If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?

[BTGmoderatorDC]

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.


OA C

Source: Official Guide

[Brent@GMATPrepNow]

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.


OA C

Source: Official Guide

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 S
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C