Data Sufficiency

BTGmoderatorDC wrote: ↑

Fri Oct 28, 2022 11:19 pm

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


OA C

Source: GMAT Prep

Target question: What is the value of xy?

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
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

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
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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
(aside: whenever a question mentions the LCM and the GCF, be sure to consider the above rule)
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
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

So, the answer is C

Cheers,
Brent