Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

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.

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.. _________________

"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde

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..

Well, the real GMAT question will ask about "distinct primes", to avoid such technicalities, though we can say that it's implied here. _________________

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]
25 Mar 2013, 19:52

Hi Bunuel,

I answer B, since statement 2 says it has 2 different primes factor (3 included for sure) answering directly to the question. Why (2) it's insufficient? I didn't understand your approach, please explain. Thanks! _________________

MV "Better to fight for something than live for nothing.” ― George S. Patton Jr

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]
26 Mar 2013, 00:40

Expert's post

marcovg4 wrote:

Hi Bunuel,

I answer B, since statement 2 says it has 2 different primes factor (3 included for sure) answering directly to the question. Why (2) it's insufficient? I didn't understand your approach, please explain. Thanks!

The second statement says that m/3 has two different prime factors, NOT m.

If m = 18, then m/3 = 6 (6 has two different prime factors: 2, and 3). 18 has two different prime factors 2 and 3. If m = 30, then m/3 = 10 (10 has two different prime factors: 2, and 5). 30 has three different prime factors 2, 3 and 5.

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]
27 Mar 2013, 15:59

@Bunuel

second statement says m has two different prime factors. Can it be taken as it has only 2 different prime factors? if m/3 is 42, the second statement is still true!?

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]
28 Mar 2013, 02:58

Expert's post

Amateur wrote:

@Bunuel

second statement says m has two different prime factors. Can it be taken as it has only 2 different prime factors? if m/3 is 42, the second statement is still true!?

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

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.

Hi Bunnel,

Can you please explain me the statement.

(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.

I didn't get how you got the answer after combing the two _________________

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]
18 Feb 2014, 05:12

My way:

First of all we are told that m = 3k where 'k' is an integer. How many different prime factors does 'm' have?

Statement 1: m = 9k, nothing about prime factors Statement 2: m/3 has two different prime factors. Well if m = 3k then 3k/3 = k has two different prime factors but no info on 'm' yet. 'k' could have 3 among its factors or not. Therefore since we are asked about different prime factors then this statement alone is not sufficient.

Statements 1 and 2 together tell us that 9k/3=3k has two different prime factors. Since m = 3k then it must be that 'k' is another different prime factors Therefore C is our answer

Hope this helps Cheers J

gmatclubot

Re: If m is divisible by 3, how many prime factors does m have?
[#permalink]
18 Feb 2014, 05:12

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...