If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?
(1) For any integer in P, the sum of 3 and that integer is also in P.
(2) For any integer in P, that integer minus 3 is also in P.
What's the best way to determine which statement is sufficient? Can any experts show?
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Statement 1: If we know that 3 is in the set, and that for every integer in the set, the sum of 3 plus that integer is also included, we know that 3 + 3 = 6 is in the set too. Similarly, we'd know that 6 + 3 = 9 is in the set and so forth. (More abstractly, if x is in the set, then x + 3 is in the set. If x + 3 is in the set, then x + 3 + 3 is in the set, and so forth. If x = 3, then we'd include every positive multiple of 3 you can conjure.) Thus we know that all positive multiples of 3 would be included. (Of course, this raises interesting philosophical questions about infinite sets, but you get the idea.) Statement 1 alone is sufficientardz24 wrote:If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?
(1) For any integer in P, the sum of 3 and that integer is also in P.
(2) For any integer in P, that integer minus 3 is also in P.
What's the best way to determine which statement is sufficient? Can any experts show?
Statement 2: Well, we know that if 3 is in the set, then 3  3 = 0 is in the set. And we'd know that if 0 is in the set, then 0  3 = 3 is in the set. and so forth. But what if 3 is the largest element in the set? There's no way to know. All we know for sure is that 3, 0, 3, 6.... are included. This statement is not sufficient.
The answer is A