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is 2^x greater than 100

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is 2^x greater than 100

by kaf » Mon Mar 16, 2009 1:23 pm
Can some one please explain why the answer to this DS question is D

Is 2^x greater than 100?

ST1 2√x = 8

ST2 2^-x < 0.01

thanks
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by Feep » Mon Mar 16, 2009 1:43 pm
This one isn't too bad.

2^x > 100 also means that x >= 7. You can do this with logarithms, if you want, or some quick trial-and-error.

(1) give a quick, easy formula to solve for x. X = 16, which is clearly greater than 7. Sufficient.

(2) gives another formula that we have to mess with a bit. 2^-x < 0.01. With the properties of negative exponents, this is 1 / (2^x) < 0.01. Cross-multiply to get 100 < 2^x. Clearly sufficient.

Answer is D.
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