Sum of Y and Z

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If y and z are integers, what is the value of ?

(1) and .

(2)

Review: Sum of Y and Z




Explanation

The question is simple enough, though we should not ignore that the y and z are integers. We can get sufficiency by solving for y and z individually or as the expression . Let's turn to the data statements, separately first.

Statement (1) narrows the sum y + z to the range between 6 and 8. For example, y + z could be 7. Indeed, y + z must be 7, since it must be an integer, as the sum of integers. And while there are different possible values of y and z that could sum to 7, the all lead to the same answer to the question being asked of us. Therefore, we have sufficient information to answer the question definitively. Statement (1) is sufficient.

Statement (2) tells us that . For example, y could be 3 and z could be 4. Indeed, this is the only possibility, since both numbers are integers. Therefore y + z is uniquely determined, and we can answer the question definitively. Statement (2) is sufficient.

The correct answer is (D).


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