Wayxi wrote:
Is the integer n a multiple of 15 ?
(1) n is a multiple of 20
(2) n + 6 is a multiple of 3
Question Stem Analysis:We need to determine whether n is a multiple of 15. Notice that if n is a multiple of 3 and 5, then n is also a multiple of LCM(3, 5) = 15.
Statement One Alone:\(\Rightarrow\) n is a multiple of 20
Since n is a multiple of 20, n is a multiple of 5. However, without knowing whether n is also a multiple of 3, we cannot determine whether n is a multiple of 15. For instance, if n = 20, n is not a multiple of 15. If n = 60, n is a multiple of 15. Since there are more than one possible answers, statement one alone is not sufficient.
Eliminate answer choices A and D.
Statement Two Alone:\(\Rightarrow\) n + 6 is a multiple of 3
Since n + 6 is a multiple of 3, we can write n + 6 = 3k for some integer k. Then, we can write n = 3k - 6 = 3(k - 2). We see that n is a multiple of 3. However, without knowing whether n is also a multiple of 5, we cannot determine whether n is a multiple of 15. For instance, if n = 3, n is not a multiple of 15. If n = 15, n is a multiple of 15. Since there are more than one possible answers, statement two alone is not sufficient.
Eliminate answer choice B.
Statement One and Two Together:From statement one, we know n is a multiple of 5. From statement two, we know n is a multiple of 3. Since n is a multiple of both 3 and 5, n is a multiple of 15. Statements one and two together are sufficient.
Answer: C _________________
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