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# K is a set of numbers such that... i) if x is in K, then -x

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Intern
Joined: 11 May 2011
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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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12 May 2011, 14:47
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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.

In my solution, I tried to prove it incorrect by using the set -3, 2, 3, 6 however E is not the right answer as the book revealed. Am I missing something? What is the proper definition of a set of numbers? That's the only thing I can see wrong with my setup.

Thanks for the help.

OPEN DISCUSSION OF THIS QUESTION IS HERE: k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Apr 2012, 14:50, edited 1 time in total.
Topic is locked
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Re: K is a set of numbers such that... [#permalink]

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12 May 2011, 16:57
(1)

2 is in k
=> -2 is in k, but this is not sufficient because 2 * -2 = -4 is in k, but 12 = 3*4

(2)

3 is in K

=> -3 is in K and -9 is in k.

Still not sufficient

(1) + (2) say that

2,-2,-3,3,4,-4,9,-9 are in K

=> 12 is in K because 3*4 = 12.

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Re: K is a set of numbers such that... [#permalink]

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12 May 2011, 17:40
1. Not sufficient.

K = {2,-2,4,-4,8,-8...}

we dont know whether K has 3 in it or not .

If 3 is in K, then 12 will be in K.
If 3 is not in K, then 12 wont be in K.

2. Not sufficient.

K = {3,-3,9,-9,27,-27...}

we dont know whether K has 2 in it or not .

If 2 is in K, then 12 will be in K.
If 2 is not in K, then 12 wont be in K.

Together

we know 2,3 are in K=> 12 is also in K.

Sufficient.

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Re: K is a set of numbers such that... [#permalink]

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13 May 2011, 02:07
1+2,

2,3,6 and 2*6=12 is also there in the list.

C
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Re: K is a set of numbers such that... [#permalink]

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13 May 2011, 07:04
(1) 2 is in k so k includes 2,-2, -4, 8, 16, -32 but not 12
(2) 3 is in k so k includes 3, -3, -9, 27 but not 12
For C -3*-4= 12

I have different reasoning problem with this question
The question is asking whether 12 is in k? so answer could be yes or no

Using the both options separately we can see 12 is not is in K, and using the both options together we can see 12 is K.

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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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11 Apr 2012, 14:43
Many thanks for the explanation to this question. I did not fully understand it but now it is beginning to make much more sense to me.
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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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11 Apr 2012, 14:49
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Expert's post
dzodzo85 wrote:
Many thanks for the explanation to this question. I did not fully understand it but now it is beginning to make much more sense to me.

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 (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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
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Re: K is a set of numbers such that... i) if x is in K, then -x   [#permalink] 11 Apr 2012, 14:49
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