Question

If $|x - y| < 5$ and $|x - y| \geq 2$ , then the maximum integral value of y, such that x is always negative is:

• A. 0
• B. -2
• C. 2
• D. -5

Hint:

$|A| < B \iff -B < A < B$.

Answer 1

The Correct Option is D

Step 1: Concept
Absolute value inequalities.

Step 2: Analysis
For $x$ to be *always* negative, even the maximum possible value of $x$ must be less than 0.
From $|x - y| < 5 \implies y - 5 < x < y + 5$.

Step 3: Calculation
For $x < 0$ always, the upper bound $y + 5$ must be $\leq 0$.
$y \leq -5$.
The maximum integral value satisfying this is -5.

Step 4: Conclusion
The value is -5. Final Answer: (D)