M7MBA wrote:What is the value of integer x?
(1) The least common multiple of x and 45 is 225.
(2) The least common multiple of x and 20 is 300.
The OA is C.
I need some help here. How can I use the statements to get the value of x?
(1) The least common multiple of x and 45 is 225.
LCM = 225 = 3^2.5^2 and 45 = 3^2.5
x = 3^n.5^2; where n = 0, 1 or 2. No unique answer value of x. Insufficient
(2) The least common multiple of x and 20 is 300.
LCM = 300 = 2^2.3.5^2 and 20 = 2^2.5
x = 2^m.3.5^2; where m = 0, 1 or 2. No unqiue answer. Insufficient
(1) and (2) combined:
From (1) and (2), we get x = 3^n.5^2 = 2^m.3.5^2
=> n = 1 and m = 0
Thus, x = 2^0.3.5^2 = 3.25 = 75. Sufficient
The correct answer:
C
Hope this helps!
-Jay
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