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# GMAT Diagnostic Test Question 40

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Re: GMAT Diagnostic Test Question 40 [#permalink]  23 Aug 2010, 21:09
The wording is too vague and allows the question to be answered in multiple ways.
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Re: GMAT Diagnostic Test Question 40 [#permalink]  27 Aug 2010, 06:45
dzyubam wrote:
Hi guys,
Please see the corrected Official Explanation. The options were corrected a bit too. I'll upload the new PDF doc today too.

Haykgev, your solution is absolutely right .
dzyubam wrote:
Explanation:

The number of ways 5 books can be chosen (with max. 1 large book) equals (total number of ways 5 books can be chosen) - (2 large + 3 small books will be chosen).
Total number of ways 5 books can be chosen = C_{10}^5 = \frac{10*9*8*7*6*5!}{5!5!} = 252.
Number of possible ways that 3 small and 2 large books will be chosen = 1*C_8^3 = 1 * 56 = 56.
Desired number of ways that 5 books can be taken = 252 - 56 = 196.

There seems to be a flaw in the answer of 196 because we have not taken into account that even 3 large and 2 small books may be chosen and also if 5 small books are chosen then the space is wasted as there is space for seven small books .1Large =3 Small . Infact on the face of it ans of 127 seems correct . Any views please

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Re: GMAT Diagnostic Test Question 40 [#permalink]  27 Aug 2010, 09:32
Answer would be (3C2*7C1) + (7C3*3C1) +1 = 21+105+1 =127
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Re: GMAT Diagnostic Test Question 40 [#permalink]  15 Dec 2010, 20:53
I think this needs to be in 700+ range questions. The usual combination questions that I have come across have been geared towards finding only one combination. In here we have to find nCr three times and then add the outcomes. Not that its difficult calculation or time consuming but just tricky. Do others agree?

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Re: GMAT Diagnostic Test Question 40 [#permalink]  04 Sep 2011, 06:54
The question clearly states, that he should have room for 1 large and 4 small books. So how can we have a combination of 8C5? Are we assuming that the it means at most 1 large book?
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Re: GMAT Diagnostic Test Question 40 [#permalink]  16 Jan 2012, 12:04
I am absolutely lost which ANswer CHoice is Right?
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Re: GMAT Diagnostic Test Question 40 [#permalink]  21 Mar 2012, 00:03
gmatpunjabi wrote:
I am absolutely lost which ANswer CHoice is Right?

lol, correct answer is C. 127 ... the previous posts should be cleaned up as the test has since been modified to correct for inaccurate/vague wording.

- 10 books total: 7 Small, 3 Large
- Size equivalents: 3Small = 1Large
- given that the space (in his bag?) can hold 1L + 4S
- no space can be wasted

--- notice this now translates to various possibilities; Since 3S=1L, the bag can also just as well hold:
3Small + 4Small = 7-Small Books
2Large + 1Small
1Large + 4Small

those 3 combinations, respectively, are summed:
7C7 + (3C2 x 7C1) + (3C1 x 7C4) = (1)(21)(105) = 127
Re: GMAT Diagnostic Test Question 40   [#permalink] 21 Mar 2012, 00:03
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