Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of √x every 10 minutes (so that after 10 minutes its speed is x√x, after 20 minutes its speed is x2, and so forth). Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?

(1) x = √y
(2) x > 8

Answer should be C.

Question: Two missiles are launched simultaneously. Missile 1 launches at a speed of \(x\) miles per hour, increasing its
speed by a factor of \(\sqrt{x}\) every \(10\) minutes (so that after \(10\) minutes its speed is \(x\sqrt{x}\), after \(20\) minutes its speed is \(x^2\), and so forth). Missile 2 launches at a speed of \(y\) miles per hour, doubling its speed every \(10\)
minutes. After \(1\) hour, is the speed of Missile 1 greater than that of Missile 2?

So we know that after \(60\) minutes:

Speed of \(x\) will be \(= x^4\)
Speed of \(y\) will be \(= 64y\)

The question is asking, is \(x^4>64y\) ?

Statement 1: \(x=\sqrt{y}\)

Lets subtitute in \(x^4>64y\):

So the question is asking, is \(y^2>64y\)
Since we know all values are positive, reduce to, is \(y>64\). We have no way to establish this.

Hence Insufficient.

Statement 2: \(x > 8\) . No info about \(y\).

Hence Insufficient.

Combined A&B:

we know that \(x>8\) and we want to find out that \(y>64\) or not.

But \(x=\sqrt{y}\)

So \(\sqrt{y}>8\), so \(y>64\).

Hence Sufficient. Answer C.
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