lheiannie07 wrote:Is the integer z divisible by 3?
(1) The LCM of z and 12 is 12
(2) The LCM of z and 15 is 45.
We need to determine whether z/3 = integer
Statement One Alone:
The LCM of z and 12 is 12.
Using the information in statement one, we see that z could equal 1, 2, 3, 4, 6, or 12 since the LCM of any of these numbers and 12 is 12. Furthermore, we cannot determine whether z/3 is an integer. For instance, if z = 1, then z/3 is not an integer, but if z = 3, then z/3 is an integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
The LCM of z and 15 is 45.
Using the information in statement two, we see that z could only equal 9 or 45 since these two numbers are the only numbers that produce an LCM of 45 when paired with 15. If z = 9, then z/3 is an integer. If z = 45, then z/3 is an integer as well. Statement two alone is sufficient to answer the question.
Answer:
B
