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Source: — Data Sufficiency |
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by Night reader » Sun Jan 23, 2011 10:32 am
OneTwoThreeFour wrote:K is a set of numbers such that if x is in K, then -x is in K, and 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


I would love to hear your rationale on this question. Personally, I find the solution to be a bit puzzling.
questions stem: is 12 in K? OR -1, -2, 1, 2, 12 are in K?
st(1) 2 is in K --> Not Sufficient, as -1, -2, 1 are left out
st(2) 3 is in K --> Not Sufficient as 3 is not relevant to the set containing 12
Combined st(1&2) Sufficient {-2; 2} and {-3;3} --> {... -3; -2; 2; 3; 6; 12; 18 ...}

IOM C
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by jaxis » Sun Jan 23, 2011 10:43 am
Night reader wrote:
OneTwoThreeFour wrote:K is a set of numbers such that if x is in K, then -x is in K, and 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


I would love to hear your rationale on this question. Personally, I find the solution to be a bit puzzling.
questions stem: is 12 in K? OR -1, -2, 1, 2, 12 are in K?
st(1) 2 is in K --> Not Sufficient, as -1, -2, 1 are left out
st(2) 3 is in K --> Not Sufficient as 3 is not relevant to the set containing 12
Combined st(1&2) Sufficient {-2; 2} and {-3;3} --> {... -3; -2; 2; 3; 6; 12; 18 ...}

IOM C
From (1)
if 2 is in k then -2 is in K.
==> -2*2=-4 and 4 are in K

From (1) & (2)

3 is in K ==>4*3 =12 is in K.
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by Night reader » Sun Jan 23, 2011 10:49 am
jaxis wrote:
Night reader wrote:
OneTwoThreeFour wrote:K is a set of numbers such that if x is in K, then -x is in K, and 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


I would love to hear your rationale on this question. Personally, I find the solution to be a bit puzzling.
questions stem: is 12 in K? OR -1, -2, 1, 2, 12 are in K?
st(1) 2 is in K --> Not Sufficient, as -1, -2, 1 are left out
st(2) 3 is in K --> Not Sufficient as 3 is not relevant to the set containing 12
Combined st(1&2) Sufficient {-2; 2} and {-3;3} --> {... -3; -2; 2; 3; 6; 12; 18 ...}

IOM C
From (1)
if 2 is in k then -2 is in K.
==> -2*2=-4 and 4 are in K

From (1) & (2)

3 is in K ==>4*3 =12 is in K.
I left {... ...} in the set not to have other values qualified
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by OneTwoThreeFour » Sun Jan 23, 2011 11:05 am
Thanks everyone! I guess I was viewing this question too narrowly. After reading question stem (1) and (2), I viewed 2 as x and 3 as y. Thus, we know that 6 and -6 must be in K. However the question never explicitly says that the product of x and y, xy, could be multiplied by x or y, which would also result a number in K. I mean, can we really conclude that x^2 * y or x * y ^2 is in K based on the question given?


Thanks
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by Night reader » Sun Jan 23, 2011 11:18 am
OneTwoThreeFour wrote:Thanks everyone! I guess I was viewing this question too narrowly. After reading question stem (1) and (2), I viewed 2 as x and 3 as y. Thus, we know that 6 and -6 must be in K. However the question never explicitly says that the product of x and y, xy, could be multiplied by x or y, which would also result a number in K. I mean, can we really conclude that x^2 * y or x * y ^2 is in K based on the question given?


Thanks
we may conclude only x,y, -x,-y, xy (not x^a or -x*(-y) .. yet -x*y )
the conditions given are enough to produce new values
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by OneTwoThreeFour » Sun Jan 23, 2011 11:46 am
After the rereading the solution in the book and the posts on this forum, I understand the logic of the problem, but I still don't think there is enough rationale to make the extra jump. For example if 2 is in K, then -2 is also in K. This part I understand. But from the solution in the book, if 2 is in K, then 4, 8, 16, must also be in K. This is based on the rationale that (If each of x and y is in K, then xy is in K.) So if 2 is in K, then 2 *2, and 2*2*2, must be in K. However, we don't know whether "y" is distinct or can be the same as x. Thus, I believe there is a logic gap in this problem.
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by Night reader » Sun Jan 23, 2011 11:51 am
OneTwoThreeFour wrote:After the rereading the solution in the book and the posts on this forum, I understand the logic of the problem, but I still don't think there is enough rationale to make the extra jump. For example if 2 is in K, then -2 is also in K. This part I understand. But from the solution in the book, if 2 is in K, then 4, 8, 16, must also be in K. This is based on the rationale that (If each of x and y is in K, then xy is in K.) So if 2 is in K, then 2 *2, and 2*2*2, must be in K. However, we don't know whether "y" is distinct or can be the same as x. Thus, I believe there is a logic gap in this problem.
may be GMAT is gap :)
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by gmat1978 » Sun Feb 20, 2011 8:41 pm
I have a quick question.

According to 1) 2 is in k: So, the set k {..., -16, -8, -4, -2, 2, 4, 8, 16, ...} does not contain 12. Is this not sufficient to answer the question - Is 12 in K?

According to 2) 3 is in k: Hence, set K {-27, -9, -3, 3, 9, 27} does not contain 12. Sufficient to answer the question?

Answer: D?. I know I am wrong because the OA is C

What am I missing. Please help

Thanks

Night reader wrote:
OneTwoThreeFour wrote:K is a set of numbers such that if x is in K, then -x is in K, and 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


I would love to hear your rationale on this question. Personally, I find the solution to be a bit puzzling.
questions stem: is 12 in K? OR -1, -2, 1, 2, 12 are in K?
st(1) 2 is in K --> Not Sufficient, as -1, -2, 1 are left out
st(2) 3 is in K --> Not Sufficient as 3 is not relevant to the set containing 12
Combined st(1&2) Sufficient {-2; 2} and {-3;3} --> {... -3; -2; 2; 3; 6; 12; 18 ...}

IOM C
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by Night reader » Mon Feb 21, 2011 1:11 am
hi gmat1978
The question in this problem is very straightforward. K is a set of numbers, please note the set K contains only x and y, BUT x and y are assigned values, otherwise how we know where does 12 come? OK? now we are looking up statement (1) and it says 2 is in K. what is 2? it's either x or y, whichever you like... So let's assign x=2, then how will set K look like? reread the problem "K is a set of numbers such that if x is in K, then -x is in K, and if each of x and y is in K, then xy is in K" Therefore, K should include 2 and -2, that's it! K E {-2;2} we stop here as statement (1) doesn't help us to solve this problem and locate 12, and we look ahead for statement (2). Statement (1) Is Not Sufficient;
Statement (2) 3 is in K --> y=3 OR K E {-3;3} again no trace of 12. Not Sufficient.

Let's combine statements (1&2): we should get x*y for set K here --> {-2;2} U {-3;3} --> how many ways we can arrange our set K? use counting actually 2*2 + 2 (plus two more values from each set, because we have values +/- ve sign) --> {-6; -3; -2; 2; 3; 6} that's it! Sufficient

OPS - this is Yes/No question, hence combined statements (1&2) are sufficient to answer NO. I don't know why in all previous posts I read 12 sitting in the set K and allowed for such mistake and non-sensitic elaboration with the possibility E. It's just C because we can answer No.
K is a set of numbers such that if x is in K, then -x is in K, and 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
gmat1978 wrote:I have a quick question.

According to 1) 2 is in k: So, the set k {..., -16, -8, -4, -2, 2, 4, 8, 16, ...} does not contain 12. Is this not sufficient to answer the question - Is 12 in K?

According to 2) 3 is in k: Hence, set K {-27, -9, -3, 3, 9, 27} does not contain 12. Sufficient to answer the question?

Answer: D?. I know I am wrong because the OA is C

What am I missing. Please help

Thanks
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by ankur.agrawal » Mon Feb 21, 2011 5:45 am
I agree with Gmat 1978. Answer should be D . Still cannot understand why its C.

Sumbody please explain again.

Thanks.
Night reader wrote:hi gmat1978
The question in this problem is very straightforward. K is a set of numbers, please note the set K contains only x and y, BUT x and y are assigned values, otherwise how we know where does 12 come? OK? now we are looking up statement (1) and it says 2 is in K. what is 2? it's either x or y, whichever you like... So let's assign x=2, then how will set K look like? reread the problem "K is a set of numbers such that if x is in K, then -x is in K, and if each of x and y is in K, then xy is in K" Therefore, K should include 2 and -2, that's it! K E {-2;2} we stop here as statement (1) doesn't help us to solve this problem and locate 12, and we look ahead for statement (2). Statement (1) Is Not Sufficient;
Statement (2) 3 is in K --> y=3 OR K E {-3;3} again no trace of 12. Not Sufficient.

Let's combine statements (1&2): we should get x*y for set K here --> {-2;2} U {-3;3} --> how many ways we can arrange our set K? use counting actually 2*2 + 2 (plus two more values from each set, because we have values +/- ve sign) --> {-6; -3; -2; 2; 3; 6} that's it! Sufficient

OPS - this is Yes/No question, hence combined statements (1&2) are sufficient to answer NO. I don't know why in all previous posts I read 12 sitting in the set K and allowed for such mistake and non-sensitic elaboration with the possibility E. It's just C because we can answer No.
K is a set of numbers such that if x is in K, then -x is in K, and 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
gmat1978 wrote:I have a quick question.

According to 1) 2 is in k: So, the set k {..., -16, -8, -4, -2, 2, 4, 8, 16, ...} does not contain 12. Is this not sufficient to answer the question - Is 12 in K?

According to 2) 3 is in k: Hence, set K {-27, -9, -3, 3, 9, 27} does not contain 12. Sufficient to answer the question?

Answer: D?. I know I am wrong because the OA is C

What am I missing. Please help

Thanks
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by rohu27 » Mon Feb 21, 2011 6:08 am
ankur,

st 1 only says that 2 is in K. it doesnt say 2 is the only element present in K. then as u said, we can conclude tht 12 is definitely not in K. but we do not know wht are the remaining elements of k. it may contain 2,12,13 etc. or may be only 2.

same applied to st 2.

hope this resolves ur confusion.

ankur.agrawal wrote:I agree with Gmat 1978. Answer should be D . Still cannot understand why its C.

Sumbody please explain again.

Thanks.
Night reader wrote:hi gmat1978
The question in this problem is very straightforward. K is a set of numbers, please note the set K contains only x and y, BUT x and y are assigned values, otherwise how we know where does 12 come? OK? now we are looking up statement (1) and it says 2 is in K. what is 2? it's either x or y, whichever you like... So let's assign x=2, then how will set K look like? reread the problem "K is a set of numbers such that if x is in K, then -x is in K, and if each of x and y is in K, then xy is in K" Therefore, K should include 2 and -2, that's it! K E {-2;2} we stop here as statement (1) doesn't help us to solve this problem and locate 12, and we look ahead for statement (2). Statement (1) Is Not Sufficient;
Statement (2) 3 is in K --> y=3 OR K E {-3;3} again no trace of 12. Not Sufficient.

Let's combine statements (1&2): we should get x*y for set K here --> {-2;2} U {-3;3} --> how many ways we can arrange our set K? use counting actually 2*2 + 2 (plus two more values from each set, because we have values +/- ve sign) --> {-6; -3; -2; 2; 3; 6} that's it! Sufficient

OPS - this is Yes/No question, hence combined statements (1&2) are sufficient to answer NO. I don't know why in all previous posts I read 12 sitting in the set K and allowed for such mistake and non-sensitic elaboration with the possibility E. It's just C because we can answer No.
K is a set of numbers such that if x is in K, then -x is in K, and 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
gmat1978 wrote:I have a quick question.

According to 1) 2 is in k: So, the set k {..., -16, -8, -4, -2, 2, 4, 8, 16, ...} does not contain 12. Is this not sufficient to answer the question - Is 12 in K?

According to 2) 3 is in k: Hence, set K {-27, -9, -3, 3, 9, 27} does not contain 12. Sufficient to answer the question?

Answer: D?. I know I am wrong because the OA is C

What am I missing. Please help

Thanks
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by Night reader » Mon Feb 21, 2011 6:26 am
@ankur, this DS has certain conditions. If x is in K then x and -x are in K. We are given one number in statement (1) 2 and one number in statement (2) 3. Either of these numbers are x OR y. We cannot say 2=x=y when we do not know about the existence of the second variable (x OR y). Each condition implies only one number - so one variable x OR y!

now set K according to statement (1) has only x and -x {-2; 2}

according to statement (2) set K has only y or -y {-3; 3}

you cannot say xy in statement 1 and 2, because we have only one value for either x OR y.

if you combine both you get x*y {-6;-3;-2;2;3;6} there's no 12 ans answer No st(1&2) Sufficient

please read the previous posts, it's not the matter of personal like or dislike - just knowledge man :(
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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by ankur.agrawal » Mon Feb 21, 2011 6:32 am
Spot on man. Thanks.

Small things : Not getting identified. Loosing confidence.

Afrai
Night reader wrote:@ankur, this DS has certain conditions. If x is in K then x and -x are in K. We are given one number in statement (1) 2 and one number in statement (2) 3. Either of these numbers are x OR y. We cannot say 2=x=y when we do not know about the existence of the second variable (x OR y). Each condition implies only one number - so one variable x OR y!

now set K according to statement (1) has only x and -x {-2; 2}

according to statement (2) set K has only y or -y {-3; 3}

you cannot say xy in statement 1 and 2, because we have only one value for either x OR y.

if you combine both you get x*y {-6;-3;-2;2;3;6} there's no 12 ans answer No st(1&2) Sufficient

please read the previous posts, it's not the matter of personal like or dislike - just knowledge man :(
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by gmat1978 » Mon Feb 21, 2011 6:59 pm
Night reader,

Thanks for taking time out to explain the answer. However, your explanation seems to contradict the OA explanation. The OA says that "Given (1) and (2), it follows that both 2 and 3 are in K. Thus, by (ii), (2)(3)=6 is in K. Therefore, by (ii), (2)(6)=12 is in K."

I am still unclear, may be I am missing something.

According to statement (1) - if 2 is in K and by satisfying (i) and (ii) - set K looks like {...., -16, -8, -4, -2, 2, 4, 8, 16,...}. Now, my question is why I can't say that 12 does not exist in set K just looking at statement 1?

Thanks

Night reader wrote:@ankur, this DS has certain conditions. If x is in K then x and -x are in K. We are given one number in statement (1) 2 and one number in statement (2) 3. Either of these numbers are x OR y. We cannot say 2=x=y when we do not know about the existence of the second variable (x OR y). Each condition implies only one number - so one variable x OR y!

now set K according to statement (1) has only x and -x {-2; 2}

according to statement (2) set K has only y or -y {-3; 3}

you cannot say xy in statement 1 and 2, because we have only one value for either x OR y.

if you combine both you get x*y {-6;-3;-2;2;3;6} there's no 12 ans answer No st(1&2) Sufficient

please read the previous posts, it's not the matter of personal like or dislike - just knowledge man :(
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