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# What is the value of n for which 4^n will have 9 factors? A) 3 B) 4 C

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What is the value of n for which 4^n will have 9 factors? A) 3 B) 4 C  [#permalink]

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07 Aug 2017, 07:03
1
1
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:06) correct 34% (01:19) wrong based on 61 sessions

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What is the value of n for which 4^n will have 9 factors?

A) 3
B) 4
C) 5
D) 6
E) 8

Source: www.GMATInsight.com

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Re: What is the value of n for which 4^n will have 9 factors? A) 3 B) 4 C  [#permalink]

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07 Aug 2017, 11:07
2
It will be B 4.
As we can simplify the term to 2^2n
now for the this term to have 9 factors , 2n+1=9.
So n=4

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Re: What is the value of n for which 4^n will have 9 factors? A) 3 B) 4 C  [#permalink]

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07 Aug 2017, 11:22
Top Contributor
GMATinsight wrote:
What is the value of n for which 4^n will have 9 factors?

A) 3
B) 4
C) 5
D) 6
E) 8

Source: http://www.GMATInsight.com

Another approach is to test the answer choices

A) n = 3
So, 4^n = 4³ = ()³ = 2^6 = (2)(2)(2)(2)(2)(2)
The factors of 2^6 are: 1, 2, 2^2, 2^3, 2^4, 2^5 and 2^6
7 factors in total. We want 9 factors.
ELIMINATE A

B) n = 4
So, 4^n = 4⁴ = ()⁴ = 2^8 = (2)(2)(2)(2)(2)(2)(2)(2)
The factors of 2^8 are: 1, 2, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 and 2^8
9 factors in total...BINGO!

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Re: What is the value of n for which 4^n will have 9 factors? A) 3 B) 4 C   [#permalink] 07 Aug 2017, 11:22
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