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If O = {x : x is a natural number, x is a multiple of 4, and x < 18}, what is O?
Correct answer: A
The governing idea is conversion from set-builder form to roster form. We need natural numbers that are multiples of 4 and are strictly less than 18. Listing the positive multiples of 4 gives 4, 8, 12, 16, 20, and so on. The inequality x < 18 keeps 4, 8, 12, and 16, but excludes 20 and every larger multiple. Thus O = {4, 8, 12, 16}, so option A is correct. Option B wrongly includes 20, option C includes numbers that are not all multiples of 4 and omits 12, while option D includes 18, which is not a multiple of 4 and also fails the strict inequality.
If A = {3, 6, 9, 12, 15}, which is the most suitable description of A?
Correct answer: A
The governing concept is recognizing a set through a common divisibility pattern. Starting with 3 and adding 3 repeatedly gives 3, 6, 9, 12, and 15. These are exactly the positive multiples of 3 that are no greater than 15, so option A describes every member and excludes numbers not in the set. Option B is incorrect because the positive factors of 15 are 1, 3, 5, and 15; numbers such as 6 and 12 are not factors of 15. Option C is incorrect because 6, 9, 12, and 15 are composite rather than prime. Option D would describe a small set such as {1, 2, 3}, not the given five-element set.
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