If \(u, v,\) and \(w\) are integers, is \(u > 0 ?\)

[M7MBA]

If \(u, v,\) and \(w\) are integers, is \(u > 0 ?\)

(1) \(u = v^2 + 1\)
(2) \(u = w^4 + 1\)

[spoiler]OA=D[/spoiler]

Source: GMAT Prep

[Jay@ManhattanReview]

If \(u, v,\) and \(w\) are integers, is \(u > 0 ?\)

(1) \(u = v^2 + 1\)
(2) \(u = w^4 + 1\)

[spoiler]OA=D[/spoiler]

Source: GMAT Prep

Note that even exponent of any integer is a non-negative integer.

Let's take each statement one by one.

(1) \(u = v^2 + 1\)

From above, we know that v^2 is a non-negative integer, so the minimum value of v^2 = 0. Thus, u > 1. Sufficient.

(2) \(u = w^4 + 1\)

Similarly, from above, we know that w^4 is a non-negative integer, so the minimum value of w^4 = 0. Thus, u > 1. Sufficient.

Correct answer: D

Hope this helps!

-Jay
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