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At a certain organization, 10 percent of the male employees are manage

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Dhruv0911
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At a certain organization, 10 percent of the male employees are manage [#permalink] New post   Updated on: 02 Mar 2023, 08:46
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At a certain organization, 10 percent of the male employees are managers and 40 percent of the female employees are not managers. If 30 percent of all the employees are managers, what percentage of the managers is male?

A) 20
B) 33⅓
C) 50
D) 60
E) It cannot be determined from the information given
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A

Originally posted by Dhruv0911 on 02 Mar 2023, 04:06.
Last edited by Bunuel on 02 Mar 2023, 08:46, edited 1 time in total.
Renamed the topic.
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Re: At a certain organization, 10 percent of the male employees are manage [#permalink] New post   03 Mar 2023, 00:33
Given: At a certain organization, 10 percent of the male employees are managers and 40 percent of the female employees are not managers.

Asked: If 30 percent of all the employees are managers, what percentage of the managers is male?


.4(100%-x%)
ManagersNon managersTotal
Male.1 x%.9 x%x%
Female.6 (100%-x%)100%-x%
Total30%70%100%


.1 x% + .6 (100%-x%) = 30%
60% - .5 x% = 30%
x% = 60%


16%
ManagersNon managersTotal
Male6%54%60%
Female24%40%
Total30%70%100%


Percentage of managers who are male = 6%/30% * 100% = 20%

IMO A
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At a certain organization, 10 percent of the male employees are manage [#permalink] New post   06 Mar 2023, 04:09
Given the time constraint of GMAT, I believe the easier process would be to place values intelligently. We know 10% of male employees are manager and 60% of female employees are managers (since 40% are non-managers). And the overall percentage of managers is 30%. Lets consider there are 100 employees out of which 30%, which is 30, are managers. Now all the numbers has to be in integers. If we start off with 1 person being the 10% male manager, the rest of the number 29 (30-1) needs to be divisible by 6 to satisfy the 60% female managers criteria. Similarly, with 2,3, 4 and 5 we see the criteria doesn't satisfy. Only 6 satisfies, since the remaining number 24 (30-6) can easily be the 60% of the Female managers.

It's a type of a LCM process, and once you practise it quite a few times, preferably mentally, it gets easier.
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Re: At a certain organization, 10 percent of the male employees are manage [#permalink] New post   09 Mar 2023, 22:23
manager not manager
male .10m .9m
female .60f .40f

.3(f+m)=.1m+.6f

.1m/(.1m+.6f)=?
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Re: At a certain organization, 10 percent of the male employees are manage [#permalink] New post   13 Mar 2023, 12:43
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Female= F
Male=M

from males we know 0,1 are manager 0,1M
from females we know that 0,4 are not manager, so 0,6 are managers 0,6F

then we know that 0,3 of the total are manager. Total is F + M so 0,3(F+M)

0,3(F+M)=0,1M+0,6F
0,2M=0,3F
2M=3F
\(\frac{M}{F}=\frac{3}{2}\)

so M:F:T
3x:2x:5x

let x be 20, so M=60, F=40, Total=100

total Male managers=60*0,1=6
total female managers=40*0,6=24
total managers=6+24=30

male managers to total managers=\(\frac{6}{30}=\frac{1}{5}=20\)

20%

IM= A
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At a certain organization, 10 percent of the male employees are manage [#permalink] New post   13 Mar 2023, 22:54
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Dhruv0911 wrote:
At a certain organization, 10 percent of the male employees are managers and 40 percent of the female employees are not managers. If 30 percent of all the employees are managers, what percentage of the managers is male?

A) 20
B) 33⅓
C) 50
D) 60
E) It cannot be determined from the information given


Given: 10% of males are managers, 60% of females are managers (because 40% are not) and overall 30% people are managers.

We can use weighted averages here: \(\frac{w1}{w2} = \frac{(A2 - Aavg)}{(Aavg - A1)} = \frac{(60 - 30)}{(30 - 10)} = \frac{3}{2}\)

So if there are 30 male employees, there are 20 female employees.
10% of male employees are managers so 3 are managers. 60% of female employees are managers so 12 are managers.
We have total 3 + 12 = 15 managers of which 3 are male i.e. 20% are male.

Answer (A)

Check: https://www.youtube.com/watch?v=_GOAU7moZ2Q
for more on the weighted average formula used.
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Re: At a certain organization, 10 percent of the male employees are manage [#permalink] New post   22 Apr 2024, 02:49
Here is the alligation diagram for this :-
KarishmaB wrote:
Dhruv0911 wrote:
At a certain organization, 10 percent of the male employees are managers and 40 percent of the female employees are not managers. If 30 percent of all the employees are managers, what percentage of the managers is male?

A) 20
B) 33⅓
C) 50
D) 60
E) It cannot be determined from the information given

Given: 10% of males are managers, 60% of females are managers (because 40% are not) and overall 30% people are managers.

We can use weighted averages here: \(\frac{w1}{w2} = \frac{(A2 - Aavg)}{(Aavg - A1)} = \frac{(60 - 30)}{(30 - 10)} = \frac{3}{2}\)

So if there are 30 male employees, there are 20 female employees.
10% of male employees are managers so 3 are managers. 60% of female employees are managers so 12 are managers.
We have total 3 + 12 = 15 managers of which 3 are male i.e. 20% are male.

Answer (A)

Check: https://www.youtube.com/watch?v=_GOAU7moZ2Q
for more on the weighted average formula used.

­
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Re: At a certain organization, 10 percent of the male employees are manage [#permalink]
22 Apr 2024, 02:49
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