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

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johnycute
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If m is divisible by 3, how many prime factors does m have? [#permalink] New post   04 Jan 2007, 23:44
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A
B
C
D
E

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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: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   05 Jan 2007, 04:37
1) m has two prime factore 3 and 3 … still we don’t no the total number of prime factors.

Insufficient

2) m = 3^x * a ^y * b ^z … so we know that m has 3 different prime factors but still we don’t know the total number of prime factors

Insufficeient


My answer is E
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Re: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   Updated on: 05 Jan 2007, 08:50
answer is C in my opinion....

st1: insuff, for example m=9 has only one prime factor. 18 has 2.
st2: insuff, for example m=18 (then m/3=6 has two prime factors) has 2 prime factors, and m=30 (m/3=10 has two prime factors) has 3 prime factors.

together they are sufficient:
st2 says that m/3 has 2 prime factors. so m/3=p^x*q^y where p and q are primes.
st1 claims that one of the two factors found in st2 is 3. or in other words
m/3=3^x*q^y (q is prime, x and y are integers)

from this we can infer: m = 3^(x+1)*q^y
so m has exactly 2 factors.

hence C is the answer....

Originally posted by hobbit on 05 Jan 2007, 08:23.
Last edited by hobbit on 05 Jan 2007, 08:50, edited 1 time in total.
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Re: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   Updated on: 05 Jan 2007, 09:05
For me (C) :)

Stat 1
Brings nothing to conclude. We could have 2, 3 or 4.... prime factors.

INSUFF

Stat 2
o If m = 3*2*5 then m/3 = 2*5
o If m = 3*3*5 then m/3 = 3*5

We have the possibility to have 2 or 3 prime factors for m.

INSUFF

Both (1) and (2)
We are sure that m/3 has 3 like 1 prime factor and another prime factor only.

Thus,
m = 3^a*X^b where a is the power of 3, X is a prime number and b is the power of this prime number. Meanwhile, m has 2 prime factors.

SUFF.

Originally posted by Fig on 05 Jan 2007, 08:35.
Last edited by Fig on 05 Jan 2007, 09:05, edited 1 time in total.
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Re: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   05 Jan 2007, 08:50
of course C .... i gave an explanation for C just mistakenly wrote B.... (I edited it to eliminate any confusion....)
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Re: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   05 Jan 2007, 09:33
I always get confused in these kinda problems? I cannot figure out whether the question is asking for all different prime factors or just all prime factors. I think the answer is C if the question is asking for all different prime factors, but E if its asking for all prime factors, including repeats.
Any explanation would be helpful.
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Re: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   05 Jan 2007, 10:02
800_gal wrote:
I always get confused in these kinda problems? I cannot figure out whether the question is asking for all different prime factors or just all prime factors. I think the answer is C if the question is asking for all different prime factors, but E if its asking for all prime factors, including repeats.
Any explanation would be helpful.


in the set of all factors there are no repeats, and so is the set of prime factors.
so 4 has 3 factos 1,2,4 and only one prime factor (2)
it is true that 4 can be divided twice to 2... the decomposition of 4 to multiples of prime numbers has 2 twice.... but you must differentiate between decomposition of a number into primes and the prime factors of a number.... these are two different things.
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Re: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   05 Jan 2007, 13:18
Thanks hobbit that really helps, I am taking the GMAT on Monday... Kinda freaking out at this point. :)
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Re: If m is divisible by 3, how many prime factors does m have? [#permalink] New post   05 Jan 2007, 15:14
johnycute 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/3 = multiple of 3 => m = 3 * mult of 3. m could be 3*3*1, 3*3*9824374978234, etc. Insuff => B, C or E.

(2) m/3 = p1 * p2 => m = 3 * p1 * p2. m could be 3*2*5, 3*3*5, 3*5*7, etc. Insuff => C or E.

(1&2) m = 3 * mult of 3 and m = 3 * p1 * p2 => m = 3 * 3 * prime => m has 2 prime factors: 3 and "prime".

C.



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Re: If m is divisible by 3, how many prime factors does m have? [#permalink]
05 Jan 2007, 15:14
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