Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 102

In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
26 Aug 2010, 07:40
Question Stats:
79% (02:34) correct 21% (02:50) wrong based on 1090 sessions
HideShow timer Statistics
In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females? A. 3/5 B. 2/3 C. 3/4 D. 4/5 E. 5/6
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59674

In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
26 Aug 2010, 08:12
udaymathapati wrote: In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
A. 3/5 B. 2/3 C. 3/4 D. 4/5 E. 5/6 Given weighted average employees who are at least 35 years old: \(\frac{0.5m+0.4f}{m+f}=0.42\). Question: \(\frac{f}{m+f}=?\) \(\frac{0.5m+0.4f}{m+f}=0.42\); \(50m+40f=42m+42f\); \(4m=f\); \(\frac{f}{m}=4\); \(\frac{f}{m+f}=\frac{4}{5}\). Answer: D.
_________________




Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 920
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: Percent Problem
[#permalink]
Show Tags
26 Aug 2010, 09:46
I have a different approach that may be useful for you: Let's say that “x” is the % of male employees in the corporation. So, (1x) is the % of female employees in the same company. Therefore: \((50%)(x) + (40%)(1x) = 42%\) Expressed in fractions: \((1/2)(x) + (2/5)(1x) = 21/50\) We solve the equation and we have: \(x = 1/5\) \((1x) = 4/5\) Answer: 4/5 : D I think I deserve kudos
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html GMAT Club Premium Membership  big benefits and savings




Intern
Joined: 16 Jul 2010
Posts: 8

Re: Percent Problem
[#permalink]
Show Tags
19 Oct 2010, 07:58
Hi Buneul 
I understood your explanation until the last step. How do you get from f/m= 4 to the 4/5?
Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 59674

Re: Percent Problem
[#permalink]
Show Tags
19 Oct 2010, 14:33
Atrain13gm wrote: Hi Buneul 
I understood your explanation until the last step. How do you get from f/m= 4 to the 4/5?
Thanks! \(4m=f\) > \(\frac{f}{m+f}=\frac{4m}{m+4m}=\frac{4m}{5m}=\frac{4}{5}\). Hope it's clear.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9869
Location: Pune, India

Re: GWD #1 Math 11
[#permalink]
Show Tags
05 Apr 2012, 20:34
eybrj2 wrote: In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
a) 3/5
b) 2/3
c) 3/4
d) 4/5
e) 5/6 You can use the weighted averages formula for a 10 sec solution. No of females/No of males = (50  42)/(42  40 ) = 4/1 No of females as a fraction of total employees = 4/(4+1) = 4/5 For details of this method, check: http://www.veritasprep.com/blog/2011/03 ... averages/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Board of Directors
Joined: 01 Sep 2010
Posts: 3416

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
02 Jun 2012, 19:06
your post on veritas blog is amazing Karishma
_________________



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
29 Sep 2014, 00:20
Let Male employees = x
Let Female employees = y
Total Employees = x+y
We require to find \(\frac{y}{x+y}\)
Setting up the equation:
\(\frac{50x}{100} + \frac{40y}{100} = \frac{42}{100} (x+y)\)
\(\frac{y}{x} = 4\)
\(\frac{y}{x+y} = \frac{4}{1+4} = \frac{4}{5}\)
Answer = E



Director
Joined: 23 Jan 2013
Posts: 522

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
05 Oct 2015, 21:42
x total number of employees f  all females xf  all males
we need f/x
50(xf)+40f=42x 50x50f+40f=42x 10f=8x f/x=8/10=4/5
D



Intern
Joined: 24 Apr 2016
Posts: 6

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
22 Aug 2016, 07:08
.5m+.40f=.42 m+f=1
solve these two equations, f=4/5



Intern
Joined: 11 Apr 2016
Posts: 38
Location: India
Concentration: Marketing, Technology
WE: Business Development (Computer Software)

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
06 Nov 2016, 20:47
I used the 2 way chart to help create the expression :
(50/100)x + (40/100)y = 42/100(x+y) .... where x is number of males, y is number of females and x+y is total.
Now when you simplify it, you will get 4x = y. Means for every 4 females there is 1 male... No of females is 80% or 4/5



Manager
Joined: 02 Jan 2017
Posts: 67
Location: Pakistan
Concentration: Finance, Technology
GPA: 3.41
WE: Business Development (Accounting)

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
16 Dec 2017, 09:32
Males + Females =100  Equation 1
50 * Males + 40 * Females = 42 [ Males + Females ]  Equation 2
Solve for Females.
You will get 80 Answer ( Which is 80%)
therefore = 80/100=4/5



VP
Joined: 09 Mar 2016
Posts: 1229

In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
28 Mar 2018, 13:07
VeritasPrepKarishma wrote: eybrj2 wrote: In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
a) 3/5
b) 2/3
c) 3/4
d) 4/5
e) 5/6 You can use the weighted averages formula for a 10 sec solution. No of females/No of males = (50  42)/(42  40 ) = 4/1 No of females as a fraction of total employees = 4/(4+1) = 4/5 For details of this method, check: http://www.veritasprep.com/blog/2011/03 ... averages/Hi VeritasPrepKarishma, What if i use alligations method 5040 42 28 as far i remember the value that is closer to the mean has more weight right? so here # of female employees is more (its not surprising actually, they have always been smarter than men ) how to proceed further ? let me try ... so 2 here has more weight hence it should be in numerator, and 8 has less weight and should be in denominator hence \(\frac{2}{8}\) > \(\frac{1}{4}\) so ratio of females to men is 1 to 4 ? but the mean was closer to percentage of females, shouldnt females be more than men ?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9869
Location: Pune, India

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
29 Mar 2018, 00:04
dave13 wrote: VeritasPrepKarishma wrote: eybrj2 wrote: In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
a) 3/5
b) 2/3
c) 3/4
d) 4/5
e) 5/6 You can use the weighted averages formula for a 10 sec solution. No of females/No of males = (50  42)/(42  40 ) = 4/1 No of females as a fraction of total employees = 4/(4+1) = 4/5 For details of this method, check: http://www.veritasprep.com/blog/2011/03 ... averages/Hi VeritasPrepKarishma, What if i use alligations method 5040 42 28 as far i remember the value that is closer to the mean has more weight right? so here # of female employees is more (its not surprising actually, they have always been smarter than men ) how to proceed further ? let me try ... so 2 here has more weight hence it should be in numerator, and 8 has less weight and should be in denominator hence \(\frac{2}{8}\) > \(\frac{1}{4}\) so ratio of females to men is 1 to 4 ? but the mean was closer to percentage of females, shouldnt females be more than men ? The method of allegation is the same as the weighted average formula I have used. To ensure that there is no confusion, use w1/w2 = (A2  Aavg)/(Aavg  A1) No diagram is required here. The details of this are provided in the link given in my post above.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



VP
Joined: 09 Mar 2016
Posts: 1229

In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
29 Mar 2018, 09:48
VeritasPrepKarishma, thanks! I wish your website featured search box i wanted to find the link where it is explained whhe sometimes numeratot and denominato values switch places but couldnt find it...



VP
Joined: 31 Oct 2013
Posts: 1492
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
20 Apr 2018, 16:36
udaymathapati wrote: In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
A. 3/5 B. 2/3 C. 3/4 D. 4/5 E. 5/6 No. of male=m No. of Female=f (0.5)*m + (0.4)f = 0.42(m+f) 0.5m + 0.4f = 0.42m + 0.42f 0.08m = 0.02f 8m=2f (multiply both side by 100) 4m=f f/m=4 : 1 So, m+f = 5 f/(m+f)=4/5, which is option D.



Manager
Joined: 08 Sep 2016
Posts: 100

In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
23 Apr 2018, 16:08
Alternate way  you can set up two equations:
Males = M and Females = F Set the total to be 100 since we are dealing with percents and no value has been provided.
M+F = 100 (equation 1)
The question says 50% of males and 40% of females are at least 35. The question also says that 42% of total employees are at least 35. .5M + .4F = 42 > multiply each term by 100 50M+ 40F = 4200 > reduce down by dividing each by 10 5M+4F= 420 (equation 2)
Subtracting equation 2 from equation 1. You get M=20 and F=80.
F/M+F = 80/20+80 = 80/100 80/100 = 4/5
answer D



Manager
Joined: 31 Jul 2017
Posts: 197
Location: Tajikistan

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
01 Sep 2018, 05:54
VeritasKarishma wrote: eybrj2 wrote: In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
a) 3/5
b) 2/3
c) 3/4
d) 4/5
e) 5/6 You can use the weighted averages formula for a 10 sec solution. No of females/No of males = (50  42)/(42  40 ) = 4/1 No of females as a fraction of total employees = 4/(4+1) = 4/5 For details of this method, check: http://www.veritasprep.com/blog/2011/03 ... averages/ VeritasKarishma, you are perfect and your solutions are very well constructed and easy to follow. Thanks a lot for your valuable contribution!!!



Manager
Joined: 11 Aug 2018
Posts: 109

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
11 Sep 2018, 05:34
dave13 wrote: VeritasPrepKarishma wrote: eybrj2 wrote: In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
a) 3/5
b) 2/3
c) 3/4
d) 4/5
e) 5/6 You can use the weighted averages formula for a 10 sec solution. No of females/No of males = (50  42)/(42  40 ) = 4/1 No of females as a fraction of total employees = 4/(4+1) = 4/5 For details of this method, check: http://www.veritasprep.com/blog/2011/03 ... averages/Hi VeritasPrepKarishma, What if i use alligations method 5040 42 28 as far i remember the value that is closer to the mean has more weight right? so here # of female employees is more (its not surprising actually, they have always been smarter than men ) how to proceed further ? let me try ... so 2 here has more weight hence it should be in numerator, and 8 has less weight and should be in denominator hence \(\frac{2}{8}\) > \(\frac{1}{4}\) so ratio of females to men is 1 to 4 ? but the mean was closer to percentage of females, shouldnt females be more than men ? I think this is more cleaner
Attachments
2.jpg [ 39.27 KiB  Viewed 6734 times ]



Intern
Joined: 07 Jul 2019
Posts: 1

Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
Show Tags
09 Oct 2019, 11:18
Let m be the total number of male employees and f be the total number of female employees. Find out f/(m+f) = ?
Given 0.5m and 0.4f are 35 years old. Again 0.42(m+f) are 35 years old. [Since, total = m+f] Therefore, 0.5m + 0.4f = 0.42(m+f) Divide both sides by (m+f) Therefore, 0.5(m/(m+f)) + 0.4(f/(m+f)) = 0.42 Let f/(m+f) = a Therefore, 0.5(1a) + 0.4a = 0.42 Solving this, a = 4/5
Thus female employees are 4/5th of total employees.




Re: In a corporation, 50 percent of the male employees and 40
[#permalink]
09 Oct 2019, 11:18



Go to page
1 2
Next
[ 21 posts ]



