BTGmoderatorDC 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
OA C
Source: GMAT Prep
Target question: Is xy a multiple of 8?
Statement 1: The greatest common factor of x and y is 10
There are several values of x and y that satisfy statement 1. Here are two:
case a: x=10 and y=10. Here, xy=100, which means
xy is NOT a multiple of 8
case b: x=10 and y=20. Here, xy=200, which means
xy IS a multiple of 8
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 100
There are several values of x and y that satisfy statement 2. Here are two:
case a: x=1 and y=100. Here, xy=100, which means
xy s NOT a multiple of 8
case b: x=2 and y=100. Here, xy=200, which means
xy IS a multiple of 8
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 100
So, from our handy rule, xy = (10)(100) = 1,000, which means
xy IS a multiple of 8
Since we can now answer the
target question with certainty, the combined statements are SUFFICIENT
So, the answer is C
Cheers,
Brent
