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A photographer will arrange

A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person [...]

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Written by Take GRE Team on July 30th, 2007 with 10 comments.
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A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the personstanding in front of him or her. How many such arrangements of the 6 people are
possible?
A. 5
B. 6
C. 9
D. 24
E. 36

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GRE Question of the Day by Take GRE Team on July 30th, 2007 with 10 answers.
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10 Answers

Read the answer left by other GRE Takers below, or:

Get your own gravatar by visiting gravatar.com Reynard
#1. July 30th, 2007, at 7:05 PM.

only 5 such arrangements:

1 2 3
4 5 6

1 2 4
3 5 6

1 2 5
3 4 6

1 3 4
2 5 6

1 3 5
2 4 6

Get your own gravatar by visiting gravatar.com shilpa
#2. July 30th, 2007, at 7:09 PM.

i think its (B)
if we consider 6 people A,B,C,D,E,F such that A

Get your own gravatar by visiting gravatar.com amar eswar
#3. August 2nd, 2007, at 5:52 PM.

its B

Get your own gravatar by visiting gravatar.com ylmson
#4. August 3rd, 2007, at 6:39 AM.

assuming we label the people in the height order of 1,2,3,4,5,6
first column has 3 possibilities:
1
2
or
1
3
or
1
4

There are 2 possible arrangements for the first two cases, and only 1 possible arrangement for the third case, therefore there are only 5 possibilities. They are all enumerable. I choose (A)

Get your own gravatar by visiting gravatar.com zenith
#5. August 5th, 2007, at 3:27 PM.

very much a)

Get your own gravatar by visiting gravatar.com sharath_s
#6. August 5th, 2007, at 7:07 PM.

ya, its option A.

Get your own gravatar by visiting gravatar.com Hitesh
#7. September 20th, 2007, at 12:49 PM.

The answer is 6… option B….

Consider 1, 2, 3, 4, 5 and 6 as 6 different people with 6 different heights.

Now 1,2 and 3 are the shortest people so they are placed in ascending order from left to right.. They can be arranged only in 1 way.

to arrange remaining people 4,5 and 6 in second row, you can simply have 3! ways.

So total number of ways is: 6.

Dear Take Gre Team please correct me if I am wrong……

Thanks

Get your own gravatar by visiting gravatar.com armen
#8. October 8th, 2007, at 10:25 AM.

Hitesh,

it says “The heights of the people within each row must increase from left to right”, what you are proposing is to have different orders in the second raw, which is not right.

looks like a is the right answer.

thanks

Get your own gravatar by visiting gravatar.com pen name
#9. December 21st, 2007, at 11:28 PM.

the ans is a……….

Get your own gravatar by visiting gravatar.com caulfy
#10. January 4th, 2008, at 1:04 AM.

I’m going to have to say that the answer is:

4 5 6
1 2 3

3 5 6
1 2 4

3 4 6
1 2 5

2 5 6
1 3 4

2 4 6
1 3 5

The key is recognizing that 1 must go in the leftmost position of the first row and 6 must go in the rightmost position of the back row. In addition, it’s impossible to have either 4 or 5 in the middle position in the front row (either option leads to an eventual violation of the rules). Only 2 and 3 can occupy the middle position in the front row. There are 3 possible arrangements if 2 occupies it and 2 possible arrangements if 3 occupies it for a total of 5 possibilities.

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