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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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Re: DSPrime Factors [#permalink]
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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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Re: DSPrime Factors [#permalink]
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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.



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Re: DSPrime Factors [#permalink]
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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.



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Re: DSPrime Factors [#permalink]
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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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Re: DSPrime Factors [#permalink]
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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.
So, Answer is C.



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Re: DSPrime Factors [#permalink]
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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



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Re: DSPrime Factors [#permalink]
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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.
So, Answer is C. 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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