Data Sufficiency

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.

beater 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.

x = 2*3
y = 2*7
105 = 5*3*7

x*y = 2*3*2*7


Statement (1)

x = 3*3, we already know x = 2*3
x could be have 7 and 5 and cannot have 7 and 5. Insufficient.

Statement (2)

y= 5*5
for 105 we need 5*3*7. We already know, y=2*7, x = 2*3

x*y = 5*5*2*7*2*3

Sufficient.

Thus, B is the answer.

Morgoth wrote:

beater 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.

x = 2*3
y = 2*7
105 = 5*3*7

x*y = 2*3*2*7

Great breakdown, but I'd go one step further at this point:

For xy to be a multiple of 105, we need at least one 3, 5 and 7 among the factors. We have a 3 and a 7, so the only missing factor is a 5.

(1) x is a multiple of 9

Doesn't say anything about our missing 5: insufficient.

(2) y is a multiple of 25

Yay! 25 = 5*5, so we have our missing factor: sufficient.

Perfect explanation Stuart. You simply rock!

Thank you Stuart

Thanks Stuart. You made the problem much much more simple.