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C
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Difficulty:
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Question Stats:
58% (02:56) correct
42%
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wrong
based on 253
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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
(1) x = √y
(2) x > 8
23 Feb 2012, 23:00
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dvinoth86
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.
23 Feb 2012, 20:54
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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.
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.
