How many different prime factors does N have? (1) 2N has 4

Oldest

Best Reply

Author

Message

TAGS:

Senior Manager

Joined: 21 Mar 2004

Posts: 447

Location: Cary,NC

Followers: 2

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

How many different prime factors does N have? (1) 2N has 4 [#permalink]

12 Jun 2005, 12:35

How many different prime factors does N have?

(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.
Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.
BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
Each statement ALONE is sufficient to answer the question.
Statements 1 and 2 TOGETHER are NOT sufficient to answer the question
_________________

ash
________________________
I'm crossing the bridge.........

Manager

Joined: 07 Mar 2005

Posts: 95

Followers: 1

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

[#permalink]

12 Jun 2005, 12:53

(1)

So with all prime number questions, 2 probably plays some roll

2n = 4 primes

odd x odd x odd x odd = odd

odd/2 = decimal

so 2 must be one of the numbers.

When 2n has 4 distinct primes then n has 3 distinct primes. Because 2 is one of the primes and we are dividing by 2 to get n.

So A is sufficient.

(2)

In order for n^2 to have 4 distinct primes the number N must have 4 distinct primes because in n^2 all primes will double. So N must have 4 different primes.

So I guess I would go with D.

However I am sure I am missing something with negative numbers of something else weird. Also, i dont think gmat has it where (1) and (2) give you different results.

Senior Manager

Joined: 30 May 2005

Posts: 374

Followers: 1

Kudos [?]: 5 [0], given: 0

[#permalink]

12 Jun 2005, 15:56

N is a positive integer - this is the unstated attention.

(I)

2N has 4 different prime factors, of which 2 must be one
2N = 2 * (p1*p2*p3) = 2 * (product of prime factors of N)
So N has 3 prime factors

(II)

If N = p1^x1*p2^x2*...*pn^xn (where p1, p2 etc are unique prime numbers and xs are their powers), then

N^2 = p1^2x1*..

So N^2 will have the same # of prime factors as N

I'll go with D as both separately give me the answer

Director

Joined: 18 Apr 2005

Posts: 553

Location: Canuckland

Followers: 1

Kudos [?]: 3 [0], given: 0

[#permalink]

12 Jun 2005, 17:07

I am seeing this question probably for the third time. it's a good question though.

for those who answered D, here is a hint what about 2*(5*7*11) and 2*(2*5*7*11)?

Senior Manager

Joined: 17 May 2005

Posts: 273

Location: Auckland, New Zealand

Followers: 1

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

[#permalink]

12 Jun 2005, 17:38

I'll pick B

because with statement A...N could either have 3 prime factors (all that 2N has except 2)...or it could have 4

statement 2 is sufficient

Director

Joined: 01 Feb 2003

Posts: 897

Location: Hyderabad

Followers: 1

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

[#permalink]

12 Jun 2005, 17:58

sparky wrote:

I am seeing this question probably for the third time. it's a good question though.

for those who answered D, here is a hint what about 2*(5*7*11) and 2*(2*5*7*11)?

hmm...the trickster it is...

B should be it!

Senior Manager

Joined: 30 May 2005

Posts: 287

Followers: 1

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

[#permalink]

13 Jun 2005, 15:05

i will go for D

the questions is about the number of different prime factor N has

St 1
2N is an even number and 2 is already a prime factor
pick number with 2 as one of the 4 prime factors
2 x3 x5x7= 21O
So 2N=210
N =105
Hence n has 2 Prime factor 5 and 6 syes

ST2
let 's pick number
N=12
12 = 2X2X3 SO 2 prime factors
N ^2 = 144
12X 12 AGAIN
2 prime factors

so N has the same numberof prime factors as N^2
SO SUffficient syes

HENCE D

Senior Manager

Joined: 21 Mar 2004

Posts: 447

Location: Cary,NC

Followers: 2

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

[#permalink]

13 Jun 2005, 17:51

mandy wrote:

Mandy,

Try stmt A using N=210 and N=105. You will get two answers and so A is insufficient.
_________________

ash
________________________
I'm crossing the bridge.........

Senior Manager

Joined: 30 May 2005

Posts: 374

Followers: 1

Kudos [?]: 5 [0], given: 0

[#permalink]

13 Jun 2005, 18:00

oops. Sparky :oops:

[#permalink] 13 Jun 2005, 18:00

		Similar topics	Author	Replies	Last post
Similar Topics:		How many different prime factors does N have? (1) 2N has	scorer	2	24 Mar 2005, 14:23
		How many different prime factors does N have? (1) 2N has 4	rahulraao	3	05 Oct 2005, 03:15
		How many different factors does the integer n have? (1) n =	humtum0	3	14 Jun 2007, 19:04
	1	How many different factors does the integer n have? (1) n =	Jcpenny	4	11 Nov 2008, 20:37
	1	How many different factors does the integer n have? (1) n =	sagarsabnis	4	05 Jan 2010, 12:18

How many different prime factors does N have? (1) 2N has 4

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

How many different prime factors does N have? (1) 2N has 4

How many different prime factors does N have? (1) 2N has 4

Main navigation

GMAT Resources

Partners

MBA Resources