BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Distinct prime divisors

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 385
Joined: Mon Apr 16, 2012 8:40 am
Location: Pune, India
Thanked: 186 times
Followed by:29 members

by aneesh.kg » Thu Apr 19, 2012 6:56 am
One of the factors of 2N is 2, which is prime. But if 2N has just one prime divisor, N cannot be prime and has to be of the form 2^n. (If N is has any other prime factor but 2, 2N will also have that prime factor). So, N has (n+1) factors and we don't know a specific value.
Statement (1) is insufficient.

Similar logic holds for the Statement(2). If 3 is one of the factors, then N cannot be prime and has to be of the form 3^n(If N is has any other prime factor but 3, 3N will also have that prime factor). So, N has (n+1) factors and we don't know a specific value.
Statement (2) is also insufficient.

Lets try to combine the two statements. If N is of the form 2^n and 3^n, then n = 0 and N has to be 1.
Thus N has just one positive factor and the answer is (C).
Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Apr 19, 2012 7:19 am
rahulvsd wrote:How many distinct prime divisors does a positive integer N have?

A. 2N has one prime divisor
B. 3N has one prime divisor

[spoiler]OA: C. [/spoiler]
Statement 1: 2N has one prime divisor
2 is a prime divisor of 2N.
For 2N to have no OTHER distinct prime divisors, N = 2^x.
If N = 2^0 = 1, then it has NO prime divisors.
If N = 2^x (where x>0), then it has ONE distinct prime divisor: the number 2 itself.
INSUFFICIENT.

Statement 2: 3N has one prime divisor
3 is a prime divisor of 3N.
For 3N to have no OTHER distinct prime divisors, N = 3^x.
If N = 3^0 = 1, then it has NO prime divisors.
If N = 3^x (where x>0), then it has ONE distinct prime divisor: the number 3 itself.
INSUFFICIENT.

Statements 1 and 2 combined:
The only value that satisfies both statements is N=1, in which case N has NO distinct prime divisors.
SUFFICIENT.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1