Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Jul 2014, 19:58

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x, y, and z are consecutive odd integers such that 31

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 30 Jul 2007
Posts: 130
Followers: 2

Kudos [?]: 9 [0], given: 0

If x, y, and z are consecutive odd integers such that 31 [#permalink] New post 24 Aug 2008, 12:50
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 1 sessions
If x, y, and z are consecutive odd integers such that 31 < x < y < z < 101, what is the greatest prime factor of the sum 2^x + 2^y + 2^z ?

A) 2
B) 7
C) 11
D) 37
E) 41
1 KUDOS received
Intern
Intern
avatar
Joined: 20 Aug 2008
Posts: 29
Followers: 0

Kudos [?]: 2 [1] , given: 0

Re: PS - consecutive exponents [#permalink] New post 24 Aug 2008, 13:19
1
This post received
KUDOS
Hi,

Its not really complex as it looks like. It sounds different and difficult.

2^(anything) will always have one prime factor, i.e. 2. There can be nothing else, eg: 2,4,8,16,32...

now coming to question.
2^x + 2^y + 2^z
= 2^x + 2^(x+2) + 2^(x+4) [They are consecutive odd nos.]
= 2^x * [ 1 + 2^2 + 2^4 ]
= 2^x * [ 1 + 4 + 16 ]
= 2^x * 21

This should have three factors 2 and 3, 7.

So Ans is 7. [Option B]
Director
Director
User avatar
Joined: 12 Jul 2008
Posts: 519
Schools: Wharton
Followers: 15

Kudos [?]: 96 [0], given: 0

GMAT Tests User
Re: PS - consecutive exponents [#permalink] New post 24 Aug 2008, 14:34
sarzan wrote:
If x, y, and z are consecutive odd integers such that 31 < x < y < z < 101, what is the greatest prime factor of the sum 2^x + 2^y + 2^z ?

A) 2
B) 7
C) 11
D) 37
E) 41


B

2^x + 2^y + 2^z = 2^x + 2^(x+2) + 2^(x+4) = (2^x)*(1+2^2+2^4)

= (2^x)*(1+4+16) = (2^x)*21 = (2^x)*3*7

The last expression is the prime factorization of 2^x + 2^y + 2^z.

So the greatest prime factor is 7.
Re: PS - consecutive exponents   [#permalink] 24 Aug 2008, 14:34
    Similar topics Author Replies Last post
Similar
Topics:
1 If x, y, and z are consecutive odd integers, with x < y < z, avohden 1 02 Oct 2013, 14:11
If x and y are consecutive odd integers, what is the sum of dobinnoli 2 15 Dec 2009, 08:33
If x and y are consecutive odd integers, what is the sum of vannu 5 10 Jul 2009, 12:04
x , y , and z are integers. Are they consecutive? 1. y amitdgr 3 02 Oct 2008, 23:49
If x and y are consecutive odd integers, what is the sum of jimmylow 3 22 Mar 2008, 01:01
Display posts from previous: Sort by

If x, y, and z are consecutive odd integers such that 31

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.