Question

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

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

Hint:

Always test extreme values when ranges are given. Different outcomes mean the relationship cannot be determined.

Answer 1

The Correct Option is C

Step 1: Range of \(|y|\).
Since \(-4 \leq y \leq -1\), \(|y|\) ranges from 1 to 4.
Step 2: Expression analysis.
\[ x - |y| \quad \text{with } x \in \{0,1,2,3,4\}, \ |y| \in \{1,2,3,4\} \] Step 3: Possible outcomes.
- If \(x=4, y=-1\): \(4 - 1 = 3\) (positive, Quantity A>B).
- If \(x=0, y=-4\): \(0 - 4 = -4\) (negative, Quantity B>A).
Step 4: Conclusion.
Since both cases are possible, the relationship cannot be determined. Final Answer: \[ \boxed{\text{The relationship cannot be determined.}} \]