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

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

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New post 26 Apr 2019, 01:57
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 26 Apr 2019, 10:32
5
1
1
Chethan92 wrote:
S = {3,-1, other odd integers}

From S1:

5 is in S.
We cannot say whether -15 is in Set S.
Insufficient.

From S2:

Whenever two numbers are in S, their product is in S.
Again, No much info.
Insufficient.

Combining both:

Again, Insufficient.
we can say that 3*5 = 15 is present in set S.
But, no info about -15

E is the answer.


I think that answer should be C. Statement 2 says that whenever 2 number are in the set their product is also in the set. It means that 3 x -1 so -3 is in the set. As first statement mentions that 5 is in the set we can conclude that -15 is for sure in the set.

Then C should be answer.
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 26 Apr 2019, 09:53
1
S = {3,-1, other odd integers}

From S1:

5 is in S.
We cannot say whether -15 is in Set S.
Insufficient.

From S2:

Whenever two numbers are in S, their product is in S.
Again, No much info.
Insufficient.

Combining both:

Again, Insufficient.
we can say that 3*5 = 15 is present in set S.
But, no info about -15

E is the answer.
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 26 Apr 2019, 10:34
1
solikon wrote:
Chethan92 wrote:
S = {3,-1, other odd integers}

From S1:

5 is in S.
We cannot say whether -15 is in Set S.
Insufficient.

From S2:

Whenever two numbers are in S, their product is in S.
Again, No much info.
Insufficient.

Combining both:

Again, Insufficient.
we can say that 3*5 = 15 is present in set S.
But, no info about -15

E is the answer.


I think that answer should be C. Statement 2 says that whenever 2 number are in the set their product is also in the set. It means that 3 x -1 so -3 is in the set. As first statement mentions that 5 is in the set we can conclude that -15 is for sure in the set.

Then C should be answer.


Yes, correct. :)
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 27 Apr 2019, 05:21
Bunuel 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.



DS10602.01
OG2020 NEW QUESTION


#1
insufficinet
as we dont know range of set
#2
insufficeint all we can say S has -3,3 & 1

from 1 & 2
if 5 is in set then S = -15,-3,1,3,5,15
IMO C
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 28 Apr 2019, 08:11
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Bunuel 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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If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post Updated on: 29 Apr 2019, 00:33
If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?

We know that set S contains odd numbers and two of them are 3 and -1. Is -15 in S?

1. now we know that 5 is in S, but nothing about -15. Insufficient.

2. we can infer that S contains multiples of 3 and -1, such as -3, 3, 9, -9, 27, -27,... Insufficient


1+2 Since -3 and 5 are in S, their product -15 is also in S. Sufficient

Thus the correct answer is C
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Originally posted by ShukhratJon on 28 Apr 2019, 10:36.
Last edited by ShukhratJon on 29 Apr 2019, 00:33, edited 1 time in total.
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 28 Apr 2019, 13:25
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:

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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 02 May 2019, 17:25
Bunuel 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.



DS10602.01
OG2020 NEW QUESTION


We are given that S is a set of odd integers, and 3 and –1 are in S. We need to determine whether –15 is in S.

Statement One Alone:

5 is in S.

Although, we know 3, -1, and 5 are in S, we do not know whether -15 is in S.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Whenever two numbers are in S, their product is in S.

We see that 3 x -1 = -3 is in S, and therefore, -3 x 3 = -9 is in S, and so on. However, we still do not have enough information to determine whether -15 is in S. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Since 3, -1, and 5 are in S, and since whenever two numbers are in S, their product is in S, we see that:

3 x -1 = -3 and -3 x 5 = -15, so we know that -15 IS indeed in set S.

Answer: C
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If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 14 May 2019, 05:22

Solution



Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given
    • S is a set of odd integers
    • The numbers 3 and -1 are in S

We need to determine
    • Whether the number -15 is in S or not.

As we do not have any other information about the elements present in S, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, the number 5 is in the set S.
    • However, from this statement we cannot say whether the number -15 is present in S or not.
Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2


As per the information given in statement 2, whenever two numbers are present in S, their product is also present in S.
We already know that 3 and -1 are present in S.

    • Therefore, we can say that (3 × -1) or -3 is also present in S.
    • However, we can’t say whether -15 is present in S or not.
      o As to get -15, we must have a 5 present in S.
      o But we don’t have sufficient information about the presence of 5.

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)


From statements 1 and 2, we can say
    • 3, -1, -3 and 5 are present in set S.
    • Also, for any two elements present in S, their product is also present in S.
    • Therefore, we can say (-3 × 5) or -15 is also present in S.

As we can determine that -15 is present in S by combining both statements, the correct answer is option C.

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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 21 Sep 2019, 04:18
GMATPrepNow wrote:
Bunuel 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


Dear Brent/Rich/Scott

I do have a query regarding statement 2.

As -15 can not be derived with condition of statement 2 (as mentioned in above set numbers), why can't we consider answer as B.

Thanks,
Raxit.
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 21 Sep 2019, 11:55
Hi Raxit,

The initial prompt tells us two of the numbers are in Set S (re: +3 and -1), but that does NOT mean that those are the ONLY numbers in Set S. There might be other numbers - but we do not know for sure (and if there actually are other numbers in Set S, then we do not know what those numbers are). We have to consider those possibilities when dealing with Fact 2....

IF.... -5 is also in Set S, then the information in Fact 2 means that -15 would also be in Set S --> and the answer to the question would be YES.
IF.... -5 is NOT in Set S and -15 isn't already in Set S, then the answer to the question would be NO.

Thus, the answer to the question is inconsistent and Fact 2 is INSUFFICIENT.

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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?  [#permalink]

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New post 23 Sep 2019, 06:52
Raxit85 wrote:

Dear Brent/Rich/Scott

I do have a query regarding statement 2.

As -15 can not be derived with condition of statement 2 (as mentioned in above set numbers), why can't we consider answer as B.

Thanks,
Raxit.


The reason B is not the correct answer is because even when we assume statement II, -15 may or may not be in S. I am assuming we have established that -15 may not be in S; but it is also possible that -15 is actually in the set S. The questions stem says -1 and 3 are in set S and statement II says whenever two numbers are in S, so is their product; but we have no information from which we can deduce -15 is not in the set. A number of people wrote the numbers such as -3, -9, 27 etc. which are definitely in set S; but it doesn't mean that set S does not contain any other elements besides the above. That's why we can't know for sure -15 is in (or is not in) set S by assuming only statement II.
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Re: If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?   [#permalink] 23 Sep 2019, 06:52
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