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2^2k+3^2k+12=m^2 Can you see that this equation can be of the form (a+b)^2=a^2+b^2+2ab when k=1 Otherwise this form can't be simplified any further. Insufficient

2. k=1 You don't what's m so you can't compare m with a value. Insufficient

1+2 (4^1+9^1+12)=m^2 m^2=25 m=5 when k=1 2^1+3^1=5=m Hence sufficient.

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Last edited by blink005 on 05 Oct 2011, 05:41, edited 1 time in total.

2^2k+3^2k+12=m^2 Can you see that this equation can be of the form (a+b)^2=a^2+b^2+2ab when k=1 Otherwise this form can't be simplified any further. Insufficient

2. k=1 You don't what's m so you can't compare m with a value. Insufficient

1+2 (4^1+9^1+12)=m^2 m^2=5 m=5 when k=1 2^1+3^1=5=m Hence sufficient.

Do you follow?

Oh dang, yes ok I see what you mean now. I'm not great at recognizing the quadratic forms.

While this DS question is a bit "crazy looking", the math behind it is not too difficult. It is perfect for TESTing VALUES.

We're told that K is an integer and that M > 0. We're asked if 2^K + 3^K = M. This is a YES/NO question.

Fact 1: 4^K + 9^K = M^2 - 12

IF.... K = 0 4^0 + 9^0 = M^2 - 12 2 = M^2 - 12 14 = M^2 Normally, M would have 2 values, but we were told that M is POSITIVE.... M = root14 The answer to the question (is 2^0 + 3^0 = root14?) is NO.

IF..... K = 1 4^1 + 9^1 = M^2 - 12 13 = M^2 - 12 25 = M^2 M = 5 The answer to the question (is 2^1 + 3^1 = 5?) is YES. Fact 1 is INSUFFICIENT

Fact 1: K = 1

This tells us NOTHING about the value of M, so we have no way to know if the answer to the question is YES or NO. Fact 2 is INSUFFICIENT

Combined, we know that there's just one permissible value for K (1) and the resulting calculation (from Fact 1) yields just one answer: ALWAYS YES. Combined, SUFFICIENT

Re: If k is an integer and m > 0, is 2^k + 3^k = m ? [#permalink]

Show Tags

09 Oct 2017, 12:25

EMPOWERgmatRichC wrote:

Hi All,

While this DS question is a bit "crazy looking", the math behind it is not too difficult. It is perfect for TESTing VALUES.

We're told that K is an integer and that M > 0. We're asked if 2^K + 3^K = M. This is a YES/NO question.

Fact 1: 4^K + 9^K = M^2 - 12

IF.... K = 0 4^0 + 9^0 = M^2 - 12 2 = M^2 - 12 14 = M^2 Normally, M would have 2 values, but we were told that M is POSITIVE.... M = root14 The answer to the question (is 2^0 + 3^0 = root14?) is NO.

IF..... K = 1 4^1 + 9^1 = M^2 - 12 13 = M^2 - 12 25 = M^2 M = 5 The answer to the question (is 2^1 + 3^1 = 5?) is YES. Fact 1 is INSUFFICIENT

Fact 1: K = 1

This tells us NOTHING about the value of M, so we have no way to know if the answer to the question is YES or NO. Fact 2 is INSUFFICIENT

Combined, we know that there's just one permissible value for K (1) and the resulting calculation (from Fact 1) yields just one answer: ALWAYS YES. Combined, SUFFICIENT

Hi!I had a query here: if st 2 says k =1; then we get 2^1+3^1 = m; so m = 5. Why does M have nothing as a value? Why can't we assume LHS = RHS? Would be glad to know my error here.

When dealing with DS prompts, you have to be careful to differentiate between information that is given and the question that is ASKED. Here, we're asked IF 2^K + 3^K = M.

Fact 2 tells us that K=1, but it tells us NOTHING about M. IF.... M = 5, then the answer to the question is YES. IF.... M = anything other than 5, then the answer to the question is NO. Thus, since there's more than one possible answer to the given question, Fact 2 is INSUFFICIENT.

Re: If k is an integer and m > 0, is 2^k + 3^k = m ? [#permalink]

Show Tags

10 Oct 2017, 08:35

EMPOWERgmatRichC wrote:

Hi Madhavi1990,

When dealing with DS prompts, you have to be careful to differentiate between information that is given and the question that is ASKED. Here, we're asked IF 2^K + 3^K = M.

Fact 2 tells us that K=1, but it tells us NOTHING about M. IF.... M = 5, then the answer to the question is YES. IF.... M = anything other than 5, then the answer to the question is NO. Thus, since there's more than one possible answer to the given question, Fact 2 is INSUFFICIENT.