DS problem inference

[JbhB682]

Hi Experts -- I made up a problem

(it's an offset off an OG problem but i changed the numbers completely ..Changing the numbers will NOT be an issue because it's a Yes/No DS problem and my question is more on what i am allowed to infer per DS protocol)

Source : Made up

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

(1) 9 is in S.
(2) Whenever two numbers are in S, their product is in S.

[JbhB682]

Question : Between C and E, in a scenario like this, can i infer the answer to above the Yes/No DS is C

Reasoning --

With {9,-1,1,3} in the set -- there is NO WAY i can get to a product of 15. Hence i know the answer to the question is "No"

Hence i select "c"

Just wondering if this is accurate or is the answer E because i dont know if the DS question has given me all the values in the set (there could be more than 4 numbers in the set)

Thank you !

[Sage Pearce-Higgins]

Interesting problem. Let me give you my thinking, and I'll come to your question.

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

(1) 9 is in S.
Not sufficient.
(2) Whenever two numbers are in S, their product is in S.
Assessing this statement on it's own, I'd apply it to the initial set. If -1 and 3 are in the set, then their product, -3, must also be in the set. And if -3 and 3 are in the set, then their product, -9 must be in the set. And if -1 and -9 are in the set, the their product must be in the set. So statement 2 tells us that 9 is in the set. Hence statement 2 "includes" statement 1, meaning that the 2 statements together give me no more information than statement 2 alone. Consequently, I can eliminate answer C.
Next, I would look at the prime factors of -15. For -15 to be in the set, we'd need a 5 somewhere in the set. However, the initial integers in the set don't include a 5. So, given the initial information and statement 2, it looks like -15 isn't in the set, meaning that statement 2 looks like a sufficient "no" situation, i.e. the information is enough to answer the question, but with a "no".

However, if I understand your reasoning, we don't know what other unmentioned numbers are in set S, so that it's still possible that -15 could be in the set, and hence we don't have enough information and the answer is E. Strictly speaking, that's accurate logic. However, that way of thinking is not one I've seen in any GMAT problems. What's the source and number of the problem that you're tangentially discussing please?

[JbhB682]

Hi Sage -

below is the link to the question : https://gmatclub.com/forum/if-s-is-a-se ... 94287.html

Per the link in the question -- it's a straight C

[JbhB682]

If i can make a tweak to my original question

In this case , i think the answer is C if i am not mistaken ? My logic : with S1 and S2, its not possible to get a -15 (as -15 has a five which is not in S1 and S2), hence C is sufficient to answer the Yes/ No DS question

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

(1) 9 is in S.
(2) Whenever two numbers are in S, their product is in S.

Source : made up ( tweaked original question)

[Sage Pearce-Higgins]

Note how the original problem avoids that issue. GMAT often has clever ways of touching on something controversial or ambiguous, but then not actually testing it.

On reflection, I'd say that the answer to your made-up problem is E: we simply don't know if -15 is in set S. It could be (if we were given more information), but we can't say for sure that it is not.