algebra

[shrutib]

x and y are positive integers. is xy multiple of 8?

1.the greatest common divisor of x and y is 10.
2. the least common multiple of x and y is 100

[Brent@GMATPrepNow]

x and y are positive integers. is xy multiple of 8?

1.the greatest common divisor of x and y is 10.
2. the least common multiple of x and y is 100

Note: Whenever you see information about the greatest common divisor (GCD) and the least common multiple (LCM), you should keep the following rule in mind:

(GCD of x and y)(LCM of x and y) = xy

Statement 1: The greatest common divisor of x and y is 10
case a) x=10 and y=10, in which case xy is not a multiple of 8
case b) x=10 and y=80, in which case xy is a multiple of 8
NOT SUFFICIENT

Statement 2: The least common multiple of x and y is 100
case a) x=100 and y=1, in which case xy is not a multiple of 8
case b) x=100 and y=100, in which case xy is a multiple of 8
NOT SUFFICIENT


Statements 1 & 2
Use our handy formula:
(GCD of x and y)(LCM of x and y) = xy
(10)(100) = xy
1000 = xy
xy is definitely a multiple of 8
SUFFICIENT
Answer = C


Cheers,
Brent

[shrutib]

Thanks a lot for the quick response.. You have some awesome tricks.. Thanks one again.

[1947]

Alternative way to combine 1 and 2 is

1 tells us that both x and y have 2 as their factors
2 tells us that either of x and y have two 2's as its factors.

If we combine both it gives us that their are three 2's in xy

GCF*LCM = x*y is a cool way thoguh