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

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

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01 Apr 2012, 05:30
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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.
[Reveal] Spoiler: OA

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Re: S is a set of integers [#permalink]

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01 Apr 2012, 07:51
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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.

Similar questions:
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html

Hope it helps.
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Re: S is a set of integers [#permalink]

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02 Apr 2012, 18:46
Bunuel 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 --> 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.

Hope it helps.

How do you know that -a = b?

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Re: S is a set of integers [#permalink]

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03 Apr 2012, 02:23
bohdan01 wrote:
Bunuel 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 --> 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.

Hope it helps.

How do you know that -a = b?

we can interpret if a and b are two elements in the set then product of that two numbers will be in the set.so b is just another element in the set.

@Bunuel
Correct me if wrong
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Re: S is a set of integers [#permalink]

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03 Apr 2012, 04:48
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bohdan01 wrote:
Bunuel 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 --> 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.

Hope it helps.

How do you know that -a = b?

We are told that: if some number a 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.
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Re: S is a set of integers [#permalink]

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03 Apr 2012, 05:54
Bunuel 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 --> 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.

Similar questions:
og-quant-96907.html
ds-p-is-a-set-of-integers-96630.html
set-of-integers-103005.html

Hope it helps.

i agree with Bunuel's explanation.....the answer should be deduced using both the points given the question
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Re: S is a set of integers [#permalink]

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12 Oct 2012, 00:17
Bunuel wrote:
bohdan01 wrote:
Bunuel 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 --> 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.

Hope it helps.

How do you know that -a = b?

We are told that: if some number a 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

cheers

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Re: S is a set of integers [#permalink]

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12 Oct 2012, 00:30
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(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

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,...
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Re: S is a set of integers [#permalink]

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12 Oct 2012, 00:47
EvaJager wrote:
(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

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.....

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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, 14:58
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Re: S is a set of integers such that i) if a is in S, then –a [#permalink]

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27 Dec 2013, 03:37

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

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24 Jun 2014, 12:19
Bunuel 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 --> 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.

Similar questions:
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html

Hope it helps.

Hi Bunnel ,

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

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

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24 Jun 2014, 12:58
shelrod007 wrote:
Bunuel 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 --> 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.

Similar questions:
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html

Hope it helps.

Hi Bunnel ,

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, ...}

Hope it's clear.
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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, 05:20
Hello from the GMAT Club BumpBot!

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Re: S is a set of integers such that i) if a is in S, then –a   [#permalink] 09 Jul 2015, 05:20
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