A photographer will arrange 6 people of 6 different heights for a 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
Answer: A
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GMAT Prep Exam Pack 1 - Arranging/FPC Question
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Let the 6 people be represented by the numbers 1-6, inclusive, where 1 is the shortest and 6 is the tallest.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:
XX6
1XX
Place 2:
Case A:
2X6
1XX
Case B:
XX6
12X
Place 5, whose position will determine where 3 and 4 can go:
Case A:
256...246
134...135
Case B:
346...356...456
125...124...123
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].
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