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# Which of the following options should be the least value of

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Intern
Joined: 14 Oct 2015
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Which of the following options should be the least value of [#permalink]  15 Oct 2015, 10:30
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Question Stats:

75% (00:31) correct 25% (00:53) wrong based on 8 sessions
Which of the following options should be the least value of n that satisfies the inequality, $$2^n > (10^{15})$$ ?

A. 30

B. 45

C. 60

D. 75

E. 90

and the right answer is 60
please explain as I could not even get the sense on how to start solving it.
[Reveal] Spoiler: OA
Intern
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Re: Inequalities [#permalink]  09 Oct 2017, 20:04
1
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(2)^n > 10^15

\divide the powers by n

2 > 10^(15/n)

if n = 30

2 < 10^(15/30)
2 < sqrt(10)
which is incorrect.

if n = 45

2 < 10^(15/45)
2 < cuberoot(10)
which is incorrect.

if n = 60

2 > 10^(15/60)
2 > (10)^(1/4).

therefore least value of n = 60.
Intern
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Re: Inequalities [#permalink]  14 Oct 2017, 23:46
2
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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.

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

The answer should be 50. 45 makes it less, so choose 60.
Re: Inequalities   [#permalink] 14 Oct 2017, 23:46
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