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K is a set of numbers such that (i) If x is in K, then -x

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Re: K is a set of numbers such that (i) If x is in K, then -x [#permalink]

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New post 29 May 2014, 21:55
shagalo wrote:
VeritasPrepKarishma wrote:
shagalo wrote:
can any one tell me why (1) and (2) are insufficient ?
(1) shows that the set is …. -16,-8,-4,-,2,4,8,16….( there is no 12 here) so it is sufficient.
(2) shows that the set is …. -27,-9,-3,3,9,27,…… ( there is no 12 here) so it is sufficient.
so the answer is D … each alone is sufficient.

any explanation please? thanks


How does statement 1 show that 12 is not in the set? All statement 1 tells you is that 2 is there and hence -2 is there. We don't know anything about other elements. How did you get 4, 8 etc. We are not given that if 2 is there, only powers of 2 will be there.

------------------
Sorry but your explanation is not clear.
and i got these numbers " -16,-8,-4,-,2,4,8,16…" after applying the statement (1) on the equation (i) and (ii).
what i understood is that if you applied statement (1) "2 in K", then you will get this set of numbers " -16,-8,-4,-,2,4,8,16…" which do not include 12. the same apply on statement (2).
could you explain what is the flaw in my understanding.

Thanks



Given:
(i) If x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K
Stmnt 1: 2 is in K

This implies 2, -2, -4 (2*-2), -8 (2*-4), 8 (-2*-4), etc are in the set. 4 will not be there. But how do you know that no other elements are there in the set? Could we have a set like this: {12, 2, 24, -2, -12, -24 ...}
Does it satisfy all 3 conditions given above? Yes.
The set {2, -2, -4, -8, ...} satisfies all 3 conditions too.

Hence we don't know what the set actually looks like. Just because the set has 2 doesn't mean it cannot have 12.
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Re: K is a set of numbers such that (i) If x is in K, then -x [#permalink]

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New post 31 May 2014, 23:46
K is a set of numbers such that

(i) If x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K

Is 12 in K?

(1) 2 is in K
(2) 3 is in K

Statement 1) if 2 is in K, then -2 should be in K. Is 12 in K ? Not sufficient
Statement 2) Same as above not sufficient.

Both the statement) 2 is in K, then -2 is in K.
3 is in K, -3 is in K
2 and 3 both are in K, then 6 is in K

Till now we have K has {2,3,-2,-3,6}

Now as 6 is in K and also 2 is also in K, 12 has to be in K

Hence Sufficient - Option C)
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Re: K is a set of numbers such that (i) If x is in K, then -x [#permalink]

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New post 29 Sep 2015, 03:45
Hi Bunuel,

Could please post the correct question . I think there is power missing in the main question here .
Please re-post the correct question .
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Re: K is a set of numbers such that (i) If x is in K, then -x [#permalink]

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New post 29 Sep 2015, 03:52
abhisheknandy08 wrote:
Hi Bunuel,

Could please post the correct question . I think there is power missing in the main question here .
Please re-post the correct question .


Nothing is missing there. The original question below:

K is a set of numbers such that

(i) If x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K

Is 12 in K?

(1) 2 is in K
(2) 3 is in K

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K is a set of numbers such that (i) If x is in K, then -x [#permalink]

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New post 15 Jul 2016, 10:19
K is a set of numbers such that
(i) If x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K

Is 12 in K?

(1) 2 is in K
According to the restrictions if 2 (i.e " x") is in Set K then -2(i.e. "-x") should also be in Set K
since 2 and -2 are technically different numbers you can consider them x and y. Now (xy)= 2 * -2 = -4 should be there. Since -4 is there then its negative counterpart should be there too i.e "-(-4)" =4 and so on
K={2,-2, -4,4,-8,8,16,--16,32,-32,........}
Insufficient , we don not know apart from 2 and it's derivative what other numbers are inside Set K.

(2) 3 is in K
According to the restrictions if 3 is in k then -3 should also be in K
K={3,-3,-9,9,27,-27,81,-81.. } Insufficient , we do not know apart from 2 and it's derivative what other numbers are inside K

Merge both
K={2,-2,3,-3,4,-4,6,-6,12,-12,24,-24,27,-27...}

SUFFICIENT

ANSWER IS C
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Last edited by LogicGuru1 on 19 Sep 2016, 08:29, edited 1 time in total.

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Re: K is a set of numbers such that (i) If x is in K, then -x [#permalink]

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New post 18 Sep 2016, 05:52
Bunuel wrote:
afyl128 wrote:
My First post :-D

K is a set of numbers such that

(i) If x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K

Is 12 in K?

(1) 2 is in K
(2) 3 is in K

for (1) know that 2, -2 is in K
for (2) know that 3, -3 is in K
Together have [-3, -2, 2, 3, 6]

So I would say neither is sufficient??


Hi, and welcome to the club. Below is the solution for your problem.

(1) 2 is in K --> according to (i) -2 is n K --> according to (ii) -2*2=-4 is in K --> according to (i) -(-4)=4 is in K and so on. Thus we know that 2, -2, -4, 4, 8, -8, 16, -16, ... are in K, so basically powers of 2 and their negative pairs. Is 12 in K? We don't know. Not sufficient.

(2) 3 is in K --> according to (i) -3 is n K --> according to (ii) -3*3=-9 is in K --> according to (i) -(-9)=9 is in K and so on. Thus we know that 3, -3, -9, 9, 27, -27, 81, -81, ... are in K, so basically powers of 3 and their negative pairs. Is 12 in K? We don't know. Not sufficient.

(1)+(2) From (1) 4 is in K and from (2) 3 is in K, hence according to (ii) 4*3=12 must also be in K. Sufficient.

Answer: C.

Hope it's clear.


When I was working on this questions I understood from statement 1+2 that 12 could be on the set. But as he asks: is 12 in the set? Well I assumed it could be in the set or not, why can I assume the set is not finite? I got a similar Gmat question wrong for assuming the opposite.

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Re: K is a set of numbers such that (i) If x is in K, then -x [#permalink]

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New post 18 Sep 2016, 08:30
Coruja wrote:
Bunuel wrote:
afyl128 wrote:
My First post :-D

K is a set of numbers such that

(i) If x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K

Is 12 in K?

(1) 2 is in K
(2) 3 is in K

for (1) know that 2, -2 is in K
for (2) know that 3, -3 is in K
Together have [-3, -2, 2, 3, 6]

So I would say neither is sufficient??


Hi, and welcome to the club. Below is the solution for your problem.

(1) 2 is in K --> according to (i) -2 is n K --> according to (ii) -2*2=-4 is in K --> according to (i) -(-4)=4 is in K and so on. Thus we know that 2, -2, -4, 4, 8, -8, 16, -16, ... are in K, so basically powers of 2 and their negative pairs. Is 12 in K? We don't know. Not sufficient.

(2) 3 is in K --> according to (i) -3 is n K --> according to (ii) -3*3=-9 is in K --> according to (i) -(-9)=9 is in K and so on. Thus we know that 3, -3, -9, 9, 27, -27, 81, -81, ... are in K, so basically powers of 3 and their negative pairs. Is 12 in K? We don't know. Not sufficient.

(1)+(2) From (1) 4 is in K and from (2) 3 is in K, hence according to (ii) 4*3=12 must also be in K. Sufficient.

Answer: C.

Hope it's clear.


When I was working on this questions I understood from statement 1+2 that 12 could be on the set. But as he asks: is 12 in the set? Well I assumed it could be in the set or not, why can I assume the set is not finite? I got a similar Gmat question wrong for assuming the opposite.


The stem gives clear description of the set and it's not saying that the set is finite.
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