Fuchs family daughters- could'nt he have some sons? : GMAT Problem Solving (PS)
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# Fuchs family daughters- could'nt he have some sons?

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Manager
Joined: 16 May 2011
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Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
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Fuchs family daughters- could'nt he have some sons? [#permalink]

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06 Jul 2011, 11:44
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A photographer sets the 6 daughters of the Fuchs family in two equal rows. In each row,
the girls are ordered from the tallest on the left to the shortest on the right, and no girl on
the second row is shorter than the one in front of her. If no two girls are of equal height,
how many ways are there to set the Fuchs daughters for a photo?
(A) 4
(B) 5
(C) 6
(D) 24
(E) 36
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Re: Fuchs family daughters- could'nt he have some sons? [#permalink]

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06 Jul 2011, 12:17
firstly I would like to ask..."FUCHS", seriously? the book wrote that? lol

solution has been discussed before http://gmatclub.com/forum/combinatory-problem-help-needed-70671.html...its a difficult problem
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Re: Fuchs family daughters- could'nt he have some sons? [#permalink]

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07 Jul 2011, 02:13
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I II III
1 2 3

Consider these to be the 6 places.
Consider the 6 heights to be H1, H2, H3, H4, H5 and H6 in increasing order.

It is obvious that H1 has to be at place 1 since H1 is shortest and H6 has to be at place III since H6 is tallest.
We only have to worry about H2, H3, H4 and H5.
Think about place 2 - People at places 3 and II have to be taller so H4 and H5 cannot come here. Only possibilities - H2/H3
Think about place 3 - Person there has to be taller than person at place 2. Only possibilities - H3/H4/H5
Think about place I - Person there has to be shorter than person at place II. Only possibilities - H2/H3/H4
Think about place II - Person there has to be taller than people at place I and 2. Only possibilities - H4/H5

Now just combine them in all possible ways:
H2, H3, H4, H5
H2, H4, H3, H5
H2, H5, H3, H4
H3, H4, H2, H5
H3, H5, H2, H4

5 ways
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Re: Fuchs family daughters- could'nt he have some sons? [#permalink]

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08 Jul 2011, 09:10
fivedaysleft wrote:
firstly I would like to ask..."FUCHS", seriously? the book wrote that? lol

Don't laugh so hard...
I know a person from the same country as your avatar hero that uses the same last name in his emails (Fuchs). However, his original last name is with "k" instead of "h". It was funny because every time he would write his last name on the internet some software would ban his posts, so I guess he had to do something about it.
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Re: Fuchs family daughters- could'nt he have some sons? [#permalink]

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08 Jul 2011, 10:17
Ha ha ha! Great posts....
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Re: Fuchs family daughters- could'nt he have some sons? [#permalink]

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08 Jul 2011, 19:49
fivedaysleft wrote:
firstly I would like to ask..."FUCHS", seriously? the book wrote that? lol

solution has been discussed before http://gmatclub.com/forum/combinatory-problem-help-needed-70671.html...its a difficult problem

Would be somewhat entertaining on the real GMAT!
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Re: Fuchs family daughters- could'nt he have some sons? [#permalink]

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08 Aug 2011, 11:45
dimri10 wrote:
A photographer sets the 6 daughters of the Fuchs family in two equal rows. In each row,
the girls are ordered from the tallest on the left to the shortest on the right, and no girl on
the second row is shorter than the one in front of her. If no two girls are of equal height,
how many ways are there to set the Fuchs daughters for a photo?
(A) 4
(B) 5
(C) 6
(D) 24
(E) 36

bad question - no logic or formula just painting on the paper. I hope I will not see such questions during real exam.
Re: Fuchs family daughters- could'nt he have some sons?   [#permalink] 08 Aug 2011, 11:45
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# Fuchs family daughters- could'nt he have some sons?

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