Two missiles are launched simultaneously.

The question stem is long, so spend some time there. The more information there is to unpack, the easier it is to lose track of details, and a question like this is designed to overwhelm you with information. It can help to note these givens now, taking care to separate the information out into a Missile A column and a Missile B column.

Missile A
starts at \(x\) mph
increases by \(\sqrt{x}\)
every 10 minutes

Missile B
starts at \(y\) mph
increases by \(y\)
every 10 minutes

The question asks which missile is going faster after 1 hour (or 6 increments of 10 minutes), so fundamentally you'll need to know something about the relationship between \(x\) and \(y\). If you're inclined to do problems algebraically, you can process this question through an algebraic lens:

Missile 1: \(x\) * \(\sqrt{x}^6\) --> \(x\) * \(x^3\) --> \(x^4\)
Missile 2: \(y\) * \(y^6\) --> \(y^7\)

So the question can be rewritten as Is \(x^4 > y^7 \)?

Statement (1) does a lot. Algebraically, it offers an equivalency between \(x\) and \(\sqrt{y}\), so you'll be able to rewrite the question in terms of just one of the variables:

\(x^2 = y\) <-- (squared both sides of statement (1) to make substitution easier)
Is \(x^4 > (x^2)^7 \)? <-- (substituted \(x^2\) for \(y\) in the question stem)
Is \(x^4\) \(>\) \(x^1^4\) ? <-- (restated question)

Because \(x\) represents a speed, it is definitely a positive number. Furthermore, the wording of the question stem implies that \(x\) is greater than 1, as that's the only way that increasing by a factor of \(\sqrt{x}\) would be equivalent to \(x\sqrt{x}\) (if instead \(x\) were between 0 and 1, it would have to be multiplied by \(1+\sqrt{x}\) to produce an increase). Therefore, \(x^4\) is definitely not greater than \(x^1^4\), and because this statement gives you a definite answer, it is sufficient. Eliminate (B), (C), and (E).

Statement (2) only mentions \(x\), making it pretty unpromising in a question that asks for a comparison between \(x\) and \(y\). Not sufficient. The answer is (A).

As a side note, you can also approach this question in a less intensely mathematical way. On a basic level, this question asks you to figure out if some smaller group of \(x\)'s is greater than some larger group of \(y\)'s (because Missile 1 is only increasing by \(\sqrt{x}\) whereas Missile 2 is increasing by a full \(y\)). Statement (1) implies that \(y\) is greater than \(x\), so Missile 2 is definitely going faster.