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Re: If k is an integer greater than 1, is k wqual to 2^r for [#permalink]

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19 Sep 2005, 21:27

But 6 is divisible by an odd integer other than 1. It's divisible by 3.

The only positive integers greater than 1 that don't have any odd factors greater than 1 are powers of 2. So statement 2 is sufficient on its own.

... And once again I just answered my own question. (I feel dumb now). I'd initially answered D, thinking that statement 1 was also sufficient in itself. But of course, 192 is a multiple of 64, and 192 is not a power of 2. So D is wrong. B it is.

Re: If k is an integer greater than 1, is k wqual to 2^r for [#permalink]

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19 Sep 2005, 21:31

coffeeloverfreak wrote:

But 6 is divisible by an odd integer other than 1. It's divisible by 3.

The only positive integers greater than 1 that don't have any odd factors greater than 1 are powers of 2. So statement 2 is sufficient on its own.

... And once again I just answered my own question. (I feel dumb now). I'd initially answered D, thinking that statement 1 was also sufficient in itself. But of course, 192 is a multiple of 64, and 192 is not a power of 2. So D is wrong. B it is.

You right. This is really tricky if one doesnt know these number system properties (especially if she is not good in number picking like me).

Re: If k is an integer greater than 1, is k wqual to 2^r for [#permalink]

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05 Oct 2005, 19:24

i think it is E.

II) states that it is not divisible by any odd number > 1, which implies k is even. however, what we need to say if K is a power of 2. For example, 10 is even , but is not a power of 2. I am assuming here that the notation, 2^ r , denotes, 2 raised to r and not 2 multiplied by r.

Re: If k is an integer greater than 1, is k wqual to 2^r for [#permalink]

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05 Oct 2005, 20:04

We're given k > 1, r > 0. We're asked if k = 2^r

From statement 1, we're told k is a multiple of 2^6. This could be 3(2^6), 4(2^6). Since there are so many values of k, we can't tell.

From statement 2, we're told k is not divisbile by any odd integer greater than 1. This means k is even and a power of 2. Any other even number that has a prime factor other than 2 will be divisible by any odd integer > 1. For e.g., if k=18, then 18 = 3*3*2. It's divisible by 3. However, if k = 16, then 2^4 and this is equal to 2^r if r is 4.

The answer B is correct if we're asked if k can be represented in the form 2^r where r is a positive value.

However, we're asked here if k EQUALS 2^r and we do not have information for r.