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If k is an integer, is 2^k + 3^k = m ?
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Updated on: 21 Aug 2013, 12:26
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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
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Originally posted by danzig on 21 Aug 2013, 12:05.
Last edited by Bunuel on 21 Aug 2013, 12:26, edited 1 time in total.
Edited the OA.



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Re: If k is an integer, is 2^k + 3^k = m ?
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21 Aug 2013, 12:16
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 ?
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30 Aug 2013, 01:26
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:\(4^k + 9^k = m^2  12\)this 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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 Stne



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Re: If k is an integer, is 2^k + 3^k = m ?
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30 Aug 2013, 04:41
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:\(4^k + 9^k = m^2  12\)this 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 25Please share your views It does matter. If m=5, then the question is: does \(2^k + 3^k = 5\)? And you cannot square this.
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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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Re: If k is an integer, is 2^k + 3^k = m ?
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30 Aug 2013, 07:00
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:\(4^k + 9^k = m^2  12\)this 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 25Please 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
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Re: If k is an integer, is 2^k + 3^k = m ?
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25 Dec 2014, 10:58
Hi All, This question can be solved with a combination of TESTing VALUES and some basic algebra/arithmetic skills. We're told that K is an integer and we're asked if 2^K + 3^K = M. This is a YES/NO question. Fact 1: 4^K + 9^K = M^2  12 At first glance, I would want to TEST something simple... K = 1 4^1 + 9^1 = M^2  12 4 + 9 = M^2  12 25 = M^2 M = +5 or 5 In the question, we have to track BOTH options... Is 2^1 + 3^1 = 5? The answer is YES Is 2^1 + 3^1 = 5 The answer is NO Fact 1 is INSUFFICIENT Fact 2: K = 1 This tells us NOTHING about M, so the answer COULD be YES or it COULD be NO. Fact 2 is INSUFFICIENT Combined, we have the same options that we had in Fact 1  a YES and a NO. Combined, INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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