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

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Joined: 23 Feb 2015
Posts: 1265
Is x<1/2? 1) 2^x<1/4 2) 2^2x<2  [#permalink]

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26 Mar 2019, 08:46
1
00:00

Difficulty:

35% (medium)

Question Stats:

75% (01:19) correct 25% (01:00) wrong based on 32 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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26 Mar 2019, 12:17
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Top Contributor
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

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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