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S is a set of integers such that i) if a is in S, then –a is

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S is a set of integers such that i) if a is in S, then –a is [#permalink] New post 14 May 2003, 15:41
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S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?[/b]

(1) 1 is in S.

(2) 2 is in S.

OPEN DISCUSSION OF THIS QUESTION IS HERE: s-is-a-set-of-integers-such-that-i-if-a-is-in-s-then-a-130000.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jul 2012, 05:34, edited 1 time in total.
Edited the question and added the OA.
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 [#permalink] New post 14 May 2003, 16:17
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Ans : B

2 is in => -2 is in.

2 and -2 are in, thus 2*(-2) are in=> -4 is in S.

Yes - Suff.
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Re: S is a set of integers such that i) if a is in S, then a is [#permalink] New post 30 Jul 2012, 05:28
ju_1 wrote:
S is a set of integers such that

i) if a is in S, then тАУa is in S, and
ii) if each of a and b is in S, then ab is in S.

Is тАУ4 in S?

(1) 1 is in S.

(2) 2 is in S.


i honestly did not understand the problem, can some one help me here...
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Re: S is a set of integers such that i) if a is in S, then a is [#permalink] New post 30 Jul 2012, 05:36
Expert's post
harshavmrg wrote:
ju_1 wrote:
S is a set of integers such that

i) if a is in S, then тАУa is in S, and
ii) if each of a and b is in S, then ab is in S.

Is тАУ4 in S?

(1) 1 is in S.

(2) 2 is in S.


i honestly did not understand the problem, can some one help me here...


S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

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k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: s-is-a-set-of-integers-such-that-i-if-a-is-in-s-then-a-130000.html
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Re: S is a set of integers such that i) if a is in S, then a is   [#permalink] 30 Jul 2012, 05:36
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S is a set of integers such that i) if a is in S, then –a is

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