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# Two missiles are launched simultaneously. Missile 1 launches

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Manager
Joined: 19 Oct 2011
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Two missiles are launched simultaneously. Missile 1 launches  [#permalink]

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Updated on: 23 Feb 2012, 22:45
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Difficulty:

75% (hard)

Question Stats:

60% (02:56) correct 40% (02:14) wrong based on 158 sessions

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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

Originally posted by dvinoth86 on 23 Feb 2012, 20:22.
Last edited by Bunuel on 23 Feb 2012, 22:45, edited 1 time in total.
Edited the question and added the OA
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Posts: 56277
Two missiles are launched simultaneously. Missile 1 launches  [#permalink]

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23 Feb 2012, 23:00
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dvinoth86 wrote:
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

After 1 hour the speed of Missile 1 will be $$x*(\sqrt{x})^6=x^4$$;
After 1 hour the speed of Missile 2 will be $$y*2^6=64y$$;

Question: is $$x^4>64y$$

(1) $$x=\sqrt{y}$$. Substitute $$x$$, the question becomes: is $$(\sqrt{y})^4>64y$$? --> is $$y^2>64y$$? or is $$y>64$$? (since y<0 is not possible). We don't know that. Not sufficient.

(2) $$x > 8$$. Clearly insufficient, since no info about y.

(1)+(2) From (2) $$x>8$$, which according to (1) means $$\sqrt{y}>8$$ --> $$y>64$$. Exactly what we wanted to know. Sufficient.

Another way.

Question: is $$x^4>64y$$

(1) $$x=\sqrt{y}$$ --> $$x^2=y$$. Substitute $$y$$, the question becomes: is $$x^4>64x^2$$? --> is $$x^2>64$$? or is $$x>8$$? (since x<-8 is not possible). We don't know that. Not sufficient.

(2) $$x > 8$$. Clearly insufficient, since no info about y.

(1)+(2) From (1) question became "is $$x>8$$?", and (2) $$x>8$$ directly answers it. Sufficient.

Hope it's clear.
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23 Feb 2012, 20:54
5

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 $$y>64$$.

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Re: Two missiles are launched simultaneously. Missile 1 launches  [#permalink]

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05 Mar 2018, 00:22
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Re: Two missiles are launched simultaneously. Missile 1 launches   [#permalink] 05 Mar 2018, 00:22
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