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N Positive integer

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by GMATGuruNY » Sat Oct 10, 2015 6:09 am
oquiella wrote:If n is a positive integer and k+2= 3^n, which of the following could NOT be a value of k?

A. 1
B. 4
C. 7
D. 25
E. 79
When 2 is added to k, the result must be a POWER OF 3.
Add 2 to each of the answer choices:
A: 1+2 = 3.
B: 4+2 = 6.
We can stop here.
Since 6 is not a power of 3, it is not possible that k=4.

The correct answer is B.
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by [email protected] » Sat Oct 10, 2015 8:52 am
Hi oquiella,

Since N is a POSITIVE INTEGER and we're told that K+2 = 3^N, you might find it helpful to list out the first several 'powers of 3'...

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81

We're asked for what CANNOT be the value of K. Now, looking at the answer choices, if you add 2 to each of them, then you'll find 4 'matches' to the numbers in this list (and one number that does NOT match).

Final Answer: B

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by Jeff@TargetTestPrep » Mon Dec 18, 2017 4:49 pm
oquiella wrote:If n is a positive integer and k+2= 3^n, which of the following could NOT be a value of k?

A. 1
B. 4
C. 7
D. 25
E. 79
We see that (k + 2) must be 3 raised to a power. We can go through each answer choice.

(A) 1

If k = 1, we have 1 + 2 = 3^n or 3 = 3^n. We see that n = 1, so k can be 1.

(B) 4

If k = 4, we have 4 + 2 = 3^n or 6 = 3^n. Since 3^1 = 3 and 3^2 = 9, there is no positive integer n such that 3^n = 6, and hence k can't be 4.

Answer: B

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