Determining the Parity of y

Hard Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be two positive integers such that the following conditions hold:

1. $x$ is an odd integer.

2. The sum of $x$ and $y$ is greater than 100: $x + y > 100$.

Determine whether $y$ is an even integer.

To answer this question, evaluate the following statements:

Statement (1): $y$ is greater than 50.

Statement (2): $x + y = 110.$

Both statements together are necessary to determine if $y$ is even.

Each statement alone can determine if $y$ is even.

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