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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 --> 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.

Hope it helps.

How do you know that -a = b?

We are told that: if some numbera is in S, then –a is also in S, and if each of a and b is in S, then their product, ab is also in S.

(2) says that 2 is in S, then -2 also must be in S and since both 2 and -2 are in S then their product 2*(-2)=-4 must also be in S.

Hope it's clear.

Bunuel - Im also confused, could you kindly help? (2) says that 2 is in S so this can be a or b right? So if 2 is a then -2 is -a if 2 is b then -2 is -b Aren't these mutually exclusive i.e how can we take 2 to be a and -2 to be b?

Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get -4

(2) says that 2 is in S so this can be a or b right? So if 2 is a then -2 is -a if 2 is b then -2 is -b Aren't these mutually exclusive i.e how can we take 2 to be a and -2 to be b?

Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get -4

please help!

cheers

------------------ 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.

It doesn't matter what you call the number. i) States that if a number is in S, then its opposite is also in S. Meaning, if 1 is in S, then -1 is also in S. If -3 is in S, then -(-3) = 3 is also in S. ii) States that if two numbers are in S, then their product is also in S. Doesn't matter even the two numbers are equal. For example, if 2 is in S, then 2*2 = 4 is also in S. If 2 and -2 are in S, then 2*(-2) = 4 is also in S, 2*4 = 8, -2*4 = -8,...
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

(2) says that 2 is in S so this can be a or b right? So if 2 is a then -2 is -a if 2 is b then -2 is -b Aren't these mutually exclusive i.e how can we take 2 to be a and -2 to be b?

Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get -4

please help!

cheers

------------------ 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.

It doesn't matter what you call the number. i) States that if a number is in S, then its opposite is also in S. Meaning, if 1 is in S, then -1 is also in S. If -3 is in S, then -(-3) = 3 is also in S. ii) States that if two numbers are in S, then their product is also in S. Doesn't matter even the two numbers are equal. For example, if 2 is in S, then 2*2 = 4 is also in S. If 2 and -2 are in S, then 2*(-2) = 4 is also in S, 2*4 = 8, -2*4 = -8,...

ahhh.. I guess i didn't give enf credit to stipulated conditions It says ii) if EACH of a and b is in S, then ab is in S.

So for ANY A or B in the set then a*b in the set so we definitely know 2 and -2 are in the set hence we are Good.....

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

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26 Dec 2013, 13:58

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I am a little confused with this one . In stmt A ) i get the elements in the set as 1 and -1 ... i did not find 12 so i thought the Set S has only two elements .. hence We could answer the question that 12 is not present in the set ?

However later on i saw that this is not sufficient to answer the question how can 12 be present in the set with Stmt 1 yields on two values 1 , -1 ?

I am a little confused with this one . In stmt A ) i get the elements in the set as 1 and -1 ... i did not find 12 so i thought the Set S has only two elements .. hence We could answer the question that 12 is not present in the set ?

However later on i saw that this is not sufficient to answer the question how can 12 be present in the set with Stmt 1 yields on two values 1 , -1 ?

Thanks and Regards , Sheldon Rodrigues

1 and -1 may NOT be the only numbers in S. S could contain a whole bunch of other numbers. For example, the set could be: {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...} {..., -5, -3, -1, 1, 3, 5, ...}

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

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09 Jul 2015, 04:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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