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 person standing 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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GMAT Set 10 Q25
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Let the 6 people be represented by the numbers 1-6, inclusive, where 1 is the shortest person and 6 is the tallest person.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 some one in second row. The heights of the people with in each row should be increasing from left right, and each person in the second row must be taller than the person standing 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
Fill the MOST RESTRICTED positions first and work down to the LEAST RESTRICTED positions.
Place 1 and 6:
1XX
XX6
Place 2:
Case A:
1XX
2X6
Case B:
12X
XX6
Place 5, whose position will determine where 3 and 4 can go:
Case A:
134...135
256...246
Case B:
125...124...123
346...356...456
Total options = 5.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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