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

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Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 608

Kudos [?]: 1154 [0], given: 39

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

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24 May 2011, 07:25
00:00

Difficulty:

25% (medium)

Question Stats:

89% (01:09) correct 11% (02:37) wrong based on 19 sessions

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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.

Solution:
(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 [Ans. C]

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.

[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Kudos [?]: 1154 [0], given: 39

Manager
Joined: 07 Oct 2010
Posts: 174

Kudos [?]: 179 [0], given: 10

Re: Is 12 is in K? [#permalink]

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24 May 2011, 09:17
Baten80 wrote:
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.

Solution:
(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 [Ans. C]

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.

A. 2 is in K ... therefore -2 will be there ....according to first condition
Also -4 and 4 will be there ..... According to 1st and 2nd condition 2*-2 = -4
But, wont get 12 as an ans

Also, it is not mentioned that how many numbers are present in K therefore, we can assume that other than 2 there can be more number e.g. 12 ...then we can or can not get the ans ... Thus , Option A is insufficient

B. this option is insufficient for the same above mentioned reason

But, combining 2 options tells us that K definitely contain3 and 2 ..thus 4 ...........as shown above
and According to 2nd condition 3*4 = 12

Thus, ans is C

Kudos [?]: 179 [0], given: 10

Director
Joined: 01 Feb 2011
Posts: 725

Kudos [?]: 146 [0], given: 42

Re: Is 12 is in K? [#permalink]

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24 May 2011, 19:31
Well. Think this way.

statement 1 doesn't say 2 is the only element in K.
same with statement 2 . It does not say 3 is the only element in K.

1. Not sufficient

has 2 in K

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

if K has element 3 as well , then 12 is in K.

if K does not contain 3 , then 12 is not in K.

2. Not sufficient

has 3 in K

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

if K has element 2 as well , then 12 is in K.

if K does not contain 2 , then 12 is not in K.

Together we know

K has both 2 and 3. Hence it will have 6 and 12. Hence Sufficient.

Baten80 wrote:
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.

Solution:
(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 [Ans. C]

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.

Kudos [?]: 146 [0], given: 42

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 608

Kudos [?]: 1154 [0], given: 39

Re: Is 12 is in K? [#permalink]

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25 May 2011, 11:11
vyassaptarashi wrote:
Baten80 wrote:
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.

Solution:
(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 [Ans. C]

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.

A. 2 is in K ... therefore -2 will be there ....according to first condition
Also -4 and 4 will be there ..... According to 1st and 2nd condition 2*-2 = -4
But, wont get 12 as an ans

Also, it is not mentioned that how many numbers are present in K therefore, we can assume that other than 2 there can be more number e.g. 12 ...then we can or can not get the ans ... Thus , Option A is insufficient

B. this option is insufficient for the same above mentioned reason

But, combining 2 options tells us that K definitely contain3 and 2 ..thus 4 ...........as shown above
and According to 2nd condition 3*4 = 12

Thus, ans is C

How the 12 will be in k?
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Kudos [?]: 1154 [0], given: 39

Manager
Joined: 07 Oct 2010
Posts: 174

Kudos [?]: 179 [0], given: 10

Re: Is 12 is in K? [#permalink]

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25 May 2011, 11:30
Baten80 wrote:
How the 12 will be in k?

Do read my post carefully .... i have explained in Option A ...since 2 is present 4 must be present

And according to option B ...3 is present

At the end of the post i have said that since 3 and 4 both are present then according to the 2nd condition i.e. ii) if each of x and y is in K, then xy is in K
3 = X and 4 = y and XY = 3*4 = 12

Kudos [?]: 179 [0], given: 10

Manager
Joined: 07 Jun 2011
Posts: 69

Kudos [?]: 11 [0], given: 31

Re: Is 12 is in K? [#permalink]

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14 Aug 2011, 23:49
I back C

from statement 1, the set consists of all multiples of 2. But to have 12 we need multiples of 2 and 3

12 = 2^2 * 3

statement 1 gives the following set: { 2,-2,-4,4,8....} there is nowhere a multiple of 3 being introduced.

statement 2: gives a set with different multiples of 3 but we also need 2. There for C

Kudos [?]: 11 [0], given: 31

Re: Is 12 is in K?   [#permalink] 14 Aug 2011, 23:49
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