105 = 3*5*7Striver wrote:If positive integer X is a multiple of 6 and positive integer Y is a multiple of 14, is XY a multiple of 105?
(1) X is a multiple of 9.
(2) Y is a multiple of 25.
For xy to be a multiple of 105, it must be divisible by 3, 5 and 7.
x is a multiple of 6, so x is divisible by 2 and 3. Thus xy is divisible by 3.
y is a multiple of 14, so y is divisible by 2 and 7. Thus xy is divisible by 7.
What we don't know is whether xy is divisible by 5.
Question rephrased: Is x or y a multiple of 5?
Statement 1: x is a multiple of 9
If x = 54 and y = 14, then neither x nor y is a multiple of 5.
If x = 54 and y = 140, then y is a multiple of 5.
INSUFFICIENT.
Statement 2: y is a multiple of 25
Thus, y is a multiple of 5.
SUFFICIENT.
The correct answer is B.
