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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]

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New post 24 Feb 2011, 14:15
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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?


(1) 1 is in S.
(2) 2 is in S.
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S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 24 Feb 2011, 14:28
banksy wrote:
. 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.
(2) 2 is in S.


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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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 24 Feb 2011, 14:30
(1) 1 is in S. Thus, -1 is there. If 1 and -1 are there; then 1*-1=-1 is there; We don't know anything other than that. -4 may or may not be there. Sufficient.

(2) 2 is in S. Thus, -2 is there. If 2 and -2 are both there, -4 must be there. We know -4 is there. Don't care about anything else.
Sufficient.

Ans: "B"
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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 22 Mar 2016, 02:24
Sorry, I am lost here, if we know that a =-2 then how do we now that b= 2 ? to reach the conclusion that -4 is in S.
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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 22 Mar 2016, 03:01
sony1000 wrote:
Sorry, I am lost here, if we know that a =-2 then how do we now that b= 2 ? to reach the conclusion that -4 is in S.


Hi,
you don't require to know what is a or what is b..
a and b are just two integers in the SET...
similarly when we know 2 is there, -2 will be there..
if 2 and -2 are there, 2*-2=-4 is there..

further if -4 is there, 4 is there..
so 4*-4=-16 is also there..
also 2*4=8 is there.. and so on

so a and b stand for any two integers in the set..

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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 22 Mar 2018, 02:41
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