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# greatest prime factor

Author Message
VP
Joined: 08 Apr 2009
Posts: 1214
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012

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17 Jul 2009, 14:39
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:03) correct 0% (00:00) wrong based on 4 sessions

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what is the greatest prime factor of 4^(17)-2^(28)?

A) 2
B) 3
C) 5
D) 7
E) 11

D

--== Message from GMAT Club Team ==--

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Last edited by asimov on 19 Jul 2009, 21:27, edited 2 times in total.
Manager
Joined: 08 Jul 2009
Posts: 164

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17 Jul 2009, 18:54
Are you sure there is not a typo in this q?
Manager
Joined: 15 Apr 2008
Posts: 50
Location: Moscow

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18 Jul 2009, 01:18
sher676 wrote:
Are you sure there is not a typo in this q?

Yes, the equation should be 4^(17)-2^(28)?
VP
Joined: 08 Apr 2009
Posts: 1214
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012

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18 Jul 2009, 07:44
Sorry, I mistyped it. I just edited the original post.
Manager
Joined: 30 May 2009
Posts: 212

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19 Jul 2009, 19:38
2
KUDOS
4^17 - 2^28
= 2^34 - 2^28
= 2^28 ( 2^6 - 1)
= 2^28 (64 - 1)
= 2^28 (63)

As you can see the greatest prime factor of 63 is 7.

Hence 2^28 * 63 also has 7 as the greatest prime factor. Therefore answer should be D. What is the OA?
VP
Joined: 08 Apr 2009
Posts: 1214
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012

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19 Jul 2009, 21:27
thanks for the great explanation. the OA is D.
Manager
Joined: 27 Jun 2008
Posts: 144

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20 Jul 2009, 03:41
Grt Explanation sdrandom1 +1

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: greatest prime factor   [#permalink] 20 Jul 2009, 03:41
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