500
If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45
What is "k+30" (D)
Explanation
Difficulty: Medium
Since k is divisible by 2, 3, and 15, k must be a multiple of 30, as 30 is the least common multiple of 2, 3, and 15. Some multiples of 30 are 0, 30, 60, 90, and 120.
If you add two multiples of 30, the sum will also be a multiple of 30. For example, 60 and 90 are multiples of 30 and their sum, 150, is also a multiple of 30.
If you add a multiple of 30 to a number that is not a multiple of 30, the sum will not be a multiple of 30. For example, 60 is a multiple of 30 and 45 is not. Their sum, 105, is not a multiple of 30.
The question asks which answer choice is divisible by 2, 3, and 15; that is, which answer choice is a multiple of 30. All the answer choices are in the form of "k plus a number." Only choice (D), k + 30, has k added to a multiple of 30. The sum of k and 30 is also a multiple of 30, so the correct answer is choice (D).