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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
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K is a set of numbers such that... i) if x is in K, then -x [#permalink] New post 24 May 2011, 06:25
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

80% (01:40) correct 20% (02:37) wrong based on 10 sessions
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.

So to me answer Answer is D, but you know the right answer is C.


Thus help is badly needed!
[Reveal] Spoiler: OA

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Re: Is 12 is in K? [#permalink] New post 24 May 2011, 08:17
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.

So to me answer Answer is D, but you know the right answer is C.


Thus help is badly needed!



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
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Re: Is 12 is in K? [#permalink] New post 24 May 2011, 18:31
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.

Answer is C.


















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.

So to me answer Answer is D, but you know the right answer is C.


Thus help is badly needed!
Director
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Re: Is 12 is in K? [#permalink] New post 25 May 2011, 10:11
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.

So to me answer Answer is D, but you know the right answer is C.


Thus help is badly needed!



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?
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Re: Is 12 is in K? [#permalink] New post 25 May 2011, 10:30
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
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Re: Is 12 is in K? [#permalink] New post 14 Aug 2011, 22:49
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
Re: Is 12 is in K?   [#permalink] 14 Aug 2011, 22:49
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