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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE Math Challenge #80-value of n such that (1/2^n)<0.001 [#permalink]
Expert's post 00:00

Question Stats: 78% (00:45) correct 21% (00:34) wrong based on 19 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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Sandy
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Re: GRE Math Challenge #80-value of n such that (1/2^n)<0.001 [#permalink]
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]
1
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Expert's post
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

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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Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails 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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