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

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Manager
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S is a set of integers such that i) if a in in S, then -a is [#permalink]  24 Jan 2004, 02:06
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S is a set of integers such that
i) if a in in S, then -a is in S
ii) if each of a and b are in S, then ab is in S.
Is -4 is S

1) 1 is in S
2) 2 is in S
Manager
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They have assumed that a and b can be the same number. Subsitutue a=b=2.
Senior Manager
Joined: 11 Nov 2003
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The correct reasoning is as follows:

statemenet 2 says that 2 is in S. This will lead to the conclusion that -2 is in S. So we know that 2 (=a)as well as -2(=b) are in S. So ab = -4 is in S. Thus the second statement is suffecient.

SVP
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ashwyns wrote:

They have assumed that a and b can be the same number. Subsitutue a=b=2.

If they have assumed that a and b are the same number than they can also assume that a and b are not the same number

I bellieve E is my final answer
SVP
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gmatblast wrote:
The correct reasoning is as follows:

statemenet 2 says that 2 is in S. This will lead to the conclusion that -2 is in S. So we know that 2 (=a)as well as -2(=b) are in S. So ab = -4 is in S. Thus the second statement is suffecient.

How did you make b = -2. I did not understand the logic.
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Bhai wrote:
gmatblast wrote:
The correct reasoning is as follows:

statemenet 2 says that 2 is in S. This will lead to the conclusion that -2 is in S. So we know that 2 (=a)as well as -2(=b) are in S. So ab = -4 is in S. Thus the second statement is suffecient.

How did you make b = -2. I did not understand the logic.

Bhai

I am not sure if it caused any confusion when I referred to statement 2. In the problem statement we are given TWO characteristics of set S.

Then we are given two statements to do the suffeciency test.

Now question: Is -4 in S?

STATEMENT 1 : 1 is in S

let us apply both the characteristics one by one

Applying the first characteristics:

1 is in S => -1 is in S

So S = {1, -1} right?

Now apply the second characteritics

We know that 1 and -1 are member of S. so based on second charactreistics, (1)(-1) = -1 should be in S. But this does not add any value because we already know that -1 is member oF S.

So after applying both the characteristics, statement 1 does nt say anything about numbers other than 1 and -1. So other numbers could be memebrs of S or they could not be. We do not know. So statement 1 INSUFFICIENT.

STATEMENT 2 : 2 is in S

Again let us use both the given characterisics of S one by one.

Applying the first characteristic:

2 is in S => -2 is in S

So we now know that S = {2, -2} CORRECT?

Now apply the second characteristic

We know that 2 and -2 are members of S. so based on second charactreistics, (2)(-2) = -4 is in S.

So this answers the question in YES. So statement 2 is SUFFECIENT.

Note that we can further conclude that since -4 is in S, +4 is in S as well. (based on the first characteristic). Now we can also say that since +4 and -4 are in S (4)(-4) = -16 is in S (based on second characteristic). This will be never ending cycle. Of course for this problem, we need to stop as soon as we identified that -4 is the member of S.

Hope this helps.
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