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Is x<1/2? 1) 2^x<1/4 2) 2^2x<2

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Is x<1/2? 1) 2^x<1/4 2) 2^2x<2  [#permalink]

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New post 26 Mar 2019, 08:46
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:19) correct 24% (01:00) wrong based on 33 sessions

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Is \(x<\frac{1}{2}\)?
1) \(2^x<\frac{1}{4}\)
2) \(2^{2x}<2\)

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Re: Is x<1/2? 1) 2^x<1/4 2) 2^2x<2  [#permalink]

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New post 26 Mar 2019, 12:17
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Top Contributor
AsadAbu wrote:
Is \(x<\frac{1}{2}\)?
1) \(2^x<\frac{1}{4}\)
2) \(2^{2x}<2\)


Target question: Is \(x<\frac{1}{2}\)?

Statement 1: \(2^x<\frac{1}{4}\)
\(\frac{1}{4}=\frac{1}{2^2}=2^{-2}\)

So, we can rewrite statement 1 as: \(2^x<2^{-2}\)
This tells us that \(x < -2\)
If \(x < -2\), then we can be certain that \(x < \frac{1}{2}\)
The answer to the target question is YES, x IS less than 1/2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: \(2^{2x}<2\)
\(2^{2x}=(2^2)^x=4^x\)
Also, \(2 = 4^\frac{1}{2}\)

So, we can rewrite statement 2 as: \(4^x<4^\frac{1}{2}\)
This means that \(x < \frac{1}{2}\)
Once again, the answer to the target question is YES, x IS less than 1/2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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Re: Is x<1/2? 1) 2^x<1/4 2) 2^2x<2   [#permalink] 26 Mar 2019, 12:17
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