Properties of Consecutive Even Integers

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If r, s, and t are consecutive even integers and , which of the following must be true?

I.

II. is an even integer.

III. is an even integer.

Review: Properties of Consecutive Even Integers


Explanation

In this question, the numbers r, s, and t could be 4, 6, 8, or 52, 54, 56, to pick two cases of many. We can also think of them as r, , . That observation leads us to see that Roman numeral I must be true. Answer choices (B) and (D) are out. Roman numeral II must be true, because is always an integer and t is even, so the factor of 2 will carry over into the product and make it even. We can evaluate Roman numeral III with numbers or algebra. It says that







This is true. Therefore, III must also be true. All three must be true.

The correct answer is (E).


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