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What is the largest integer n such that 1/2^n
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27 May 2020, 10:20
27 May 2020, 10:20
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Question Stats:
83% (00:46) correct
16% (01:14) wrong based on 37 sessions
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What is the largest integer n such that \(\frac{1}{2^n}> 0.01\) ?
(A) 5
(B) 6
(C) 7
(D) 10
(E) 51
(A) 5
(B) 6
(C) 7
(D) 10
(E) 51
Re: What is the largest integer n such that 1/2^n
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27 May 2020, 10:20
27 May 2020, 10:20
Expert Reply
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Re: What is the largest integer n such that 1/2^n
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27 May 2020, 13:41
27 May 2020, 13:41
1
Carcass wrote:
What is the largest integer n such that \(\frac{1}{2^n}> 0.01\) ?
(A) 5
(B) 6
(C) 7
(D) 10
(E) 51
(A) 5
(B) 6
(C) 7
(D) 10
(E) 51
We want: \(\frac{1}{2^n}> 0.01\)
Rewrite as: \(\frac{1}{2^n}> \frac{1}{100}\)
If \(2^n = 100\), then \(\frac{1}{2^n}= \frac{1}{100}\)
If \(2^n > 100\), then \(\frac{1}{2^n} < \frac{1}{100}\)
If \(2^n < 100\), then \(\frac{1}{2^n} > \frac{1}{100}\)
So, for this question, we need the largest value of \(n\) so that \(2^n < 100\)
\(2^6 = 64\) and \(2^7 = 64\)
So 6 is the largest integer value of \(n\) so that \(2^n < 100\)
Answer: B
Cheers,
Brent
