rickyishere wrote:I have a conceptual issue on questions like these, can someone please suggest a good approach ?
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
Thanks in advance
-Ricky
always break down numbers and variables by primes.
x = 2*3 (because x is divisible by 6 so X must have all the prime factors of 6)
y = 2*7 (because y is divisible by 14 so y must have all the prime factors of 14)
105 = 5*3*7
we want to know whether xy = (105) (some other number) or another example would be 6 = 3x2
we already know that xy have the following prime factors:
x*y = 2*3*2*7
to check whether a number is a multiple of another number, it must have all the prime factors of that other number.
so
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.
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
