length

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 265
Joined: 03 Jul 2012
Followed by:6 members

length

by grandh01 » Tue Sep 18, 2012 9:45 pm
What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6

OA IS B

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: 02 Apr 2010
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by [email protected] » Tue Sep 18, 2012 9:51 pm
grandh01 wrote:What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6

OA IS B
To maximize the length of an integer less then 1,000, we should minimize its prime bases.
Minimum prime base = 2
So, 2^x < 1,000
or x < 10
Maximum length = 9 for 2^9 = 512
Also, note that 2^9 is not the only integer whose length is 9, for example 2^8 * 3 = 768 < 100 also has the length of 8 + 1 = 9

The correct answer is B.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 15955
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

by [email protected] » Wed Sep 19, 2012 5:41 am
grandh01 wrote:What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6

OA IS B
I think I should mention that we're missing a pretty important part of this question. The GMAT does not expect people to know the term "length of an integer"

Excerpt from another question: For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k.
For example, if k = 24, the length of k is equal to 4, since 24 = (2)(2)(2)(3)
If k = 30, the length of k is equal to 3, since 30 = (2)(3)(5)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

User avatar
Community Manager
Posts: 1060
Joined: 13 May 2011
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Sat Sep 22, 2012 8:31 am
Brent: If such a question appears in the exam, will it contain this information - 'For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k.' ?
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 15955
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

by [email protected] » Sat Sep 22, 2012 9:35 am
neelgandham wrote:Brent: If such a question appears in the exam, will it contain this information - 'For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k.' ?
The GMAT would never assume that you know what "length of an integer" means. In fact, I don't believe there's an existing mathematical definition of this term that matches the GMAT's definition.
As such, the GMAT would supply have sort of definition accompanying this term (and any other unfamiliar/made-up terms).

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image