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Company Z has 54 employees. If the number of employees having birthday

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niharika1001
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Company Z has 54 employees. If the number of employees having birthday [#permalink] Company Z has 54 employees. If the number of employees having birthday   Updated on: 18 Aug 2015, 14:37
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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
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E

Originally posted by niharika1001 on 18 Aug 2015, 14:34.
Last edited by Bunuel on 18 Aug 2015, 14:37, edited 1 time in total.
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Company Z has 54 employees. If the number of employees having birthday [#permalink] Company Z has 54 employees. If the number of employees having birthday   18 Aug 2015, 14:50
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niharika1001
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

Question in which the options will help us.

Given: number of people having their birthdays on wednesdays = W > any other day (=6).

The correct answer will give you a number divisible by 6 when you do (54 - correct answer). Only options A and D give a number divisible by 6 when subtracted from 54 as shown below:

A. 6 ----> 54-6 =48 , divisible by 6. Keep
B. 7 ----> 54-7 =47 , not divisible by 6. Eliminate.
C. 8 ----> 54-8 =46 , not divisible by 6. Eliminate.
D. 9 ----> 54-9 =45 , not divisible by 6. Eliminate.
E. 12 ----> 54-12 =42 , divisible by 6. Keep

Using option A, we get number of people with bdays on wednesday = 6 and the number of people on other days = 48/6=8. This is NOT allowed as the question mentions that the number of people having birthdays on wednesdays is greater than the number of people having bdays on any other day of the week. Thus eliminate A and E is the correct answer.

Check: Per E, number of people having bdays on wednesdays = 12, number of people on other days = 42/6 = 7. This does satisfy the requirement of the question and is thus the correct.
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Re: Company Z has 54 employees. If the number of employees having birthday [#permalink] Company Z has 54 employees. If the number of employees having birthday   18 Aug 2015, 14:52
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niharika1001
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

Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 54.

Now, plug options for x. Only A and E give an integer value for y. But only for E x > y as needed.

Answer: E.
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Re: Company Z has 54 employees. If the number of employees having birthday [#permalink] Company Z has 54 employees. If the number of employees having birthday   18 Aug 2015, 15:11
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Great help thanks !!
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Re: Company Z has 54 employees. If the number of employees having birthday [#permalink] Company Z has 54 employees. If the number of employees having birthday   12 Aug 2024, 14:44
What we know:
- All days have the same number of employees with birthdays except Wednesday
- Wednesday has more employees with birthdays than each of the other days
- The total number of employees is 54

Question: What is the minimum number of employees that have a birthday on Wednesday?

Plugging in the answer choices works well, but we can avoid that with a little algebra and a little insight.

Consider if all days had the same number of employees with birthdays (let's call this x), then the number of employees would be a multiple of 7. Wednesday has an extra number of employees (let's call it y) with birthdays to bring the total up to 54. So 7x + y = 54. Or, 54 is y more than a multiple of 7. To minimize y, we must maximize x. The greatest multiple of 7 less than 54 is 49. This is 5 less than 54, so Wednesday must have 5 extra employees with birthdays. Therefore each day has 7 employees with birthdays, but Wednesday has 7+5 = 12 employees with birthdays.

Answer E­
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Re: Company Z has 54 employees. If the number of employees having birthday [#permalink]
12 Aug 2024, 14:44
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