Percentage Problem

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damianx2012: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Dec 12, 2019 7:28 am

Percentage Problem

by damianx2012 » Thu Dec 12, 2019 7:38 am

Hello,

this might be the kind of question which is very easy to solve, how ever even after trying to find the solution for 3 hours, I still cant get to the right answer. So perhaps someone might help and explain, why the solution is 20 %.

Question:

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 employees are managers, what percentage of the managers ist male?

Answer
A 20 %
B 33 %
C 50 %
D 60 %
E Can not be determined

Thanks very much in Advance

$$$$

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Source: Beat The GMAT — Problem Solving | Thu Dec 12, 2019 7:38 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Thu Dec 12, 2019 11:23 am

Hi damianx2012,

We're told that at a certain organization, 10 percent of the male employees are managers, 40 percent of the female employees are NOT managers and 30 percent of ALL employees are managers. We're asked what percentage of the managers are MALE. This question gives us some specific percentages to work with - and this is ultimately a "Weighted Average" question, so we should approach it with that formula in mind (although we'll also TEST VALUES at the end to make the calculations easier to deal with):

To start, we are given information on two groups:
1) 10% of the MALE employees are managers
2) 60% of the FEMALE employees are managers (since 40% of females are NOT managers, 100% - 40% = 60% of females ARE managers)

We can refer to these groups as .1M and .6F

Then we're told that 30% of ALL employees are managers. Here we can set up the average formula:

(.1M + .6F)/(M + F) = .3

We're asked to find the percentage of ALL managers who are MALE - so we need to find .1M/(.1M + .6F)

(.1M + .6F)/(M + F) = .3
.1M + .6F = .3M + .3F
.3F = .2M
3F = 2M
F/M = 2/3

This means that for every 2 females, there are 3 males. We know that 10% of the males and 60% of the females are managers; since we're dealing with percentages, let's TEST M = 300 and F = 200

10% of 300 = 30 Male managers
60% of 200 = 120 Female managers
30 + 120 = 150 TOTAL managers

Of those 150 total managers, 30 of them are male.... 30/150 = 3/15 = 1/5 = 20%

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Dec 15, 2019 6:26 pm

damianx2012 wrote:Hello,

this might be the kind of question which is very easy to solve, how ever even after trying to find the solution for 3 hours, I still cant get to the right answer. So perhaps someone might help and explain, why the solution is 20 %.

Question:

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 employees are managers, what percentage of the managers ist male?

Answer
A 20 %
B 33 %
C 50 %
D 60 %
E Can not be determined

Thanks very much in Advance $$$$

We can let m = the number of male employees and f = the number of female employees. We can create the equation:

0.1m + 0.6f = 0.3(m + f)

m + 6f = 3(m + f)

m + 6f = 3m + 3f

3f = 2m

f = 2m/3

We see that the number of female employees is two-thirds as many as the number of male employees. Now we can let m = 30 and f = 20. So we have 0.1 x 30 = 3 male managers and 0.6 x 20 = 12 female managers. Therefore, male managers are 3/(3 + 12) = 3/15 = 1/5 = 20% of all managers in the organization.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]