Question

Let \( x \) and \( y \) be integers such that \( 0 \leq x \leq 5 \) and \( -4 \leq y \leq -1 \). \[ \text{Quantity A: } x - |y| \quad \text{Quantity B: } 0. \]

• A. Quantity A is greater
• B. The relationship cannot be determined from the information given
• C. Quantity B is greater
• D. Quantity A and Quantity B are equal

Hint:

When absolute values are involved, consider all possible values and ranges of the variables.

Answer 1

The Correct Option is B

Step 1: Analyze the values of \( x \) and \( y \).
Since \( x \) can be between 0 and 5, and \( y \) can be between -4 and -1, the absolute value of \( y \) is between 1 and 4. Hence, \( |y| \) could be 1, 2, 3, or 4.

Step 2: Calculate possible values for \( x - |y| \).
For different values of \( x \) and \( y \), the relationship can vary:
- If \( x = 5 \) and \( |y| = 1 \), then \( x - |y| = 4 \), which is greater than 0.
- If \( x = 0 \) and \( |y| = 4 \), then \( x - |y| = -4 \), which is less than 0.


Step 3: Conclusion. Since the relationship depends on the values of \( x \) and \( y \), it cannot be determined.