A photograph will arrange 6 people of 6 different heights for a photography 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 with each row must increase frm left to right, and each person in the second row must be taller than the person standing in front of him/her. hOW MANY SUCH ARRANGEMENTS of the 6 people are possible ?
I got 6 but the right answer is 5. wHY ?? any answer ? Many thanks
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Arrangements for a photography
This topic has expert replies
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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
Student Review #2
Student Review #3
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
Student Review #2
Student Review #3
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi yass20015,
In Quant questions such as these, the number of possible arrangements is sometimes so limited that you can actually just list them out - in that way, you can visualize the solution and just do a bit of 'brute force' work:
Here, we're told to arrange 6 people (who all have DIFFERENT heights) into two rows of 3 so that each person in the first row is 'in front' of a taller person in the second row AND heights increase from 'left to right.' We're asked how many arrangements of people are possible.
If we label the six people as 1, 2, 3, 4, 5, 6 (with 1 the shortest, and each number being 'taller' than the one immediately preceding it), we would have the following options...
456
123
356
124
346
125
256
134
246
135
There are NO other options.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
In Quant questions such as these, the number of possible arrangements is sometimes so limited that you can actually just list them out - in that way, you can visualize the solution and just do a bit of 'brute force' work:
Here, we're told to arrange 6 people (who all have DIFFERENT heights) into two rows of 3 so that each person in the first row is 'in front' of a taller person in the second row AND heights increase from 'left to right.' We're asked how many arrangements of people are possible.
If we label the six people as 1, 2, 3, 4, 5, 6 (with 1 the shortest, and each number being 'taller' than the one immediately preceding it), we would have the following options...
456
123
356
124
346
125
256
134
246
135
There are NO other options.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
