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
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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If m and n are positive integers
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mangomangodolly
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1. LCM of x,y is 5y ,here we can assume x= 5.a & y = k.a; in this scenario LCM would be 5.k.a= 5y= k.x
Therefore depending on value of a, x can assume multiple values hence insufficient.
2. lcm(x, lcm(x,y)) = lcm(x,y) = 300
for 300 to be lcm of two numbers there are couple of contenders (12,25);(4,75)
hence IMO E
Therefore depending on value of a, x can assume multiple values hence insufficient.
2. lcm(x, lcm(x,y)) = lcm(x,y) = 300
for 300 to be lcm of two numbers there are couple of contenders (12,25);(4,75)
hence IMO E
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Target question: What is the value of x?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
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
Last edited by Brent@GMATPrepNow on Thu Sep 03, 2015 1:37 pm, edited 1 time in total.
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