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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 [...]
Written by Take GMAT Team on July 3rd, 2009 with
31 comments.
Read more articles on GMAT Problem Solving and GMAT Question of the Day.
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
Written by Take GMAT Team on July 3rd, 2009 with
31 comments.
Read more articles on GMAT Problem Solving and GMAT Question of the Day.
Read the comments left by other users below, or:
gaurav
#2.
July 30th, 2007, at 2:46 PM.
should be A i.e.5
consider 1 2 3 4 5 6 to be persons in increasing order fr heights…
so the arrnagements can be
456
123
246
135
346
125
256
134
356
124
what is OA?
James
#3.
July 30th, 2007, at 3:39 PM.
OA means ?
krishna
#5.
July 30th, 2007, at 8:17 PM.
see that 1 and 6 positions are constant.
once we get that fact …question seems easy.
Ardhendu
#6.
July 31st, 2007, at 3:32 PM.
Ans GMAT team
Take GMAT Team
#8.
July 31st, 2007, at 8:06 PM.
This is just hint, We will give the correct answer after discussion.
sudhish
#9.
July 31st, 2007, at 11:12 PM.
D – 24, since it arrangements, 6 & 1 are fixed in the second and first row (from the camera) the remaining 4 people can occupy any of the six postions in 24 diff ways
sudhish
#10.
July 31st, 2007, at 11:16 PM.
any postion meaning – satisfying the height precedence rule
AP
#12.
August 3rd, 2007, at 12:05 AM.
A – 5 ways
kishgem
#13.
September 13th, 2007, at 8:14 AM.
answer is 36 – E
There are six position.
A B C
D E F
For Position A – Number of possibilities is 3
For Position B – 2
For position C – 1
Same for D, E, F
3 * 2 * 1 * 3 * 2 * 1 = 36
TAKEGMAT – please correct me if I am wrong
Vibz
#14.
October 6th, 2007, at 6:05 PM.
Answer is A – 5 ways…
We need to remember that according to the height precedence rule, not only is left to right in increasing order of height, but the front row is also shorter than the person stadnding immediately behind.
So, even if 123 is constant, there is only ONE way to arrange the remaining people. Same applies to all other combinations. Given that the 1st and the last place can be occupied in the same way in all cases, we can work out 5 different arrangements.
john
#15.
January 18th, 2008, at 3:10 PM.
answer is 5
gaurav’s explanation is perfect
sd
#16.
May 19th, 2008, at 2:09 PM.
A-
Looser
#17.
November 17th, 2008, at 1:54 AM.
1,2,3,4,5,6 – people ordered by height.
Possible arrangements:
456 356 346 256 246
123 124 125 134 135
duke
#18.
December 11th, 2008, at 12:57 AM.
36. this is the way it can be filled.
2 3 (6)1
__ __ __
1(1) 3 3
__ __ __
Binita
#19.
July 3rd, 2009, at 6:09 PM.
6 ways.. Answer is ‘B’.
Eman
#20.
July 4th, 2009, at 12:26 AM.
Ans is 5 using 2 rules:
1)L to R increasing order
2)back row has a taller height than the front row.
the only rows possible are as follows
456(123), 356(124), 256(134), 346(125), 246(135)
Amitav
#21.
July 4th, 2009, at 12:43 AM.
The answer is E.
Sharath
#22.
July 4th, 2009, at 8:52 AM.
A
Comb is
456 246 256 346 356
123 135 134 125 124
daniella sankar
#23.
July 4th, 2009, at 10:23 PM.
Ans is E
Praveen
#24.
July 6th, 2009, at 8:48 AM.
The answer provided by Gaurav seems to be correct and also in sync with the hint from GMAT Team.
A) 5
sems to the correct answer.
krishna74
#25.
July 7th, 2009, at 3:12 PM.
B : 6 is the answer
Shal
#26.
July 10th, 2009, at 10:43 AM.
36
Dharm
#27.
July 12th, 2009, at 12:48 AM.
OPtion A
Shal
#28.
July 13th, 2009, at 1:06 PM.
@GMAT team: What is the correct answer??
Pankaj Dahiya
#29.
July 14th, 2009, at 12:52 PM.
A B C D E F – six people ordered according to ascending heights
Now it’s quite clear that ‘A’ takes first row left most position, and ‘F’ takes second row right most position.
__ __ F
A __ __
Now we are left with B, C, D and E.
The position above ‘A’ can be filled in three ways (leaving the tallest among them for the next position, as the person in next position should be taller than the person in this one.)
3 __ F
A __ __
Now we are left with three people.
The position below ‘F’ can be filled in two ways (leaving the shortest among them for the previous position, as the person in previous position should be shorter than the person in this one.)
3 __ F
A __ 2
Now we are left with two people, the taller one takes the position adjacent to F and the shorter one takes the position adjacent to A. i.e. only one possible way.
So, Total no. of ways = 3*2*1*1 = 6
vic
#30.
July 19th, 2009, at 9:29 AM.
5-
456(123)
356(124)
346(125)
256(134)
246(135)
people who refer 6 pls list the ccombinatons, like above, showing 6.
thanks
Kofi DL
#31.
July 29th, 2009, at 10:22 PM.
I have 5 positions….
456
123
346
125
246
135
356
124
256
134
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solidcolor
Did
#1. July 30th, 2007, at 12:52 PM.
A