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# If m is divisible by 3, how many prime factors does m have?

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Senior Manager
Joined: 05 Jun 2008
Posts: 289
If m is divisible by 3, how many prime factors does m have? [#permalink]

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20 Sep 2008, 10:44
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If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors.

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Manager
Joined: 21 Aug 2008
Posts: 186

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20 Sep 2008, 11:19
vivektripathi wrote:
If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors.

if m/3, then m equals 3, 6, 9, 12, 15, 18, ...

From 1)
m/3 divisible by 3...then m=9,18,27...how many prime factors? 9 = 1, 18 = 2, so INSUF.

From 2)
m/3 has two different prime factors...then m= 18, 42,...only two prime factors. so SUF.

ANS should be B.
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20 Sep 2008, 13:29
if m=25*2*3 then in that case m has 3 prime factors..m/3 will have 2 diff prime factors

if m=18 prime factors are 3 and 2..m/3 still has 2 diff prime factors..

B is not sufficient..

My ans is E..

Richardson wrote:
vivektripathi wrote:
If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors.

if m/3, then m equals 3, 6, 9, 12, 15, 18, ...

From 1)
m/3 divisible by 3...then m=9,18,27...how many prime factors? 9 = 1, 18 = 2, so INSUF.

From 2)
m/3 has two different prime factors...then m= 18, 42,...only two prime factors. so SUF.

ANS should be B.
VP
Joined: 05 Jul 2008
Posts: 1333

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20 Sep 2008, 13:45
vivektripathi wrote:
If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors.

(1) m is divisible by 3 and m/3 is divisible by 3, this means m is divisible by 9

possible m values = {9,18,27...} 9 has 2 PF (3 X3) , 18 has 3 PF ( 2X3X3) Insuff

(2) m is divisible by 3 { 3,6,9,12,15,18...} and m/3 has two diff prime factors .

Does it mean that m/3 has only 2 different prime factors such as ( 2 and 3) or can it be (2 , 2 and 3) still be two different prime factors. It seems the later but confused.
VP
Joined: 17 Jun 2008
Posts: 1285

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20 Sep 2008, 23:27
vivektripathi wrote:
If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors.

1) is insufficient since clearly m can be 21[3],27[3],54[4] etc
2)m/3 has 2 diff prime factors means that 3,2 or 2,7 means m has 3 prime factors IMO B
even im confused as to 2 prime factors(which are diff) of or set of two diff prime factors

whats the source of this question?can we expect such Q in GMAT
_________________

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Its Now Or Never

Intern
Joined: 02 Sep 2008
Posts: 45

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22 Sep 2008, 09:34
Why could not be C?

As, m/3 is divisible by 3. So one prime factor is 3.

And, m/3 has two different prime number so one is 3 and second could be any thing..

In that case, m has only two prime factors: 3 and any other.

Retired Moderator
Joined: 05 Jul 2006
Posts: 1734

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22 Sep 2008, 10:38
vivektripathi wrote:
If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors.

from tem

m= 3x

from 1

3x/3 = intiger x ( m at least have 3^2 and some other unkonwn factors

from 2

x includes 2 different prime facotrs

thus 3x has 3 different prime factors .........thus m has 3 prime factors ........B is my answer
VP
Joined: 17 Jun 2008
Posts: 1477

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22 Sep 2008, 10:50
Twoone wrote:
Why could not be C?

As, m/3 is divisible by 3. So one prime factor is 3.

And, m/3 has two different prime number so one is 3 and second could be any thing..

In that case, m has only two prime factors: 3 and any other.

You are right. It should be C. I simply overlooked this.

From stmt1 and stmt2: n/3 could be 6,12,15,18..... and hence n will always have 3 and one more prime factor.

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Re: DS-Prime Factors   [#permalink] 22 Sep 2008, 10:50
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