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Two missiles are launched simultaneously. Missile 1 launches

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

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New post Updated on: 23 Feb 2012, 22:45
1
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

62% (02:04) correct 38% (01:36) wrong based on 146 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
Spoiler: OA

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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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Re: DS: Inequalities [#permalink]

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New post 23 Feb 2012, 20:54
5
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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Two missiles are launched simultaneously. Missile 1 launches [#permalink]

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New post 23 Feb 2012, 23:00
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1
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.

Answer: C.


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.

Answer: C.

Hope it's clear.
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Re: Two missiles are launched simultaneously. Missile 1 launches [#permalink]

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