GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2019, 11:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In a corporation, 50 percent of the male employees and 40

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
6
58
00:00

Difficulty:

25% (medium)

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
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
12
15
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: $$\frac{f}{m+f}=?$$

$$\frac{0.5m+0.4f}{m+f}=0.42$$;

$$50m+40f=42m+42f$$;

$$4m=f$$;

$$\frac{f}{m}=4$$;

$$\frac{f}{m+f}=\frac{4}{5}$$.

_________________
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

### Show Tags

26 Aug 2010, 09:46
22
1
1
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, (1-x) is the % of female employees in the same company.
Therefore:
$$(50%)(x) + (40%)(1-x) = 42%$$

Expressed in fractions:
$$(1/2)(x) + (2/5)(1-x) = 21/50$$

We solve the equation and we have:
$$x = 1/5$$

$$(1-x) = 4/5$$

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/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings
##### General Discussion
Intern
Joined: 16 Jul 2010
Posts: 8

### Show Tags

19 Oct 2010, 07:58
1
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

### Show Tags

19 Oct 2010, 14:33
4
1
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
14
6
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

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
9
1
1
Let Male employees = x

Let Female employees = y

Total Employees = x+y

We require to find $$\frac{y}{x+y}$$

Setting up the equation:

$$\frac{50x}{100} + \frac{40y}{100} = \frac{42}{100} (x+y)$$

$$\frac{y}{x} = 4$$

$$\frac{y}{x+y} = \frac{4}{1+4} = \frac{4}{5}$$

Director
Joined: 23 Jan 2013
Posts: 522
Schools: Cambridge'16
Re: In a corporation, 50 percent of the male employees and 40  [#permalink]

### Show Tags

05 Oct 2015, 21:42
2
x- total number of employees
f - all females
x-f - all males

we need f/x

50(x-f)+40f=42x
50x-50f+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
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
GMAT 1: 650 Q47 V34
GPA: 3.41
Re: In a corporation, 50 percent of the male employees and 40  [#permalink]

### Show Tags

16 Dec 2017, 09:32
1
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

50-------------------------40

------------42-------------

2-------------------------8

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
2
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

50-------------------------40

------------42-------------

2-------------------------8

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

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

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
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

50-------------------------40

------------42-------------

2-------------------------8

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(1-a) + 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 ]

Display posts from previous: Sort by