Hi All,

We're told that X and Y are positive integers GREATER than 1 such that (X - Y) is an EVEN integer and X/Y is an EVEN integer. We're asked which of the following numbers must be NON-PRIME integers. This question can be solved with a mix of Number Property rules and TESTing VALUES.

To start, we should define the Number Properties that apply to the information in the prompt:

1) Since X and Y are positive integers GREATER than 1 - and (X - Y) is EVEN, X and Y are either BOTH even (re: 4 - 2 = 2) or BOTH odd (7 - 3 = 4).

2) Since X/Y is an EVEN integer, X MUST be an EVEN MULTIPLE of Y. For example 4/2 = 2, 12/3 = 4, 36/6 = 6, etc.

Based on these Number Properties, we can work through the Roman Numerals rather quickly:

I. X

Since Y is GREATER than 1 and X is an EVEN MULTIPLE of Y, we know that X will be 4 or a greater even number. Thus, it will NEVER be a prime.

Roman Numeral 1 is part of the correct answer.

Eliminate Answer B and C.

II. (X+Y)

Since X and Y will either be BOTH even or BOTH ODD, the sum will either be (even + even = even) or (odd + odd = even). Thus, this sum will NEVER be a prime.

Roman Numeral 2 is part of the correct answer.

Eliminate Answer A.

III. Y/X

Since X will ALWAYS be bigger than Y, this fraction will always be a fraction that is less than 1. Therefore, while it won't be a prime number, it won't be an INTEGER either.

Roman Numeral 3 is NOT part of the correct answer.

Eliminate Answer E.

Final Answer:

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Rich

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