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15 Oct 2015, 11:37
Kudos
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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.
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.
18 Oct 2015, 04:15
Kudos
Bookmarks
Sujan Sareen
You posted the same question twice, hence reposting my solution:
Hi Sujan Sareen,
This is an approximation question, so we would follow a sequence of steps to arrive at the correct approximation.
10^15 = 2^15* 5^15
So, we know that we need to have at least 15 2's in 2^n. - (i)
Next step would be to approximate 5^15.
We can write 5^15 = ((5)^3)^5 = 125^5
We are considering 125, because 125 is closest to 128, which is a power of 2
The closest to 125^5 in terms of powers of 2 would be 128^5
This can be written as (2^7)^5 = 2^35
Hence we should have 35 2's in 2^n - (ii)
Now adding the 2's in (i) and (ii)
We get 50.
The closest option to this is 60
Hence Option C is the correct answer.
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