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

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 out the video: https://www.youtube.com/watch?v=_GOAU7moZ2Q
and the Blog post: https://anaprep.com/arithmetic-weighted-averages/

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.

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

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

.5m+.40f=.42
m+f=1

solve these two equations,
f=4/5

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.

I think this is more cleaner

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.

why isn't this method giving correct ans.?

let total employees = 100
let female employees = x
so male employees = 100-x

so acc. to question :

{50/100 x (100-x)} + {40/100 x x} = 42/100

this gives x = 49.58

Hi Trex88
Thanks for your query.



Firstly, I want to appreciate your approach - it is crisp and direct and can save solution time. BUT while your approach was smart, you made a very careless mistake in executing it.

I’m calling it careless because looking at most of your solution, it doesn’t appear that you don’t have the core skill needed. Let me dive right in!


Here’s the left-hand side of your equation (it is perfect!):

• 50% of male employees + 40% of female employees
• = {50/100 × (100 – x)} + {40/100 × (x)}.

Now, here is the right-hand side of your equation:

• 42/100

Does it look off to you? It has something very important just completely missing!

Well, you missed mentioning 42% of WHAT! Specifically, you did not write the 100 on the right-hand side. You could have avoided this if you were very careful while translating the question: it said, “42% of all the employees are at least 35 years old.”

• Thus, the correct expression on the right-hand side should be {(42/100) × 100}. [NOT just 42/100].

Try solving the correct equation again. You will get x = 80. And so, the final required fraction = x/100 = 80/100 = 4/5.


And that’s it! It was just a blink that made you go wrong despite having such a direct approach.


Hope this helps!

Best,
Aditi Gupta,
Quant expert, e-GMAT

Bunuel

while i got the answer right, is my solution correct?

Atleast 35yrs old;
0.42(T) = 0.5(M) + 0.4(F) <--- eq(1)

more than 35yrs old;
0.58(T) = 0.5(M) + 0.6 (F) <---- eq(2)

subtracting eq(1) from eq(2) we get;
0.16(T) = 0.2(F)
0.8(T) = F
\(\frac{8}{10}\) = \(\frac{F}{T}\)
\(\frac{F}{T}\) = \(\frac{4}{5}\) = Option D

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