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If n is a positive integer and k + 2 = 3^n, which of the fol [#permalink]
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17 Mar 2014, 00:20
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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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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17 Mar 2014, 00:20



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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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17 Mar 2014, 04:31
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
Answer B Time Taken 1:09 Difficulty level 550



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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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18 Mar 2014, 02:16
Answer = B = 4 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 Answer = 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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18 Mar 2014, 08:11
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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06 Jun 2014, 00:12
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



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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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06 Jun 2014, 06:14
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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Re: If n is a positive integer and k + 2 = 3^n, which of the fol [#permalink]
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22 Nov 2015, 20:39
I plugged in for n So 3^12=1 3^22=7
Hey look.... we skipped 4! Answer 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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28 Aug 2016, 20:46
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^n2 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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29 Aug 2016, 01:34
[quote="Bunuel"] The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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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Re: If n is a positive integer and k + 2 = 3^n, which of the fol [#permalink]
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26 Nov 2016, 02:40
k = 3^n  2 = Odd^n  Even = O  E = O. Thus, it can never be an even number. Answer choice 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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02 Jul 2017, 10:12
k + 2 + 3^n suggests K is a number that is 2 plus multiple of 3. 4 violates this. Choice 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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08 Jul 2017, 09:19
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
Hence 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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14 Jul 2017, 05:16
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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16 Jul 2017, 17:42
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. Answer: 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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17 Aug 2017, 06:32
All the options are odd except B. k= 3^n 2= Odd Even= Odd e.g. 32= 1 54= 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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22 Aug 2017, 12:50
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, 32=1 92=7 72=5 12=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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26 Aug 2017, 08:06
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
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