Bunuel wrote:
Is m a multiple of 6?
(1) More than 2 of the first 5 positive integer multiples of m are multiples of 3.
(2) Fewer than 2 of the first 5 positive integer multiples of m are multiples of 12.
Does this mean that:
(1) m is any number that is a multiple of 3?
If 3, then 3, 6, 9, 12, 15 are multiples of m.
If 6, then 6, 12, 18, 24, 30 are multiples of m.
If so, then m could be any multipe of 3, and all of them are not multiples of 6.
(2) 12, 24, 36, 48, 60 are multiples of 12.
What am i missing here? If m is 1 then fewer than 2 of the first 5 are multiples of 12, obviously. The first five is 1, 2, 3, 4, 5.
If m is 2, then fewer than 2 of the first 5 are multiples of 12. The first five is 2, 4, 6, 8, 10.
How could we tell anything from this information?
I feel that I dont understand the word multiple correctly even after reading definitions about it.
Edit: I think I get it.
1) if 3, then 3, 6, 9, 12, 15 are multiples of m. if 6, then (6), 9, (12), 15, (18) and thus more than 2.
2) says that if m is 6, then the five multiples would have been 6, 12, 18, 24, 30, i.e. at least 2 multiples of 12 (12, 24), so m can not be 6. For every other number than 6, or multiples of 6 or 12, statement 2 holds true. So the answer is No, m is not a multiple of 6.
Good lord, this took me 30 minutes to grab. However, many a mickle makes a muckle!