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Company Z has 54 employees. If the number of employees having birthd
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02 Mar 2025, 23:28
02 Mar 2025, 23:28
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Company Z has 54 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
A. 6
B. 7
C. 8
D. 9
E. 12
A. 6
B. 7
C. 8
D. 9
E. 12
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Re: Company Z has 54 employees. If the number of employees having birthd
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18 Mar 2025, 13:42
18 Mar 2025, 13:42
Expert Reply
We know that company $Z$ has 54 employees and the number of employees having birthday on Wednesday is more than the number of employees having birthday on any other day of the week; we need to find the minimum number of people who have their birthday on Wednesday.
Since we need to minimize the number the number of people having birthday on Wednesday, we would prefer to have people having birthdays on Wednesday close to those who have birthday on the day other than Wednesday.
As there are 7 days in a week, 7-7 persons can have birthday on different 7 days of the week, so we left with $\(54-7 \times 7=54-49=5\)$ persons out of which 3 persons can be given 3 different days other than Wednesdays and the remaining 2 can have birthdays on Wednesday only, so that Wednesday can have maximum people.
Thus the minimum possible number of people having birthday on Wednesday can be $\(7+2=9\)$
Hence the answer is (D).
Since we need to minimize the number the number of people having birthday on Wednesday, we would prefer to have people having birthdays on Wednesday close to those who have birthday on the day other than Wednesday.
As there are 7 days in a week, 7-7 persons can have birthday on different 7 days of the week, so we left with $\(54-7 \times 7=54-49=5\)$ persons out of which 3 persons can be given 3 different days other than Wednesdays and the remaining 2 can have birthdays on Wednesday only, so that Wednesday can have maximum people.
Thus the minimum possible number of people having birthday on Wednesday can be $\(7+2=9\)$
Hence the answer is (D).
Re: Company Z has 54 employees. If the number of employees having birthd
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25 Apr 2025, 03:51
25 Apr 2025, 03:51
Hello, the stem says ".. is more than .. birthdays on any other day of the week, each of which have same number of birth-days", does not that mean that the remaining 6 days of the week have the same number of birthdays? And thus the number of employees (excluding those of Wednesday) should be a multiple of 6? What I am missing here!
Thanks,
Thanks,
