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[magical cook]

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.

[kajcha]

IMO C

[magical cook]

Unfortunately answer is different.

Can anyone help?

[ratindasgupta]

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.

if x is multiple of 6, then it has 2 and 3 as factors. y similarly has 2 and 14 as factors. so xy will atleast have 2, 3 and 7 as factors.

Now 105 has 3, 5 and 7 as factors. so for xy to be divisible by 105, xy must also contain 5 as one of its factors.

1) if x is a multiple of 9, then x is may or may not be a multiple of 5 also. and y too may or may not be a multiple of 5. So INSUFF

2) since y is a multiple of 25, y is also a multiple of 5. So xy is a multiple of 3, 5 and 7. Hence it is a multiple of 105. So SUFF.

Answer is B.

[magical cook]

Thank you!

[ratindasgupta]