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If k is an integer greater than 1, is k equal to 2^r for

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

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New post 27 Oct 2008, 10:49
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If k is an integer greater than 1, is k equal to \(2^r\) for some positive integer r?

(1) k is divisible by \(2^6\)

(2) k is not divisible by any odd integer great than 1



Please explain your answer.

Thanks

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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 11:01
1)you can have 192/64 or 128/64 so insuff
2) K is even, insuff

together insuff

E
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 11:10
tarek99 wrote:
If k is an integer greater than 1, is k equal to \(2^r\) for some positive integer r?

(1) k is divisible by \(2^6\)

(2) k is not divisible by any odd integer great than 1

Please explain your answer.

Thanks


I will go for (B)

(1) When k= 2^8, then, Yes.
When k= 3* 2^8, then No. Insuff
(2) Any integer not divisible by an odd integer greater than 1 could be represented in the form 2^r. Hence suff.
I couldn't think of any example otherwise.
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 11:29
leonidas wrote:
tarek99 wrote:
If k is an integer greater than 1, is k equal to \(2^r\) for some positive integer r?

(1) k is divisible by \(2^6\)

(2) k is not divisible by any odd integer great than 1

Please explain your answer.

Thanks


I will go for (B)

(1) When k= 2^8, then, Yes.
When k= 3* 2^8, then No. Insuff
(2) Any integer not divisible by an odd integer greater than 1 could be represented in the form 2^r. Hence suff.
I couldn't think of any example otherwise.


I didn't understand your analysis of statement 2. Would you please explain how?
thanks
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 11:31
If k is an integer greater than 1, is k equal to 2^r for some positive integer r?

(1) k is divisible by \(2^6\)

(2) k is not divisible by any odd integer great than 1

from one

K = x*2^6............x can = 2 or any intiger..........insuff

from2

k is intiger and it is not deviable by any odd intiger ( it can be odd eg 7/5) or even ( 4/3)...insuff

both

K =X*2^6 AND STILL X CAN BE ODD OR EVEN.........INSUFF

E
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 11:40
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tarek99 wrote:
leonidas wrote:
tarek99 wrote:
If k is an integer greater than 1, is k equal to \(2^r\) for some positive integer r?

(1) k is divisible by \(2^6\)

(2) k is not divisible by any odd integer great than 1

Please explain your answer.

Thanks


I will go for (B)

(1) When k= 2^8, then, Yes.
When k= 3* 2^8, then No. Insuff
(2) Any integer not divisible by an odd integer greater than 1 could be represented in the form 2^r. Hence suff.
I couldn't think of any example otherwise.


I didn't understand your analysis of statement 2. Would you please explain how?
thanks


=> It is easy for us to find an integer greater than 1 that is not divisible by an odd interger (>1) and represent it in the form of 2^r. For example- 2^8 is not divisible by any odd integer.
=>In order to prove that (2) is insuff, we have to find an integer which is not divisble by an odd integer and that cannot be represented in the form of 2^r. There is no number greater than 1 which satisfies this condition. Any integer which cannot be divisible by an odd integer is an even integer which can be represented in the form of 2^r.

Not sure, if I confused you more :)
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 12:53
i too think ans should be E..

K>1 thats what the stem says..its positive,

2) says its not a multiple of any odd integer which means k=2^r

we could have something like 7/5
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 17:21
tarek99 wrote:
If k is an integer greater than 1, is k equal to \(2^r\) for some positive integer r?

(1) k is divisible by \(2^6\)

(2) k is not divisible by any odd integer great than 1

Please explain your answer.

Thanks


k = some positive integer greater than 1

the question stem is asking is k of the form \(2^r\). When will it be of this form ? when it has only 2 as its prime factor.

(1) k is divisible by \(2^6\). This just means k has \(2^6\) as its factor, but it does not say this is the ONLY factor. There could be some odd factors as well !

(2) k is not divisible by any odd integer > 1. This means k has only even factors. When you have only even factors, it can be written in the \(2^x\) form.

I pick B.
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 17:28
amitdgr wrote:

(2) k is not divisible by any odd integer > 1. This means k has only even factors. When you have only even factors, it can be written in the \(2^x\) form.

I pick B.


Let's say k has 6 as a factor. which means k = 6L with out knowing L we can't write k in the form of 2 ^ r for example if L=3, K=18 Can 18 be written as a factor of 2 ^ r? NO. if k=8L and L =4 K= 2 ^ 5.

Am I doing any thing wrong?
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 17:36
icandy wrote:
amitdgr wrote:

(2) k is not divisible by any odd integer > 1. This means k has only even factors. When you have only even factors, it can be written in the \(2^x\) form.

I pick B.


Let's say k has 6 as a factor. which means k = 6L with out knowing L we can't write k in the form of 2 ^ r for example if L=3, K=18 Can 18 be written as a factor of 2 ^ r? NO. if k=8L and L =4 K= 2 ^ 5.

Am I doing any thing wrong?


The way i understood the statement in the problem, if k has only even factor, it has only even prime factors.

k=6 means k has 3 as one of its factors.

I may be completely wrong.
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 17:50
amitdgr wrote:
icandy wrote:
amitdgr wrote:

(2) k is not divisible by any odd integer > 1. This means k has only even factors. When you have only even factors, it can be written in the \(2^x\) form.

I pick B.


Let's say k has 6 as a factor. which means k = 6L with out knowing L we can't write k in the form of 2 ^ r for example if L=3, K=18 Can 18 be written as a factor of 2 ^ r? NO. if k=8L and L =4 K= 2 ^ 5.

Am I doing any thing wrong?


The way i understood the statement in the problem, if k has only even factor, it has only even prime factors.

k=6 means k has 3 as one of its factors.

I may be completely wrong.


Ok. I get it. I got it wrong. K cannot have 6 as a factor because it will automatically make 3 a factor and that is not in line with (2) That makes only 2 the remaining factor.
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Re: DS: Try this GMATprep problem [#permalink]

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New post 27 Oct 2008, 17:52
Agree with amitdgr.
"k is not divisible by any odd integer great than 1"

Can someone show an integer which is not divisible by an odd integer(>1) and which could not be expressed in the form of 2^r?

Is k equal to 2^r? is a YES from (2).
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Re: DS: Try this GMATprep problem [#permalink]

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New post 28 Oct 2008, 16:36
Initially I had picked E :roll:
Changed to B :)

Good problem tarek99, and good explanation leonidas
+1 for both of you
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Re: DS: Try this GMATprep problem [#permalink]

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New post 28 Oct 2008, 16:43
Ahh the key word is any odd integer..


I initially went with B and changed to E but now I agree with B

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Re: DS: Try this GMATprep problem   [#permalink] 28 Oct 2008, 16:43
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