clinton wrote:Is the integer n a multiple of 15?
1.) n is multiple of 20
2.) n + 6 is a multiple of 3?
Could someone show me an easier way to solve without choosing numbers?
Solution:
We need to know whether n is a multiple of 15 or not.
Now 15 = 3*5.
So n should have both 3 and 5 as its factors.
Let us consider first (1) alone.
It only means that 5 is a factor of n but it does not necessarily tell us whether n is a multiple of 15 or not.
Take for example 40.
40 is a multiple of 20 but not a multiple of 15 whereas 60 is a multiple of 20 and 15 both.
Or (1) alone is not sufficient.
Let us consider (2) alone.
It says that n+6 is a multiple of 3.
This only tells us that n is a multiple of 3 but we do not come to know whether it is a multiple of 5 or not.
Or (2) alone is not sufficient.
Next combine both statements together and check.
On combining we have that n is a multiple of 3 and 5 both.
Hence it is a multiple of 15.
The correct answer is (C).
