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If x is a small negative integer and y is a large positive integer, which of the following expressions must be positive?

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Question:

A
y - x

explanation

Before considering the answer choices, recall the properties of positive and negative integers. Both multiplication and division of a positive integer with a negative integer always yield a negative integer. Consequently, the only possible answer choice that must be positive is y − x.

An alternative solution is choosing a small negative integer for x, −1, and a large positive integer for y, 100, and substituting these values into each of the answer choices.

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