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# In an office having 50 employees, (1/4)th of the males and (1/5)th of

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Math Expert
Joined: 02 Sep 2009
Posts: 59590
In an office having 50 employees, (1/4)th of the males and (1/5)th of  [#permalink]

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26 Sep 2018, 04:52
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Difficulty:

15% (low)

Question Stats:

78% (01:54) correct 22% (02:10) wrong based on 72 sessions

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In an office having 50 employees, (1/4)th of the males and (1/5)th of the females eat company breakfast. What is the greatest possible number of employees in the office eat company breakfast?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 25

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Joined: 19 Oct 2013
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Re: In an office having 50 employees, (1/4)th of the males and (1/5)th of  [#permalink]

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28 Sep 2018, 14:52
1
M + F = 50

If F = 40 then 40 * 1/5 = 8
M = 10 not divisble by 4 so not possible.

Try the other way around F = 10 then 10 * 1/5 = 2

And M = 40 * 1/4 = 10

So 10 + 2 = 12

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Joined: 22 May 2016
Posts: 3730
In an office having 50 employees, (1/4)th of the males and (1/5)th of  [#permalink]

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13 Oct 2018, 19:10
1
1
Bunuel wrote:
In an office having 50 employees, (1/4)th of the males and (1/5)th of the females eat company breakfast. What is the greatest possible number of employees in the office eat company breakfast?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 25

To maximize the number of people eating breakfast, maximize the number of men, and minimize the number of women. A greater fraction of men eat breakfast.

$$\frac{1}{4}$$ of men eat breakfast: the number of men must be divisible by 4
$$\frac{1}{5}$$ of women eat breakfast: the number of women must be divisible by 5

Trial and error is quick.
M + W = 50
Minimize the number of women:
Subtracting 5s (from 50) is easier than subtracting 4s.

Minimum # of women: 5
Then there are (50 - 5) = 45 men. Will not work. 45 is not divisible by 4.

Next multiple of women is 10
If there are 10 women, there are 40 men
That works. 40 is divisible by 4.

# of men who eat breakfast: $$40*\frac{1}{4}=10$$
# of women who eat breakfast: $$\frac{10}{5}=2$$

Total: $$(10 + 2 )= 12$$

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In an office having 50 employees, (1/4)th of the males and (1/5)th of   [#permalink] 13 Oct 2018, 19:10
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