Bunuel wrote:
Is 2^x greater than 100?
(1) \(2^{\sqrt{x}}=8\)
(2) \(\frac{1}{2^x} < 0.01\)
Let's rephrase the question: Is 2^x > 100?
Now, we know that
2^6 = 64 and
2^7 = 128
Therefore, 2^x >100 for any integer value of x>6. So, in other words, the question is asking if x >6?
Statement 1:
2^(x/2) = 2^3
i.e. x/2 = 3
x = 6
Since x is NOT greater than 6, so this statement is SUFFICIENT ---- eliminate B, C, E
Statement 2:
1/2^x < 1/100
Since the terms on both sides are POSITIVE, we can cross multiply without changing the Inequality sign
100 < 2^x ---- this is possible only when x>6
So, this statement is also SUFFICIENT ----eliminate A
Correct Answer - D (both statements are individually SUFFICIENT to answer the question)