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# If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n =

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If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n = [#permalink]

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11 Sep 2012, 17:55
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75% (01:45) correct 25% (00:58) wrong based on 111 sessions

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If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n =

A. 3
B. 6
C. 12
D. 23
E. 24

A tough question.

[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Sep 2012, 00:43, edited 1 time in total.
Edited the question.
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Re: If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n = [#permalink]

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11 Sep 2012, 20:30
2^2n + 2^2n + 2^2n + 2^2n = 4^24

=> 4 x 2^2n = 4^24 = 2^48

=> 2^2 x 2^2n = 2^48

=> 2^(2n+2) = 2^48

=> 2n+2 = 48=> n =23

Hope it helps!
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Re: If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n = [#permalink]

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11 Sep 2012, 22:38
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carcass wrote:
If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n =

1) 3

2) 6

3)12

4)23

5)24

A tough question.

Not really! The takeaway from this question is: when you have addition/subtraction between terms with exponents, you need to think about taking common. Also, in all exponent questions, consider making the base of every term same, if possible.

$$2^{2n} + 2^{2n} + 2^{2n} + 2^{2n} = 4^{24}$$

Taking $$2^{2n}$$ common,

$$2^{2n}(1 + 1 + 1 + 1) = 2^{48}$$

$$2^{2n}*4 = 2^{48}$$
$$2^{2n}*2^2 = 2^{48}$$
$$2^{2n+2} = 2^{48}$$

Now simply put 2n + 2 = 48
n = 23
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Re: If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n = [#permalink]

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30 Nov 2013, 11:46
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Re: If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n = [#permalink]

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26 Feb 2014, 01:32
4. 2^2n = 4^24

4. 4^n = 4^24

4^(n+1) = 4^24

Equating powers, n+1=24; n=23 Answer = D
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Re: If 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n =   [#permalink] 26 Feb 2014, 01:32
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