus \(x\) is clearly greater than \(y\). So, statement 1 alone is sufficient to determine this.

Analyze Statement 2

Statement 2: Both \(x\) and \(y\) are positive. This does not give any information about the relative sizes of \(x\) and \(y\). So, statement 2 alone is not sufficient to determine which is greater.

Combine Statements (if necessary)

Combining both statements, we already know from statement 1 that \(x > 3y\) and both are positive. Since statement 1 alone is sufficient to determine that \(x\) is greater than \(y\), we do not gain any new information from combining the two statements.

Conclusion

Based on the analysis, statement 1 alone is sufficient to determine that \(x\) is greater than \(y\). Therefore, the answer is A.

Key concepts

Graduate Management Admission Test

The Graduate Management Admission Test (GMAT) is a standardized exam used globally for admissions into graduate business programs. This test assesses a range of skills to determine if you are ready for the rigors of business school.
The GMAT covers these main areas:

• Analytical Writing Assessment
• Integrated Reasoning
• Quantitative Section
• Verbal Section

The GMAT’s quantitative section is crucial because it tests your ability to understand and solve mathematical problems. This section evaluates your knowledge in areas like arithmetic, algebra, geometry, and word problems.

Mathematics Problem-Solving

Mathematics problem-solving is a skill that involves understanding and tackling mathematical challenges effectively. In the context of the GMAT, it’s not just about knowing the mathematical theories but also about applying them.
Here are some tips:
1. Ensure you know the basics: Always be comfortable with fundamental concepts in algebra and arithmetic.
2. Read the problem carefully: Often, understanding the problem is half the battle won.
3. Break down the problem: Take it step-by-step rather than trying to solve everything at once.
4. Practice regularly to build speed and accuracy.

Inequalities

Inequalities are mathematical statements indicating that two expressions are not equal and have a certain order. For instance, the inequality \( \frac{x}{3} > y \) tells us that when \(x\frac{x}{3}\) is divided by 3, the result is still greater than y.
To solve inequalities:

• Treat them like equations when adding, subtracting, multiplying, or dividing by a positive number.
• Remember that multiplying or dividing by a negative number reverses the inequality sign.
• Graphing can help visualize solutions.

Example from the exercise: We started with \( \frac{x}{3} > y \) and multiplied both sides by 3 to get \( x > 3y \), simplifying the comparison.

Quantitative Section

The quantitative section of the GMAT consists of two types of questions: Problem Solving and Data Sufficiency. This section specifically measures your ability to reason quantitatively and solve mathematical problems accurately.
Problem Solving: These questions are straightforward and require basic math skills.
Data Sufficiency: These questions are designed to test your ability to analyze the presented data and determine if there is enough information to solve the problem.
Practicing diverse questions will help strengthen your quantitative skills and manage your time better during the test.

Test Strategies

Developing effective test strategies is key to succeeding in the GMAT. Here are a few strategies that can help:

• Time Management: Allocate specific times to each section and stick to them. Practice pacing yourself through mock tests.
• Understand the Question Types: Familiarize yourself with different question formats, especially Data Sufficiency and Problem Solving questions.
• Eliminate Wrong Choices: When you're unsure of the answer, eliminate the obviously incorrect options to increase your chances of finding the right one.
• Stay Calm and Focused: Maintain composure to think clearly and avoid simple mistakes.

By integrating these strategies into your study routine, you'll gain confidence and perform better on test day.