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

1

This post received KUDOS

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]
20 Nov 2018, 15:30

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:

Re: What is the least integer n such that [#permalink]
20 Nov 2018, 16:48

1

This post received KUDOS

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.

Re: What is the least integer n such that [#permalink]
21 Nov 2018, 16:52

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.

Re: What is the least integer n such that [#permalink]
03 Dec 2018, 05:07

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