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# Tricky Math Question - Error in Question (pls do not refer)

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Intern
Joined: 09 Sep 2010
Posts: 12

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Tricky Math Question - Error in Question (pls do not refer) [#permalink]

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13 Feb 2011, 01:48
00:00

Difficulty:

(N/A)

Question Stats:

20% (01:26) correct 80% (00:26) wrong based on 5 sessions

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Q- In the junior basketball league there are 18 teams, 2/3 of them are bad and 1/2 are rich. What can't be the number of teams that are rich and bad?
a)4 b)6 c) 10 d)13 e)15

The given explanation is :
12 teams are bad and 9 are rich.
The no. of teams which are rich and that are bad must be between 9 and (9+12-18=3)

The only answer, which is not in that range is (C)

[Reveal] Spoiler: OA

Last edited by sandhyash on 13 Feb 2011, 07:39, edited 1 time in total.

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Manager
Joined: 20 Dec 2010
Posts: 168

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Location: Stockholm, Sweden

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13 Feb 2011, 03:32
They can be both bad and rich.

Think of it as a Venn-diagram, left circle bad and right circle rich.

If 10 are both bad and rich, that implies that at least 10 are bad, but only 9 are bad so it cannot be true.
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Kudos [?]: 62 [0], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128905 [0], given: 12183

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13 Feb 2011, 03:58
Moved to PS subforum.

sandhyash wrote:
Q- In the junior basketball league there are 18 teams, 2/3 of them are bad and 1/2 are rich. What can't be the number of teams that are rich and bad?

a) 4
b) 6
c) 10
d) 13
e) 15

The given explanation is :
12 teams are bad and 9 are rich.
The no. of teams which are rich and that are bad must be between 9 and (9+12-18=3)

The only answer, which is not in that range is (C)

How can the number of teams that are BOTH rich and bad be more than the teams that are rich (9)? So 9 is the upper limit for the number of teams that are BOTH rich and bad. The lower limit for the the number of teams that are BOTH rich and bad is 3: TOTAL=Bad+Rich-Both+Neither --> 18=12+9-Both+Neither --> Both=3+Neither, so if there are no teams that are neither bad or rich then Both=3.

So there are 3 values among answer choices which can't be the number of teams that are both rich and bad: C, D, and E.

P.S.
 ! Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

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Intern
Joined: 06 Feb 2011
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13 Feb 2011, 06:16
Yes! C,D& E all can't be both bad and rich. And yet the OA states that only C is correct. How is this so?

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Intern
Joined: 09 Sep 2010
Posts: 12

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13 Feb 2011, 07:37
thanks for your prompt response. Sorry for posting my question here, I did not know where to post my query on the website.

As for the solution, even this was not making sense to me. I was practising from a coaching class material from an academy. I had a feeling that there must be an error in question but I did not want to be over confident either. I dont wish to confuse more people with this question hence I am deleting this thread.

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Senior Manager
Joined: 21 Mar 2010
Posts: 306

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Re: Tricky Math Question - Error in Question (pls do not refer) [#permalink]

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14 Feb 2011, 12:31
sandhyash wrote:
Q- In the junior basketball league there are 18 teams, 2/3 of them are bad and 1/2 are rich. What can't be the number of teams that are rich and bad?
a)4 b)6 c) 10 d)13 e)15

The given explanation is :
12 teams are bad and 9 are rich.
The no. of teams which are rich and that are bad must be between 9 and (9+12-18=3)

The only answer, which is not in that range is (C)

I Used the manhattan gmat technique for word translation problems for such questions. make a table of rich/not rich /total along columns and

Bad/not bad/total along rows. Is there an easier way to solve these- provided the answer was right?

Kudos [?]: 31 [0], given: 33

Re: Tricky Math Question - Error in Question (pls do not refer)   [#permalink] 14 Feb 2011, 12:31
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