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If n is a positive integer and p = 3.021 × 10n, what is the value of n

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Kudos [?]: 133072 [0], given: 12403

If n is a positive integer and p = 3.021 × 10n, what is the value of n [#permalink]

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New post 12 Oct 2017, 04:09
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Difficulty:

  45% (medium)

Question Stats:

41% (00:52) correct 59% (01:06) wrong based on 33 sessions

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Kudos [?]: 133072 [0], given: 12403

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Kudos [?]: 257 [2], given: 35

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If n is a positive integer and p = 3.021 × 10n, what is the value of n [#permalink]

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New post 12 Oct 2017, 08:25
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Bunuel wrote:
If n is a positive integer and p = 3.021*10^n, what is the value of n?

(1) 3,021 < p < 302,100
(2) 10^3 < p < 10^5


Statement 1: \(3021<3.021*10^n<302100\). divide both sides of the inequality by \(3.021\) to get

\(10^3<10^n<10^5\) as \(n\) is an integer, only value in this range is \(n=4\). Sufficient

Statement 2: \(1000<p<100000\)

now if \(n=3\), then \(p = 3021\) and \(1000<3021<100000\)

but if \(n = 4\), then \(p=30210\) and \(1000<30210<100000\)

Hence there is no unique value. Insufficient

Option A

Kudos [?]: 257 [2], given: 35

If n is a positive integer and p = 3.021 × 10n, what is the value of n   [#permalink] 12 Oct 2017, 08:25
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If n is a positive integer and p = 3.021 × 10n, what is the value of n

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