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Sub 505 (Easy)|   Algebra|   Exponents|      
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Bunuel
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If n is a positive integer and x + 3 = 4^n, which of the following cou 12 Feb 2019, 00:59
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C
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5% (low)

Question Stats:

84% (01:04) correct 16% (01:20) wrong based on 133 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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C
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KSBGC
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If n is a positive integer and x + 3 = 4^n, which of the following cou Updated on: 12 Feb 2019, 01:51
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.
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Bunuel
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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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.
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kumarankit01
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If n is a positive integer and x + 3 = 4^n, which of the following cou 12 Feb 2019, 01:05
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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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KanishkM
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If n is a positive integer and x + 3 = 4^n, which of the following cou 12 Feb 2019, 01:37
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Bunuel
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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\(x = 4^n - 3\)

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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If n is a positive integer and x + 3 = 4^n, which of the following cou 12 Feb 2019, 01:46
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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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leomanna10
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If n is a positive integer and x + 3 = 4^n, which of the following cou 12 Feb 2019, 01:55
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Bunuel
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
Show more

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.
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If n is a positive integer and x + 3 = 4^n, which of the following cou 09 Jun 2024, 15:00
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

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