Bunuel
If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?
(1) 5 is in S.
(2) Whenever two numbers are in S, their product is in S.
Given: S is a set of odd integers and 3 and –1 are in S Target question: Is –15 in S ? Statement 1: 5 is in S So far, set S looks like this: {-1, 3, 5, . . . .}
So,
-15 may or may not be in set S Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Whenever two numbers are in S, their product is in S.So far, set S looks like this: {-1, 3, -3, -9, 9, 27, -27, -81, 81, . . . . , }
So,
-15 may or may not be in set S Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined If we have the set {-1, 3, 5, . . . .} AND we know that, whenever two numbers are in S, their product is in S, then we can see that 15 (the product of 3 and 5) is also in set S.
If 15 is in set S, then we can see that -15 (the product of -1 and 15) is also in set S.
The answer to the target question is
YES, -15 IS in set SSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent