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Math Expert V
Joined: 02 Sep 2009
Posts: 58340
If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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Difficulty:   15% (low)

Question Stats: 88% (01:02) correct 13% (00:57) wrong based on 40 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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VP  D
Joined: 31 Oct 2013
Posts: 1471
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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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 KSBGC on 12 Feb 2019, 01:04.
Last edited by KSBGC on 12 Feb 2019, 01:51, edited 3 times in total.
Manager  S
Joined: 13 Oct 2018
Posts: 85
Location: India
GPA: 3.1
WE: Information Technology (Computer Software)
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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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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Director  G
Joined: 09 Mar 2018
Posts: 996
Location: India
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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1
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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Manager  S
Joined: 19 Jan 2019
Posts: 88
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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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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Intern  B
Joined: 11 Dec 2018
Posts: 10
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

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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, 01:55
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