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If k is an integer, is 2^k + 3^k = m ?

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If k is an integer, is 2^k + 3^k = m ? [#permalink] New post 21 Aug 2013, 11:05
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  45% (medium)

Question Stats:

45% (02:02) correct 55% (01:18) wrong based on 60 sessions
If k is an integer, is 2^k + 3^k = m ?

(1) 4^k + 9^k = m^2 - 12

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of k in the original question, so the question now is:is k = 5 ?

Now we replace the value of k in statement (1), so:

m^2 = 25

So,m = +/- 25

There is not indication whether m is possitive.

IMO, the answer: E
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Aug 2013, 11:26, edited 1 time in total.
Edited the OA.
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Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post 21 Aug 2013, 11:16
Expert's post
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

(1) 4^k + 9^k = m^2 - 12

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of k in the original question, so the question now is: is m = 5 ?

Now we replace the value of k in statement (1), so:

m^2 = 25

So, m = +/- 5

There is not indication whether m is possitive.

IMO, the answer: E


Yes, you are right. When we combine we get that m is either 5 or -5. If m=5 then the answer is YES but if m=-5, then the answer is No.

Answer: E.
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Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post 30 Aug 2013, 00:26
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

(1) 4^k + 9^k = m^2 - 12

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of k in the original question, so the question now is:is k = 5 ?

Now we replace the value of k in statement (1), so:

m^2 = 25

So,m = +/- 25

There is not indication whether m is possitive.

IMO, the answer: E


I don't know what was the original OA but I am assuming it was C, here's how I think the answer should be C, please do correct if there is a flaw in my reasoning.

Given If k is an integer, is 2^k + 3^k = m?
Squaring both sides original equation now becomes 2^{2k} +3^{2k}+2.6^k=m^2

statement 1:4^k + 9^k = m^2 - 12this can be written as 2^{2k} +3^{2k}+12 =m^2..

Comparing this with original equation we see that this will be equal to original equation only if K=1 since we do not have the value of K, hence insufficient

statement 2 : K=1 , by itself it is insufficient as we do not know the value of M

1+ 2

K=1 then m^2 = 25

this is also what we get from the original equation,doesn't matter what m is, m^2 is 25
Please share your views
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Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post 30 Aug 2013, 03:41
1
This post received
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Expert's post
stne wrote:
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

(1) 4^k + 9^k = m^2 - 12

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of k in the original question, so the question now is:is k = 5 ?

Now we replace the value of k in statement (1), so:

m^2 = 25

So,m = +/- 25

There is not indication whether m is possitive.

IMO, the answer: E


I don't know what was the original OA but I am assuming it was C, here's how I think the answer should be C, please do correct if there is a flaw in my reasoning.

Given If k is an integer, is 2^k + 3^k = m?
Squaring both sides original equation now becomes 2^{2k} +3^{2k}+2.6^k=m^2

statement 1:4^k + 9^k = m^2 - 12this can be written as 2^{2k} +3^{2k}+12 =m^2..

Comparing this with original equation we see that this will be equal to original equation only if K=1 since we do not have the value of K, hence insufficient

statement 2 : K=1 , by itself it is insufficient as we do not know the value of M

1+ 2

K=1 then m^2 = 25

this is also what we get from the original equation,doesn't matter what m is, m^2 is 25
Please share your views


It does matter. If m=-5, then the question is: does 2^k + 3^k = -5? And you cannot square this.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Manager
Manager
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Joined: 27 May 2012
Posts: 213
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Kudos [?]: 46 [0], given: 97

Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post 30 Aug 2013, 06:00
Bunuel wrote:
stne wrote:
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

(1) 4^k + 9^k = m^2 - 12

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of k in the original question, so the question now is:is k = 5 ?

Now we replace the value of k in statement (1), so:

m^2 = 25

So,m = +/- 25

There is not indication whether m is possitive.

IMO, the answer: E


I don't know what was the original OA but I am assuming it was C, here's how I think the answer should be C, please do correct if there is a flaw in my reasoning.

Given If k is an integer, is 2^k + 3^k = m?
Squaring both sides original equation now becomes 2^{2k} +3^{2k}+2.6^k=m^2

statement 1:4^k + 9^k = m^2 - 12this can be written as 2^{2k} +3^{2k}+12 =m^2..

Comparing this with original equation we see that this will be equal to original equation only if K=1 since we do not have the value of K, hence insufficient

statement 2 : K=1 , by itself it is insufficient as we do not know the value of M

1+ 2

K=1 then m^2 = 25

this is also what we get from the original equation,doesn't matter what m is, m^2 is 25
Please share your views


It does matter. If m=-5, then the question is: does 2^k + 3^k = -5? And you cannot square this.


Well if you say so, there are many ways algebraic equations can be manipulated and I thought they could be squared .Thank you +1
_________________

- Stne

Re: If k is an integer, is 2^k + 3^k = m ?   [#permalink] 30 Aug 2013, 06:00
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