If K is a multiple of 11, is KL a multiple of 154 ?
K=11*m with m a constant
KL=11*m*L
1) L has all same factors as 42
42=2*3*7
So L has at least these factors: 2, 3, 7
In that case L only has these factors, we can write:
KL=11*m*2*3*7
KL=154*3*m because 154=11*7*2 (you can start by looking at what are the factors of 154 in order to know what you are looking for)
So you see that KL is a multiple of 154.
Sufficient.
2) K is divisible by 21
It also means K is a multiple of 21, which can be written like that:
K=21*p (with p a constant)
K=11*m with m a constant, that we have from the beginning
You can see that K is a multiple of 21 and 11
So K will have among its factors: 11, 7, 3
(154=11*7*2, so we need a 2) The problem is that we do not know if K has a factor of 2, L could also have or not a 2. So we do not know if KL is a multiple of 154.
[For example imagine the smallest value of K which is 21*11=231. That is a not a multiple of 154. If L=2 so KL = 462 and it is a multplie of 154. If L=3, KL is not a multiple of 154]
Insufficient.
So it is A for me.
That's not so long, but I can be wrong. The important thing is to translate "x is a multiple of y" into "x=y*k with k a constant".
Tell me if it's ok.
