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# What is the least integer n such that

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What is the least integer n such that [#permalink]  17 Feb 2017, 02:58
Expert's post
00:00

Question Stats:

84% (00:55) correct 15% (01:17) wrong based on 32 sessions

What is the least integer n such that $$\frac{1}{2^n}$$ $$< 0.001$$ ?

A) 10

B) 11

C) 500

D) 501

E) There is no such least integer
[Reveal] Spoiler: OA

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Re: What is the least integer n such that [#permalink]  21 Feb 2017, 17:01
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Explanation

We rewrite 0.001 as $$\frac{1}{1000}$$ .

So if $$\frac{1}{2^n} < \frac{1}{1000}$$.

Cross multiplying we can rewrite $$1000 < 2^n$$.

So we know $$2^1 = 2, 2^2 =4 ....... 2^1^0 = 1024$$.

So if $$n \geq 10$$ then the inequality proposed in the question holds.

Hence A is the right answer.
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Re: What is the least integer n such that [#permalink]  18 Sep 2017, 15:53
How are we supposed to know that 2^10 = 1024??

Is there a shortcut? Thanks!
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Re: What is the least integer n such that [#permalink]  18 Sep 2017, 17:07
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Expert's post
clausen8657 wrote:
How are we supposed to know that 2^10 = 1024??

Is there a shortcut? Thanks!

I remember with Megabyte Gigabyte relation.

1 Gigabyte is $$2^{10}$$ Megabyte or 1024
.5 Gigabyte is $$2^9$$ Mb or 512

I remember these nubers because these are all multiples of RAM of a computer or cellphone.

Other wise remember $$2^5$$ is 32. And $$2^{10}$$ is $$32^2$$.
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Re: What is the least integer n such that [#permalink]  21 Sep 2017, 14:15
how does cross multiplying 2^(1/n) becomes 2^n
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Re: What is the least integer n such that [#permalink]  21 Sep 2017, 20:22
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saumya17lc wrote:
how does cross multiplying 2^(1/n) becomes 2^n

it is $$\frac{1}{2^n}$$ and not $$2^(1/n)$$
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Re: What is the least integer n such that [#permalink]  15 Oct 2017, 15:07
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clausen8657 wrote:
How are we supposed to know that 2^10 = 1024??

Is there a shortcut? Thanks!

It's not a bad idea to memorize powers of 2 up to 2^7
From there, you can keep multiplying by 2 to get bigger powers.

2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024

Cheers,
Brent
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Re: What is the least integer n such that [#permalink]  20 Jun 2018, 03:32
how did you cross multiply? please explain
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Re: What is the least integer n such that [#permalink]  20 Jun 2018, 04:56
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Ronaksingh wrote:
how did you cross multiply? please explain

Let's do this in steps...

We have the inequality: 1/(2^n) < 1/1000
Since 2^n is always POSITIVE, we can multiply both sides by 2^n to get: 1 < (2^n)/1000
Also, since 1000 is POSITIVE, we can multiply both sides by 1000 to get: 1000 < 2^n

Here's a video on dealing with inequalities like this:

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Re: What is the least integer n such that   [#permalink] 20 Jun 2018, 04:56
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