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# If n is a positive integer and x + 3 = 4^n, which of the following cou

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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11 Feb 2019, 23:59
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Question Stats:

93% (00:44) correct 7% (01:47) wrong based on 14 sessions

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If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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Updated on: 12 Feb 2019, 00:51
Bunuel wrote:
If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

x + 3 must not be expressed as the base of 4.

Option C) 45

45 + 3 = 48

48 can't be written as the base of 4.

Thus , the correct answer is C.

Originally posted by selim on 12 Feb 2019, 00:04.
Last edited by selim on 12 Feb 2019, 00:51, edited 3 times in total.
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Posts: 19
Location: India
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Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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12 Feb 2019, 00:05
n = 1
x = 1

n= 2
x = 13

so 4 will not have any power which can give 45

please award kudos if this is right

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Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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12 Feb 2019, 00:37
Bunuel wrote:
If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

$$x = 4^n - 3$$

Now if that is the case, n cannot be 0

cyclicity of unit digit of 4 is 4,6,4,6

Now we will be always subtracting 3 out of it, new cyclicity becomes 1,3,1,3

Key word: could not be a value of x

It will be C
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Joined: 19 Jan 2019
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Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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12 Feb 2019, 00:46
Plug in the values of X in answer choices. All the option except c will give a value of 4^n...

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Joined: 11 Dec 2018
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Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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12 Feb 2019, 00:55
Bunuel wrote:
If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

The best way to answer this question is working backward.

Plug-in the answer choices in X and try to solve the equation:

X= 4^n - 3

1) 1= 4^1 - 3 = 1 OK!

2)13 = 4^2 - 3 = 13 OK!

3)45 = 4^3 - 3= 61 NO!

So the correct answer is C. We don't need to check the other two options.
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou   [#permalink] 12 Feb 2019, 00:55
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