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

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
If 5^n > 10,000, and n is an integer, the smallest possible value of n  [#permalink]

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24 Dec 2018, 23:38
00:00

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

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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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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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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

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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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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
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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