Confusing GMAT wording regarding prime factors

by **Guest** Wed Jun 25, 2008 10:53 pm

Here's a problem I made up, but the wording has been kept very similar to a problem I read somewhere.

If integer K is positive and there is no remainder when 20K and divided by 192, what is the minimum number of prime factors K can have?

I know how to do this, but I am still confused. Is the question asking for the minimum number of ALL prime factors or DISTINCT prime factors?

I can reduce 20 to 5 and 192 to 48 to make the above equal to 5K/48. Since 5 is not a factor of 48, K must be a multiple of 48.

The number of prime factors of 48 is 5 (2, 3, 2, 2, 2). Since the equation is asking for the minimum number of prime factors K can have, K has to be equal to 48 (in other words, have the same number or prime factors). But my confusion is, is 5 the right answer or is 2 the answer (primes 2 and 3)?

Thanks in advance for your help! :D

by P Tue Jul 01, 2008 1:44 pm

May be the question was asking how many DIFFERENT prime factors?
Then the answer would be 2 as you will have (2 and 3).

by **RonPurewal** Wed Jul 02, 2008 4:01 am

P Wrote:May be the question was asking how many DIFFERENT prime factors?
Then the answer would be 2 as you will have (2 and 3).

yeah, this is correct. and if the problem asked for the number of prime factors including repeated factors, then the answer would be 5 (the number of factors in the prime factorization of 48).

if you saw this problem on the official test, the wording would be very exact; it would leave no room for doubt. also, it would very likely refer to the number of distinct prime factors, if for no other reason than that that's easier to write ("distinct" is one word, while a number of words are required to express the alternative).