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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If P is a set of integers and 3 is in P, is every positive m ##### This topic has 1 expert reply and 0 member replies ## If P is a set of integers and 3 is in P, is every positive m 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? ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2666 messages Followed by: 125 members Upvotes: 1153 GMAT Score: 770 ardz24 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 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 sufficient 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 _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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