Source: Revised GRE PDF 1st Ed. Section 5: Math; #12 (p. 76)

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# What is the least integer n such that

What is the least integer n such that 1/(2^n) < 0.001? 10, 11, 500, 501, There is no such least integer.

### 2 Explanations

8

Akanksha Bajaj

Another way to do this problem would be to compare 2^n to 1000 by doing prime factorization on 1000. Doing that would get you to 5^3 * 2^3, at that point, the trick is to find 2^something that would remotely equivalent to 125, which is 2^7 (which is 128). So you can really say that (2^7)*(2^3) is about 1000, OR 2^10 is about 1000. Now, since you're looking at a fraction and want the left side to be smaller, then yes 1/2^10 < 1/1,000. So the answer is A.

Jul 25, 2015 • Comment

Jonathan , Magoosh Tutor

This approach can work too. Nice :)

8

Chris Lele, Magoosh Tutor

Sep 26, 2012 • Comment

Tammie Abbas

Is this question considered a medium or hard?

Jonathan , Magoosh Tutor

Hi. I would say that it's closer to medium than to hard. Hope that helps.