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If S is a set of odd integers and 3 and -1...

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If S is a set of odd integers and 3 and -1...

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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.

C

Source: Official Guide 2020

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Statement 1 isn't sufficient, since it just tells us one other value in the set.

Statement 2 also isn't sufficient alone -- while using it we can determine many other values in the set (all the positive and negative powers of 3 are in the set), we have no way to know if -15 is in the set, since we can't make -15 as a product of things we know are in the set already (we'd need the prime divisors of 15, and while we have a 3, we don't know if we have a 5).

Using both Statements, since 3 and 5 are both in the set, their product, 15, must be, and then if -1 and 15 are in the set, their product -15 must be. So the two statements together are sufficient and the answer is C.

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

Answer: C

Cheers,
Brent

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Hi All,

We're told that Set S is a set of ODD INTEGERS and 3 and -1 are in S. We're asked if -15 in S. This question is more about logic and basic Arithmetic than anything else, so taking the proper notes - and thinking about the possibilities - is all that's really needed to beat it.

(1) 5 is in S.

Based on the information in Fact 1, we now know that at least 3 numbers are in Set S: -1, +3 and +5. This is clearly not enough information to determine whether -15 is also in the Set or not.
Fact 1 is INSUFFICIENT

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

With the information in Fact 2, we can determine some of the additional numbers in Set S. With -1 and +3, we know that (-1)(+3) = -3 is also in the Set. With -3 included, we also know that (-3)(+3) = -9 is in the set. With that integer we also have (-1)(-9) = +9 as well as -27 and +27. You might recognize that we'll end up with a bunch of numbers that are 'powers of 3' and their negative equivalents. This still doesn't tell us whether -15 is in the Set or not.
Fact 2 is INSUFFICIENT

Combined, we know...
(1) 5 is in S.
(2) Whenever two numbers are in S, their product is in S.

From Fact 2, we know that -3 is in the Set, so since +5 is also in the set, we know for sure that (-3)(+5) = 15 will be in the Set (and the answer to the question is ALWAYS YES).
Combined, SUFFICIENT

Final Answer: [spoiler=]C[/spoiler]

GMAT assassins aren't born, they're made,
Rich

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