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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