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25 Nov 2022, 09:45
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
49% (02:26) correct
51%
(02:14)
wrong
based on 170
sessions
History
Date
Time
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Not Attempted Yet
Each morning Betty walks from intersection P to intersection R, always walking along streets shown in the figure above and always going east or north. If she varies her walks as much as possible, taking every different path in turn before repeating the sequence of paths, on how many mornings in 48 consecutive mornings will Betty walk through intersection Q?
A. 12
B. 16
C. 24
D. 32
E. 36
Attachment:
2022-11-25_18-16-58.png [ 35.28 KiB | Viewed 4422 times ]
25 Nov 2022, 23:30
Kudos
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Number of ways to reach from P to Q = \(\frac{4! }{ 2! * 2!}\) = 6
Out of these 6 ways, there are 4 ways that pass via Q.
Now, in 48 consecutive mornings Betty would repeat the paths \(\frac{48 }{ 6} = 8\) times.
Number of times Betty walks through intersection Q = \(8 * 4 = 32\) times
Option D
Out of these 6 ways, there are 4 ways that pass via Q.
Now, in 48 consecutive mornings Betty would repeat the paths \(\frac{48 }{ 6} = 8\) times.
Number of times Betty walks through intersection Q = \(8 * 4 = 32\) times
Option D
Attachments
Screenshot 2022-11-26 115713.jpg [ 64.73 KiB | Viewed 4125 times ]
31 Aug 2025, 18:16
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gmatophobia
can you explain in little more detail? How did you come to 4!/2!*2!? What is 4 and 2 here? Also, then how do we know that there are4 ways to pass via Q?
Thanks
