x and y are consecutive odd integers.<br>Question: Can the value of (x+y) be determined <strong>UNIQUELY</strong>?<br>Statement I: (x+y)^{4}=256.<br>Statement II: (x+y)^{3} \lt 16.
For the next ten (10) items that follow:<br>Each item contains a Question followed by two Statements. Answer each item using the following instructions:
- A. Choose this option if the Question can be answered by one of the Statements alone but not by the other.
- B. Choose this option if the Question can be answered by either Statement alone.
- C. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone. ✓
- D. Choose this option if the Question cannot be answered even by using both Statements together.
Correct Answer: C. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
Explanation
Statement I: (x+y)^4 = 256 \implies x+y = 4 or -4 (not unique). Statement II: (x+y)^3 \lt 16 \implies x+y \lt 2.5 (many possibilities like 0, -4, -8). Using both, only x+y = -4 satisfies both conditions. Both statements together are necessary and sufficient.
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