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

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Manager
Joined: 17 Dec 2005
Posts: 162
If k is an integer greater than 1, is k equal to 2^r for [#permalink]

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16 Jun 2006, 18:18
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If k is an integer greater than 1, is k equal to 2^r for some positive integer r?

c1. k is divisible by 2^6

c2. k is not divisible by any odd integer greater than 1.
CEO
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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16 Jun 2006, 18:25
B

St1: K is a multiple of 2^6. So can't say that its 2^r. It may be (2^7) or may not be (3*2^6): INSUFF

St2: If K is not divisible by any odd integer then it is divisible only by 2 and numbers which are raised to the powers of 2. SUFF.

K is not divisible by 6,10,14 etc. Its divisible by only 2,4,8,16 because factors of these numbers are all even. So K can be represented in 2^r.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Intern
Joined: 23 Jun 2006
Posts: 26

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04 Jul 2006, 11:11
ps_dahiya wrote:
B

St1: K is a multiple of 2^6. So can't say that its 2^r. It may be (2^7) or may not be (3*2^6): INSUFF

St2: If K is not divisible by any odd integer then it is divisible only by 2 and numbers which are raised to the powers of 2. SUFF.

K is not divisible by 6,10,14 etc. Its divisible by only 2,4,8,16 because factors of these numbers are all even. So K can be represented in 2^r.

Intern
Joined: 23 Jun 2006
Posts: 26

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04 Jul 2006, 11:12
sorry, i just got it... i missed the "not divisible by any odd number" part
Senior Manager
Joined: 08 Jun 2004
Posts: 495
Location: Europe

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04 Jul 2006, 23:49
Yes 'B' it is,
Great explanation ps_dahiya.
SVP
Joined: 30 Mar 2006
Posts: 1728

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05 Jul 2006, 00:07
B

1) let K = 2^7 *5
It is divisible by 2^6 but k not = 2^r

2) K is not divisble by any odd number greater than 2

Hence the value of K has to be 2 and allpowers of 2

Hence B
05 Jul 2006, 00:07
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