if a and b are in a set, then ab is in the set also. If -a

Question

if a and b are in a set, then ab is in the set also. If -a is in the set, then, a is in the set. Is 12 in the set?
1) 2 is in the set.
2) -3 is in the set.

jinino · Answer

For 12 to be in the set, 1 and 2 both have to be in the set. 1) alone is not sufficient to answer the question, so eliminate D & A.

From 2), we know 3 is in the set, since -3 is in the set. This is not sufficient to answer the question either, and we can eliminate B.

1) + 2) together still do not allow us to answer the question because we only know 2, 3, and -3 are in the set, so my answer is E.

I interpret ab in the question as a number with tenth and unit digits. I wonder what the answer will be if ab in the question is meant to be a x b.

DLMD · Answer

Jinino:

I guess ab = a*b

can you come with another answer?

banerjeea_98 · Answer

First rule says if a b in a set then ab in a set and second says if -a in set then a in set. 

1) in this statement "2 is in the set" doesn't follow any of the above 2 rules, so can't tell if 12 is also in the set....insuff

2) -3 falls under the 2nd rule i.e. -a then a . So we can determine the set as (3,-3). As 12 is not part of that we can ans the ques ---"No"...Suff


Hence "B"

DLMD · Answer

Banerjeea:

the questions says a and -a in a set, but didn't mention they are the range of a set, right?

then set can be (-3, 20) so 12, 3 and -3 are all in the set.

I might think too much, but please clarify for me if you could

thx

jinino · Answer

Mmm...your logic is good but blows me away. When I read the question, I was thinking there are other numbers in the set, not just only a and b in the set. Excellent! :good

DLMD, I totally agree with banerjeea_98's solution.

DLMD · Answer

Jinino: I guess Baner is right but I just cannot figure out why a and -a defines range :oops:

mantha · Answer

From condition 1, if 2 is in set, then -2 is in set.
From condition 2, if (2, -2) in set then -4 is in set and so on...

If -3 is in set, 3 is in set.

Combining the sentences, since -3 and -4 are in the set, 12 is part of the set.

Answer is C

Am I making any assumptions not listed in the conditions??

vprabhala · Answer

i still don't understand why is it the range. what about b.. we were only talking abt being 3 right..

ssumitsh · Answer

I think the answer should be C.

if 2 and -3 are in the set, it implies that -6 is in the set (by rule 1) which means that 2*(-6) = -12 is in the set. By rule 2, this means that 12 is in the set.

jinino · Answer

I think you guys have a valid counterpoint...Don't know what to do with this question. :shock:

vprabhala · Answer

i would think its C. whats the OA?

greenandwise · Answer

I would go with "I don't know what the heck you guys are talking about"...that's my OA but look this is what I'm getting:


{a,b, then ab} and {-a the a}

So if one of the numbers is 2

For choice A {-2, 2} and {-2, b, then -2b}...know can b = -6 based on any data given....not in my opinion


For choice B {-3, 3} and {-3, b, then -3b}..know can b = -4 based on the data given...not in my opinion

Furthermore why did I even assign a to equal -2 or -3 because for all I know a = 2 or 3 or b could equal +/- 2 or 3 so either this is E or this is one of those eeny, meeny, miiney mo questions.

if a and b are in a set, then ab is in the set also. If -a

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