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05 Feb 2015, 09:25
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:37) correct
32%
(01:58)
wrong
based on 570
sessions
History
Date
Time
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Not Attempted Yet
Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location. If Pavel travels only along streets and does not travel diagonally, the shortest possible route connecting the two points is exactly 14 blocks. How many different 14-block routes may Pavel take to travel the shortest possible distance to his aunt’s house?
A. 14
B. (14!)/(8!6!)
C. (22!)/(14!8!)
D. 8!6!
E. 14!8!6!
A. 14
B. (14!)/(8!6!)
C. (22!)/(14!8!)
D. 8!6!
E. 14!8!6!
09 Feb 2015, 05:46
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Bunuel
Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location. If Pavel travels only along streets and does not travel diagonally, the shortest possible route connecting the two points is exactly 14 blocks. How many different 14-block routes may Pavel take to travel the shortest possible distance to his aunt’s house?
A. 14
B. (14!)/(8!6!)
C. (22!)/(14!8!)
D. 8!6!
E. 14!8!6!
Kudos for a correct solution.
A. 14
B. (14!)/(8!6!)
C. (22!)/(14!8!)
D. 8!6!
E. 14!8!6!
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:
Solution: B
It will probably come as a relief to learn that this very difficult problem boils down to simple combinatorics. If Pavel has to walk eight blocks north and six blocks east, we can express his route as NNNNNNNNEEEEEE. The question is thus a repeating elements permutation problem that asks us how many ways we can arrange those letters. (If this is confusing, start with smaller numbers. Say I have to walk two blocks north and one block east to get to the train station. I can walk NNE, NEN, or ENN, three different routes that will all get me to the train station.) This gives us (total # of letters)!/(# of N’s)!(# of E’s)!, or 14!/8!6!, answer (B).
General Discussion
05 Feb 2015, 19:42
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ans B..
for simplification, you can draw a box/rectangle with eight vertical and 6 horizontal lines...
the Q asks u how can u travel from one vertex to opposite vertex along these lines..
And the shortest route will consist of 8 vertical and 6 horizontal moves..
so total ways are 14! out of which 8 are one kind and 6 of the other...
ways= 14!/(8!6!)
for simplification, you can draw a box/rectangle with eight vertical and 6 horizontal lines...
the Q asks u how can u travel from one vertex to opposite vertex along these lines..
And the shortest route will consist of 8 vertical and 6 horizontal moves..
so total ways are 14! out of which 8 are one kind and 6 of the other...
ways= 14!/(8!6!)
