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If 5^n > 10,000, and n is an integer, the smallest possible value of n

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If 5^n > 10,000, and n is an integer, the smallest possible value of n  [#permalink]

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New post 24 Dec 2018, 23:38
3
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

58% (01:02) correct 42% (00:58) wrong based on 108 sessions

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If 5^n > 10,000, and n is an integer, the smallest possible value of n is


A. 4
B. 5
C. 6
D. 7
E. 8
Spoiler: OA

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If 5^n > 10,000, and n is an integer, the smallest possible value of n  [#permalink]

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New post Updated on: 06 Jan 2019, 06:56
Bunuel wrote:
If 5^n > 10,000, and n is an integer, the smallest possible value of n is


A. 4
B. 5
C. 6
D. 7
E. 8

5^n > 10,000,

10,000 = 5^4*2^4

so n has to be >5

IMO C 6
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Originally posted by Archit3110 on 25 Dec 2018, 08:08.
Last edited by Archit3110 on 06 Jan 2019, 06:56, edited 1 time in total.
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Re: If 5^n > 10,000, and n is an integer, the smallest possible value of n  [#permalink]

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New post 06 Jan 2019, 06:53
If 5^n > 10,000, and n is an integer, the smallest possible value of n is

10,000= (2*5)^4

5^4= 625
5^5= 3125
5^6= 15515

answer= 6
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If 5^n > 10,000, and n is an integer, the smallest possible value of n  [#permalink]

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New post 06 Jan 2019, 07:22
If \(5^n > 10,000\), and n is an integer, the smallest possible value of n is

\(10,000 = 5^4*2^4\)
\(2^4 = 16 >5 But 16 < 25 i.e., 5^2\)
implies 5^4 * 5^2 i.e., \(5* 5^4 < 16 * 5^4 < 25* 5^4\)

minimum value of n is 6
Option C is correct
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If 5^n > 10,000, and n is an integer, the smallest possible value of n   [#permalink] 06 Jan 2019, 07:22
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