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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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Math Expert
Joined: 02 Sep 2009
Posts: 52385
If n is a positive integer and p = 3.021 × 10n, what is the value of n  [#permalink]

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12 Oct 2017, 03:09
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:45) correct 46% (01:21) wrong based on 83 sessions

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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

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Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
Re: If n is a positive integer and p = 3.021 × 10n, what is the value of n  [#permalink]

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12 Oct 2017, 07:25
3
1
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
Director
Joined: 27 May 2012
Posts: 669
Re: If n is a positive integer and p = 3.021 × 10n, what is the value of n  [#permalink]

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14 Jul 2018, 07:54
1
niks18 wrote:
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

Dear Moderator,
Kindly explain how OA is D? IMO it should be A
statement B :
$$10^3$$< P $$< 10^5$$

since 3021 and 30210 both are between $$10^3$$ and $$10^5$$ hence does not seem sufficient.

1,000 < 3,021 <30,210 <100,000 hence value of P can be 3021 or 30210
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- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 52385
Re: If n is a positive integer and p = 3.021 × 10n, what is the value of n  [#permalink]

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14 Jul 2018, 23:43
stne wrote:
niks18 wrote:
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

Dear Moderator,
Kindly explain how OA is D? IMO it should be A
statement B :
$$10^3$$< P $$< 10^5$$

since 3021 and 30210 both are between $$10^3$$ and $$10^5$$ hence does not seem sufficient.

1,000 < 3,021 <30,210 <100,000 hence value of P can be 3021 or 30210

_________________________
The OA ia A. Edited. Thank you.
_________________
Re: If n is a positive integer and p = 3.021 × 10n, what is the value of n &nbs [#permalink] 14 Jul 2018, 23:43
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