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If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the value of n

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If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the value of n  [#permalink]

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New post 10 Apr 2019, 00:46
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

44% (01:03) correct 56% (01:31) wrong based on 39 sessions

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[GMAT math practice question]

If \(0.00012345\) is between \(\frac{1}{10^n}\) and \(\frac{1}{10^{n-1}}\), what is the value of \(n\)?

A. 2
B. 3
C. 4
D. 5
E. 6

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Re: If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the value of n  [#permalink]

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New post 10 Apr 2019, 06:16
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Top Contributor
MathRevolution wrote:
[GMAT math practice question]

If \(0.00012345\) is between \(\frac{1}{10^n}\) and \(\frac{1}{10^{n-1}}\), what is the value of \(n\)?

A. 2
B. 3
C. 4
D. 5
E. 6


We need to examine powers of 10 that are smaller than AND greater than 0.00012345

We know that: 0.0001 < 0.00012345 < 0.001
Rewrite as FRACTIONS to get: 1/10,000 < 0.00012345 < 1/1,000
Rewrite as POWERS OF 10 to get: 1/10⁴ < 0.00012345 < 1/10³

We're told that 0.00012345 is between 1/10^n and 1/10^{n-1}
So, we can now see that n = 4

Answer: C

Cheers,
Brent
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Math Revolution GMAT Instructor
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Re: If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the value of n  [#permalink]

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New post 12 Apr 2019, 01:38
=>

\(0.0001 < 0.00012345 < 0.001\)

\(10^{-4} < 0.00012345 < 10^{-3}\)

\(\frac{1}{10^4} < 0.00012345 < \frac{1}{10^3}\)

Comparing this with \(\frac{1}{10^n} < 0.00012345 < \frac{1}{10^{n-1}}\) yields \(n = 4\).

Therefore, the answer is C.
Answer: C
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Re: If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the value of n   [#permalink] 12 Apr 2019, 01:38
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