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Updated on: 19 Mar 2021, 23:57
Originally posted by Rigshim on 19 Mar 2021, 09:17.
Last edited by DisciplinedPrep on 19 Mar 2021, 23:57, edited 1 time in total.
Last edited by DisciplinedPrep on 19 Mar 2021, 23:57, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
45% (02:40) correct
55%
(03:05)
wrong
based on 22
sessions
History
Date
Time
Result
Not Attempted Yet
A person has 9 friends, 4 of whom are male. In how many ways can he plan a trip so that there are at least 2 other male friends, but not more than 3 females?
A. 32
B. 96
C. 286
D. 120
E. 250
A. 32
B. 96
C. 286
D. 120
E. 250
19 Mar 2021, 14:59
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Rigshim
Hello, Rigshim. You might want to post this question in the PS Quant forum so that it has a timer affixed to it and members can try it out. For my part, I calculated (C), 286, as the answer, tracing the logic below:
1) There can be 2, 3, or 4 males within the given constraints.
2) There can be 3, 2, 1, or 0 females within the given constraints.
3) Run the combinations for males and females independently: 4C2, 4C3, 4C4 and 5C3, 5C2, 5C1, 5C0. This yields 6, 4, 1, 10, 10, 5, and 1, respectively. (You have to remember that 0! = 1.)
4) Multiply each "male" count with each "female" count and add:
\(6*10+6*10+6*5+6*1=156\)
\(4*10+4*10+4*5+4*1=104\)
\(1*10+1*10+1*5+1*1=26\)
\(156+104+26=286\)
This was just the first way my mind thought to work the problem. I am not sure what the source may be, but to better conform to what might appear on the GMAT™, I would suggest reordering the answers to count up (i.e. shift (D) and (E) one place to the left or up and make (C) (E) instead). Anyway, thank you for sharing, and good luck with your studies.
- Andrew
19 Mar 2021, 23:01
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Rigshim, welcome to GMATClub.
Please follow the rules while making any posts. If similar behavior is seen in the future, stricter action will be taken against you.
Have a great day.
Please follow the rules while making any posts. If similar behavior is seen in the future, stricter action will be taken against you.
Have a great day.
