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26 Jan 2012, 06:36
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
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Question Stats:
43% (01:26) correct
57%
(01:39)
wrong
based on 213
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If m is divisible by 3, how many prime factors does m have?
(1) \(\frac{m}{3}\) is divisible by 3
(2) \(\frac{m}{3}\) has two different prime factors
(1) \(\frac{m}{3}\) is divisible by 3
(2) \(\frac{m}{3}\) has two different prime factors
26 Jan 2012, 07:50
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LM
If m is divisible by 3, how many prime factors does m have?
(1) \(\frac{m}{3}\) is divisible by 3 --> \(\frac{m}{3}=3k\) --> \(m=3^2*k\) --> \(m\) has at least one prime 3, but it can have more than one, in case \(k\) has some number of other primes. Not sufficient
2) \(\frac{m}{3}\) has two different prime factors --> first of all 3 is a factor of \(m\), so 3 is one of the primes of \(m\) for sure.
Now, if power of 3 in \(m\) is more than or equal to 2 then \(m\) will have have only two prime factors: 3 and one other, example: \(m=18\), (as in \(\frac{m}{3}\) one 3 will be reduced, at least one more 3 will be left, plus one other, to make the # of different factors of \(\frac{m}{3}\) equal to two. Thus \(m\) will have 3 and some other prime as a prime factors).
But if \(m\) has 3 in power of one then \(m\) will have 3 prime factors: 3 and two others, example \(m=30\) (one 3 will be reduced in \(m\) and \(\frac{m}{3}\) will have some other two prime factors, which naturally will be the primes of \(m\) as well). Not sufficient.
(1)+(2) From (1) \(3^2\) is a factor of \(m\), thus from (2) \(m\) has only two distinct prime factors: 3 and one other. Sufficient.
Answer: C.
26 Jan 2012, 08:04
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Just one thought bunuel..... The question asks for "how many prime factors". It does not ask for "how many DIFFERENT prime factors". If combined the statements tell us that \(3^2\) is a prime factor and there is a different prime factor as well, we still do not know how many times that "different" prime factor repeats. So my question is, when the question ask for number of prime factors, does it mean we should be looking at "different" prime factors or should we count the different factors each time they are repeated as well..
