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GRE Math Challenge #80-value of n such that (1/2^n)<0.001

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GRE Math Challenge #80-value of n such that (1/2^n)<0.001 [#permalink] New post 03 May 2015, 01:44
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Question Stats:

78% (00:56) correct 21% (00:42) wrong based on 14 sessions
What is the least integer value of n such that \((1/2^n)<0.001\)?

(A) 10
(B) 11
(C) 500
(D) 501
(E) there is no such least value.
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #80-value of n such that (1/2^n)<0.001 [#permalink] New post 14 Dec 2017, 06:14
sandy wrote:
What is the least integer value of n such that \((1/2^n)<0.001\)?

(A) 10
(B) 11
(C) 500
(D) 501
(E) there is no such least value.



Here
0.001 = 1/1000 now if we can make \(2^n > 1000,\)
then we can write \((1/2^n)<0.001\)

1000 = \(2^3\) * \(5^3\)

\(2^6\) \(<\) \(5^3\) \(<\) \(2^7\)

i.e \(2^3\) * \(2^7\) \(>\) \(2^3\) * \(5^3\)
or \(2^{10} > 1000\)

i.e \(\frac{1}{2^{10}}\) \(<\) 0.001

Hence the minimum value of n = 10
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Re: GRE Math Challenge #80-value of n such that (1/2^n)<0.001 [#permalink] New post 12 May 2018, 07:46
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sandy wrote:
What is the least integer value of n such that \((1/2^n)<0.001\)?

(A) 10
(B) 11
(C) 500
(D) 501
(E) there is no such least value.


We want: 1/(2^n) < 0.001
In other words, we want: 1/(2^n) < 1/1000

Let's start with answer choice A (n = 10)
We get: 1/(2^n) = 1/(2^10)
= 1/1024
Is 1/1024 < 1/1000?
Yes!

Since the question asks us to find the least integer value of n, and since 10 is the smallest answer choice, the correct answer must be A

Cheers,
Brent
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Re: GRE Math Challenge #80-value of n such that (1/2^n)<0.001   [#permalink] 12 May 2018, 07:46
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