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Is 2^x greater than 100?

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Source: — Data Sufficiency |
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Is 2^x greater than 100?

by Patrick_GMATFix » Tue Dec 10, 2013 11:54 am
Hope this helps. My signature below has more info.

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Is 2^x greater than 100?

by Stuart@KaplanGMAT » Tue Dec 10, 2013 1:20 pm
kobel51 wrote:Image
Hi!

We have a yes/no question, so if we can get a definite YES or a definite NO, we have sufficiency. If we get a maybe/sometimes/depends, we have insufficiency.

Looking at the stem, we think "we need to know about x".

(1) gives us an equation to solve for x. If we can solve for x, we can certainly answer the original question. Sufficient!

note: if you understand HOW to solve, you don't actually need to do so!

(2) looks complicated, so let's simplify!

We know that 2^x will always be positive, so it's safe to multiply both sides by 2^x (we always need to be careful with inequalities and variables!), giving us:

1 < .01(2^x).

.01 is just 1/100, so we can rewrite as:

1 < (1/100)(2^x)

Now let's multiply both sides by 100:

100 < 2^x

and since that's EXACTLY what the question is asking, (2) is also sufficient alone.

Each of (1) and (2) is sufficient alone: choose (D)!
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Is 2^x greater than 100?

by Brent@GMATPrepNow » Tue Dec 10, 2013 1:23 pm
kobel51 wrote:Image
Target question: Is 2^x > 100?

Statement 1: 2^(√x) = 8
Since 2^3 = 8, we can conclude that √x = 3, which means x = 9
Now that we know the value of x, we COULD easily determine whether or not 2^x > 100
Since we could answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1/(2^x) < 0.01
In other words, 1/(2^x) < 1/100
From this we can conclude that 2^x must be greater than 100
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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