Sujan Sareen wrote:

Which of the following options should be the least value of n that satisfies the inequality, 2^n > (10^15) ?

options are:

30

45

60

75

90

and the right answer is 60

please explain as I could not even get the sense on how to start solving it.

Dear Sujan Sareen,

I'm happy to respond.

This is Mike McGarry, from

Magoosh.

I gather that you are relatively new here at GMAT Club. I want to give you some advice. This particular forum, the "Ask GMAT Expert" forum, is for general questions (retakes, scheduling, study plans, etc.) For individual content questions, such as an individual math question, you should NOT post it here. You should post this question in the Problem Solving forum:

gmat-problem-solving-ps-140/I would recommend deleting the other version of this question that you are posted: it's considered in particular bad form to post the same question multiple times in different places.

Since I am already responding, I am happy to address this question. I will say, when you post a math question, in one of the math forums, it's a good idea to cite the source. For this particular question, it is not at all clear to me that this is GMAT-appropriate question.

This is not an approximation that you need to know for the GMAT, but 2^10 is slightly larger than a thousand (10^3).

2^10 = 1024

This is a computer science thing. You see, when a computer talks about kilobytes (kb), that's actually not 1000 bytes, but 1024 bytes. Similarly, a megabyte (Mb) is (1024)^2 bytes, and a gigabyte (Gb) is (1024)^3. Despite the quasi-metric prefixes, everything depends on powers of 2, not powers of 10.

So, to make sense of this question, you have to know that

2^10 > 10^3

Now, we simply raise both sides of that inequality to the fifth power.

(2^10)^5 > (10^3)^5

2^50 > 10^15

Using this naive approximation, it appears the best answer for n would be 50. In fact, a calculator tells me that

2^50 = 1.1258999 x 10^15

Of the five answer given, n = 45 is too small, so we have to go with n = 60.

Again, this could appear as a math problem in other contexts, but I can guarantee that the GMAT does not expect you to know this stuff.

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)