mangomangodolly wrote:If m and n are positive integers, then lcm(m,n) denotes the least common multiple of m and n. Let x be a positive integer and y be a positive integer. What is the value of x?

(1) lcm(x,y) = 5y
(2) lcm(x, lcm(x,y)) = 300

Target question: What is the value of x?

Statement 1: lcm(x,y) = 5y
There are several pairs of numbers that meet this condition. Here are two:
Case a: x=300 and y=60. Here, the LCM is 300, and 300 equals 5y
Case b: x=150 and y=60. Here, the LCM is 300, and 300 equals 5y Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: lcm(x, lcm(x,y)) = 300 There are several pairs of numbers that meet this condition. Here are two:
Case a: x=300 and y=60.
Case b: x=150 and y=60.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Case a: x=300 and y=60.
Case b: x=150 and y=60.
Since we cannot answer the target question with certainty, the combined statements are not SUFFICIENT

Answer = E

Cheers,
Brent