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Re: If k is an integer, is 2^k + 3^k = m ? [#permalink]
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
_________________

Re: If k is an integer, is 2^k + 3^k = m ? [#permalink]
30 Aug 2013, 03:41

1

This post received KUDOS

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.
_________________

Re: If k is an integer, is 2^k + 3^k = m ? [#permalink]
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

gmatclubot

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