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TAGS: Founder  Joined: 18 Apr 2015
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What is the least integer n such that [#permalink]
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Expert's post 00:00

Question Stats: 76% (00:47) correct 23% (00:51) wrong based on 228 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

_________________ Retired Moderator Joined: 07 Jun 2014
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Re: What is the least integer n such that [#permalink]
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Expert's post
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]
How are we supposed to know that 2^10 = 1024??

Is there a shortcut? Thanks! Retired Moderator Joined: 07 Jun 2014
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Re: What is the least integer n such that [#permalink]
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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]
how does cross multiplying 2^(1/n) becomes 2^n VP Joined: 20 Apr 2016
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Re: What is the least integer n such that [#permalink]
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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]
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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: 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]
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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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Re: What is the least integer n such that [#permalink]
how did you cross multiply? please explain GRE Instructor Joined: 10 Apr 2015
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Re: What is the least integer n such that [#permalink]
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Expert's post
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]
sandy wrote:
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.

Please explain, is it n>=10 or n>10. How do we sure that n=10, because the question says 1/2^n<1/10^3?
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Re: What is the least integer n such that [#permalink]
GreenlightTestPrep wrote:
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:

So, Is The answer A or B? Founder  Joined: 18 Apr 2015
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Re: What is the least integer n such that [#permalink]
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Expert's post
Dear An,

the answer is A. Sandy pointed out that n=10 which is $$2^{10}$$ still holds, simply because considering that the stem tells us the least AND that does not exist a number as a result of $$2^n = 1000$$, we must have that $$2^{10} = 1024$$, we could say that $$n > = 10$$

But these are nuances that you do know and acquire with practice. You develop a sort of instinct.

Be flexible in your approach. You can gain only benefits.

Regards
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Re: What is the least integer n such that [#permalink]
Carcass wrote:
Dear An,

the answer is A. Sandy pointed out that n=10 which is $$2^{10}$$ still holds, simply because considering that the stem tells us the least AND that does not exist a number as a result of $$2^n = 1000$$, we must have that $$2^{10} = 1024$$, we could say that $$n > = 10$$

But these are nuances that you do know and acquire with practice. You develop a sort of instinct.

Be flexible in your approach. You can gain only benefits.

Regards

I got it now. I was confused with this basic thing.

1024 > 1000
so
1/1024 < 1/1000 Manager Joined: 07 Aug 2016
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Re: What is the least integer n such that [#permalink]
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Carcass wrote:

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

0.001 means 10^-3 means 1/1,000

So anything larger than 1,000

2^10 = 1,024

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Re: What is the least integer n such that [#permalink]
it was one of questions in the exam
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Re: What is the least integer n such that [#permalink]
Alternative solution. I multiplied by 1000 in the beginning so:

1000 / 2^n < 1
8*125 / 2^n < 1 ( factoring the 2s out of 1000 )
=>
2^n > 8*125 ( the denomenator should be > numerator ) then divide all by 8=2^3
2^(n-3) > 125
=>
2^7 > 128
=>
n-3 = 7
=>
n = 10 Intern Joined: 15 Aug 2019
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Re: What is the least integer n such that [#permalink]
1
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1/2^n > 0.001
2^n > 1/0.001
2^n > 1000

now let,
2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024 >1000

so ans is A
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Re: What is the least integer n such that [#permalink]
this is actually hard Re: What is the least integer n such that   [#permalink] 19 Aug 2019, 09:06
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