melguy wrote:
What is the value of integer x?
1) The LCM of x and 45 is 225
2) The LCM of x and 20 is 300
We need to determine the value of x.
Statement One Alone:
The LCM of x and 45 is 225.
We can start by breaking 45 and 225 into prime factors.
45 = 3^2 x 5^1
225 = 3^2 x 5^2
In other words, 3^2 x 5^1 and some number x have an LCM of 3^2 x 5^2.
Thus, x could be the following:
5^2 = 25
5^2 x 3^1 = 75
5^2 x 3^2 = 225
Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
The LCM of x and 20 is 300.
We can start by breaking 20 and 300 into prime factors.
20 = 2^2 x 5^1
300 = 2^2 x 3^1 x 5^2
In other words, 2^2 x 5^1 and some number x have an LCM of 2^2 x 3^1 x 5^2.
Thus, x could be the following:
3^1 x 5^2 = 75
3^1 x 5^2 x 2^1 = 150
3^1 x 5^2 x 2^2 = 300
Statement two is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using statements one and two we see that the only value of x that fulfills both statements is 75.
Answer:
C
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