Question

Is y negative? (1) x is less than or equal to 0 (2) y is less than or equal to x 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

E. 1 and 2 together are not sufficient

Step-by-step solution

Understand the Problem

We need to determine if y is negative based on two given statements.

Analyze Statement 1

Statement 1: \( x \leq 0 \). This tells us that \( x \) is either zero or a negative number. However, it gives no direct information about \( y \). Hence, Statement 1 alone is not sufficient to determine if \( y \) is negative.

Analyze Statement 2

Statement 2: \( y \leq x \). This means that \( y \) is less than or equal to \( x \). By itself, this does not indicate whether \( y \) is negative since it depends on the value of \( x \). Therefore, Statement 2 alone is also not sufficient.

Combine Statements 1 and 2

Combine both statements: From Statement 1, we have \( x \leq 0 \). From Statement 2, we have \( y \leq x \). Because \( x \) is less than or equal to zero, \( y \), being less than or equal to \( x \), must also be less than or equal to zero. Thus, \( y \) could be zero or less, but not necessarily negative. Therefore, even together, they are not sufficient to prove \( y \) is negative.

Key concepts

GMAT Preparation

Preparing for the GMAT is a critical step for anyone aiming for a graduate business degree. The test assesses a variety of skills, from verbal reasoning to quantitative analysis. One effective way to prepare is to thoroughly understand each section, focusing on type-specific strategies. Make sure to allocate time for each section and practice regularly.

Quantitative reasoning, such as understanding algebraic inequalities, is crucial. Reviewing each problem type and practicing similar questions will build confidence. Additionally, using official GMAT prep materials ensures familiarity with the exam's format. Finally, always review your practice test results to identify areas needing improvement, and adjust your study plan accordingly.

Algebraic Inequalities

Algebraic inequalities are expressions involving variables and inequality signs like <, >, ≤, or ≥. To solve these problems, understand the rules of inequalities:

• When you add or subtract the same number from both sides of an inequality, the inequality direction remains unchanged.
• Multiplying or dividing both sides by a positive number keeps the inequality direction the same.
• Multiplying or dividing both sides by a negative number reverses the direction of the inequality.

In the given GMAT exercise, understanding how inequalities work allows you to analyze statement constraints logically. For example, knowing that if y is less than or equal to x and x is less than or equal to zero, helps conclude about y's possible values.

Quantitative Reasoning

Quantitative reasoning tests your ability to solve problems using numerical and algebraic methods. For GMAT problems like determining if y is negative, it involves:

• Analyzing given statements for mathematical relationships.
• Applying principles of algebra and logic.
• Combining multiple pieces of information.

Breaking down the problem, as seen in the exercise solution, helps you systematically evaluate whether each statement alone or combined provides a definite answer. Remember: practice enhances problem-solving speed and accuracy.

Logical Analysis

Logical analysis involves examining and synthesizing information systematically. In the context of GMAT problems, it means:

• Understanding the implications of given statements.
• Drawing conclusions based on logical deduction.
• Considering multiple scenarios to test whether statements sufficiently answer the question.

For instance, in the exercise, you must logically deduce that even though the statements provide a range for y, it doesn't definitively prove y is negative. Combining both statements involves recognizing that possibilities like y = 0 cannot be excluded, showcasing the importance of carefully detailed logical analysis.