s(n) pls helppp

[mariah]

S(n) is denoted that the number of the factors n has, for example S(120)=5, because 120=2*2*2*3*5. If S(m)=4, S(q)=12, S(mq)=?

oa 16
i see its very easy but i am having problems with such kind of Q., (with functions as well)
S(m) - 2 fac.
S(q)-3 fac
both -5 fact.
and how we get 16 please explain !

damn, i think i must get some sleep!

[DeepakR]

S(m)=4 = 2*2 hence m=2 and S(q)=12=2*2*3 hence q=3. Now mq=2*3=6.
S(mq)=S(6)=3*2=2. Is the answer 2 ?

- Deepak

[gaggleofgirls]

The question appears to be missing the word "prime" becuase what you are showing are the prime factors of the number (for example with s(120) = 5 becuase the primer number 2*2*2*3*5 = 120.

s(n) will not be unique, so you can't figure out n by kn owing s(n) (for example, s(n)=5 is true for 120, but also for 32 (2*2*2*2*2) and for 48 (2*2*2*2*3) and for 3125 (5*5*5*5*5).

The key thing here is that prime factors are reduced as low as they can go, so when you multiple one number times another (for example 120 * 32), then the number of prime factors in the product will be the number of primer factors of the first number + the number of prime factors of the second number (so, for 120 * 32, there will be 5 + 5 prime factors, which will be 2*2*2*3*5*2*2*2*2*2. Both 120*32 and 2*2*2*3*5*2*2*2*2*2 = 3840).

DeepakR you were mistaking s(n) to be the number n instead of the number of prime factors of n.

So, what the question is asking is if s(m) = 4 (if the number m has 4 prime factors) and s(q) = 12 (the number q has 12 prime factors) then how many prime factors are there in the number m*q, which I have shown will be s(m) + s(q), which for this problem = 4 + 12 = 16.

-Carrie

[Ian Stewart]

Carrie has a nice solution above. I'd add that, if you are asked 'how many prime factors does 120 have?', the question normally should be taken to mean 'how many *distinct* prime factors does 120 have?' The answer to that question is three: the only primes which divide 120 are 2, 3 and 5.

The wording in the original question above is very awkward, and I'm curious to know where the question is from - you would never see such wording on the real test, and if all the questions in your book are phrased like this one, it's time to find a better book. s(n) is measuring what is known, in Number Theory, as the 'length' of n - the number of primes, distinct or not, you would need to multiply together to get n. A number like 16 has only one prime factor - 2 - but it has length four, because we need to multiply four 2's to get 16.

You do not need to know what the 'length' of a number is for the GMAT, but there is one question in GMATPrep (I think, or one of the OGs) about this concept - they explain what the 'length' means in the question itself.

[mariah]

oa 16