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
If S is a set of odd integers and 3 and -1...
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 394
- Joined: Sun Jul 02, 2017 10:59 am
- Thanked: 1 times
- Followed by:5 members
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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.
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.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Given: S is a set of odd integers and 3 and -1 are in SAbeNeedsAnswers 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.
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
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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
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
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
S = {-x,........-1, 3, .........x}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.
C
Source: Official Guide 2020
From (1) If 5 is in S , we cannot conclude that -15 will be in S as we have no information to say that all odd integers are part of set S. Clearly (1) is NOT Sufficient.
From (2) We know that product of two numbers of the set is also part of the set. As we know 3 and -1 already part of the Set. -3 (product of 3 and -1) will be part of the set. Now becuase of -3 is part of the set, the set now has 3 numbers {-3, -1 and 3} but as per condition given -9 should also be part of the set (product of -3 and 3) So the set will have values 3 and -1 and all multiple of 3 and 9 (positive and negitive numebrs included). The inital statement does NOT say that set S has only 2 integers 3 and -1. So we dont know if -15 or any others odd integers are part of this set or NOT. Hence (2) alone is NOT Sufficient to answer the questions
Combining (1) and (2) we know that we have 5 and -3 so we can definetely conclude that -15 will be part of Data Set S.
hence
Answer is C, Both statement together are sufficient and neither alone is sufficient to answer the question.