LCM * GCF = xy
You need both. C

gmatblood wrote:If x and y are positive integers, what is the value of xy?

1. The greatest common factor of x and y is 10.
2. The least common multiple of x and y is 180.

Rule used for this :

HCF*LCM= Number 1* Number 2

Hence C It is!!

Brent@GMATPrepNow wrote:

gmatblood wrote:If x and y are positive integers, what is the value of xy?

1. The greatest common factor of x and y is 10.
2. The least common multiple of x and y is 180.

Statement 1: The greatest common factor of x and y is 10
case a: x=10 and y=10. Here, xy=100
case b: x=10 and y=20. Here, xy=200
INSUFFICIENT

Statement 2: The least common multiple of x and y is 180
case a: x=1 and y=180. Here, xy=180
case b: x=2 and y=180. Here, xy=360
INSUFFICIENT

Statements 1 & 2
There's a nice rule that says:
If x and y are positive integers, then (GCF of x and y)(LCM of x and y)=xy

Statement 1 says the GCF of x and y is 10
Statement 2 says the LCM of x and y is 180
So, from our handy rule, xy = (10)(180) = 1800
SUFFICIENT

So, the answer is C

Cheers,
Brent

Hello Brent,

Can you please tell me if the following solution is correct for showing that A and B are in-sufficient? Thanks a lot for your help.

Best Regards,
Sri

1) Let x = 100 = 2^2 x 5^2
Let y = 10 = 2^1 x 5^1

GCF of 100 and 10 = 2 x 5 = 10
xy = (100)(10) = 1000


Let x = 500 = 2^2 x 5^3
Let y = 10 = 2 x 5

GCF of 500 and 10 = 2 x 5 = 10
xy = (500)(10) = 5000


Hence, in-suff.


2) Let x = 20 = 2^2 x 5
Let y = 9 = 3^2

LCM of 20 and 9 = 2^2 x 3^2 x 5 = 180
xy = (20)(9) = 180


Let x = 36 = 2^2 x 3^2
Let y = 5

LCM of 36 and 5 = 2^2 x 3^2 x 5 = 180
xy = (36)(5) = 180


Let x = 18 = 2 x 3^2
Let y = 60 = 2^2 x 3 x 5

LCM of 18 and 60 = 2^2 x 3^2 x 5 = 180
xy = (18)(60) = 1080

Hence, in-sufficient