BTGmoderatorLU wrote:Source: Economist GMAT
If \(y\) is the sum of \(x\) consecutive positive integers, and \(x>3\), is \(y\) odd?
1) \(x\) is odd.
2) The largest number among the \(x\) consecutive integers is odd.
The OA is E
Given: \(y\) is the sum of \(x\) consecutive positive integers, and \(x>3\).
We have to determine whether \(y\) odd.
Let's take each statement one by one.
1) \(x\) is odd.
Case 1: Say there are 5 (odd) consecutive positive integers, starting from 1; thus, the numbers are 1, 2, 3, 4, and 5. Sum = y = 15, odd. The answer is yes.
Case 2: Say there are 5 (odd) consecutive positive integers, starting from 2; thus, the numbers are 2, 3, 4, 5, and 6. Sum = y = 20, even. The answer is no.
No unique answer. Insufficient.
2) The largest number among the \(x\) consecutive integers is odd.
Case 1: Say there are 5 consecutive positive integers, starting from 1; thus, the numbers are 1, 2, 3, 4, and 5 (odd). Sum = y = 15, odd. The answer is yes.
Case 2: Say there are 7 consecutive positive integers, starting from 1; thus, the numbers are 1, 2, 3, 4, 5, 6 and 7 (odd). Sum = y = 28, even. The answer is no.
No unique answer. Insufficient.
(1) and (2) together
Both the cases discussed in Statement 2 are applicable for Statement 1, too. Thus, both the statements together are insufficient.
The correct answer:
E
Hope this helps!
-Jay
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