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Math Expert V
Joined: 02 Sep 2009
Posts: 65829
If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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Question Stats: 90% (00:58) correct 10% (01:04) wrong based on 860 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 170
Category: Arithmetic Operations on rational numbers
Page: 84
Difficulty: 600

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Math Expert V
Joined: 02 Sep 2009
Posts: 65829
Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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4
1
SOLUTION

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

Substitute the answer choices for k:

(A) If k = 1, then 3^n = 1 + 2 = 3^1.

(B) If k = 4, then 3^n = 4 + 2 = 6. NOT a power of 3.

(C) If k = 7, then 3^n = 7 + 2 = 3^2.

(D) If k = 25, then 3^n = 25 + 2 = 3^3.

(E) If k = 79, then 3^n = 79 + 2 = 3^4.

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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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k+2 = 3^n
Simply Substitute

1+2 = 3 = 3^1
4+2 = 6 Not a power of 3 so rejected and hence, the answer
7+2 = 9 = 3^2
25+2 = 27 = 3^3
79 + 2 = 81 = 3^4
Only catch here is that even after looking at 6 you may not realize its the answer bcoz it is a multiple of 3

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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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1

Rewrite the equation as follows:

3^n = k + 2

Note that RHS of the equation has to be some power of 3 (with n as an integer)

Adding 1, 7, 25, 79 to 2 gives 3, 9, 27, 81 respectively which is power of 3

Only 4 stands out

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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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1
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

$$k + 2 = 3^n$$

Or, $$k = 3^n - 2$$

Or, $$k = 1 , 7, 25, 79, 241....$$ for $$n=1, 2, 3, 4, 5....$$

Since, 4 can not be a value that satisfies the equation $$k = 3^n -2$$ for positive integer $$n$$, the answer is (B)
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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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K+2 = 3^n
so K+2 must equal some power of 3
A)1+2=3 = 3^1
B)4+2=6 not equal any power of 3
C)7+2 = 9 = 3^2
D)25+2 = 27 = 3^3
E)79+2 = 81 = 3^4
Ans: B
Intern  Joined: 15 Aug 2013
Posts: 49
Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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2
k + 2 + 3^n suggests K is a number that is 2 away from the multiple of 3.
Only 4 violates and hence the answer. Choice B
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GMAT 1: 600 Q33 V40
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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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I plugged in for n
So 3^1-2=1
3^2-2=7

Hey look.... we skipped 4! Answer B.
Manager  S
Joined: 17 Aug 2015
Posts: 91
Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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1
One way to solve this problem. Since n is a pos int., this means that 3^n will always be odd (note that this is true even if n =0). Also 3^n-2 will always be odd since odd - even is always odd. So even values are not possible. Take out 4 since it could never be possible and that is our answer given the question
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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Option B
k + 2 = 3^n
k=4
4+2= 3^n
6=3^n
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Current Student S
Joined: 23 Jul 2015
Posts: 138
Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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2
k = 3^n - 2 = Odd^n - Even = O - E = O. Thus, it can never be an even number. Answer choice is B
Intern  Joined: 08 Jun 2011
Posts: 17
Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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3
k + 2 + 3^n suggests K is a number that is 2 plus multiple of 3.
4 violates this. Choice B
Intern  Joined: 08 Jun 2011
Posts: 17
Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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1
In such questions, I usually follow simple approach -
find the pattern, and then substitute
Lets see here, what does k + 2 = 3^n means ?

This means K is a number which is nothing but (some) power of 3 - 2. (powers of 3 = 3, 9, 27, 81)
Now let us substitute the answers, and ans will be straightforward.
(A) 1 = 3 - 2 it works
(B) 4 = this does not work
(C) 7 = 9 - 2. it works too
(D) 25 = 27 - 2 this does not work
(E) 79 = 81 - 2 . this worls

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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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Option B
Time taken:0:22 seconds
only B fulfills
4+2=3^n
6=3^n
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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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Quote:

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.

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Director  G
Joined: 02 Sep 2016
Posts: 620
Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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All the options are odd except B.

k= 3^n- 2= Odd- Even= Odd

e.g. 3-2= 1
5-4= 1

and so on

Also Odd^any power is odd and Even^any power is even.
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If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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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

possible values

3=3 unit digit=3
3*3=9unit digit=9
3*3*3=27unit digit=7
3*3*3*3=81unit digit=1
this will repeat again.. forever

so,
3-2=1
9-2=7
7-2=5
1-2=9 or -1

so we will never get 4, thus B is the answer to the question.
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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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1
My 50 cents here. The most efficient way to solve this is by using Odd/even Property if numbers.

Given: $$k + 2 = 3^n --> k = 3^n - 2$$

Concept: $$(Odd)^{integer} = Odd$$ and $$Odd ± Even = Odd$$

From this we see that K is necessarily an odd number. Just by glancing the answer choice we see the required answer = 4 = B
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Re: If n is a positive integer and k + 2 = 3^n, which of the fol  [#permalink]

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_________________ Re: If n is a positive integer and k + 2 = 3^n, which of the fol   [#permalink] 11 Feb 2019, 05:07

# If n is a positive integer and k + 2 = 3^n, which of the fol  