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Bunuel
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20% of the females at company A are over 50 years old, 50% of the male
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30 Jun 2021, 02:15
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Difficulty:

25% (medium)

Question Stats:

82% (02:08) correct 18% (02:42) wrong based on 212 sessions

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20% of the females at company A are over 50 years old, 50% of the males at company A are over 50 years old, and 35% of all the employees are over 50 years old. What percentage of the company is female?

A. 42%
B. 45%
C. 50%
D. 55%
E. 60%
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20% of the females at company A are over 50 years old, 50% of the male
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30 Jun 2021, 03:05
Solution:

We can solve this question methodically and also using alligation method.

Methodical way:

Let the number of males in the company be \(X\) and females be \(Y\).

So, number of females over 50 years old \(= \frac{20Y}{100} = \frac{Y}{5}\)

number of males over 50 years old \(= \frac{50X}{100} = \frac{X}{2}\)

Number of over 50 years old in the whole office \(= \frac{45}{100} \times (X+Y)\)

According to the question: \(\frac{X}{2} + \frac{Y}{5} = \frac{45}{100} \times (X+Y)\)

On solving this we will get \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Alligation Method:

Attachment:
aligation.png
aligation.png [ 2.05 KiB | Viewed 4088 times ]

So the ration \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Hence the right answer is 16.67%

Bunuel please look into the options.

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20% of the females at company A are over 50 years old, 50% of the male
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30 Jun 2021, 06:21
GMATWhizTeam
Solution:

We can solve this question methodically and also using alligation method.

Methodical way:

Let the number of males in the company be \(X\) and females be \(Y\).

So, number of females over 50 years old \(= \frac{20Y}{100} = \frac{Y}{5}\)

number of males over 50 years old \(= \frac{50X}{100} = \frac{X}{2}\)

Number of over 50 years old in the whole office \(= \frac{45}{100} \times (X+Y)\)

According to the question: \(\frac{X}{2} + \frac{Y}{5} = \frac{45}{100} \times (X+Y)\)

On solving this we will get \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Alligation Method:

Attachment:
aligation.png

So the ration \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Hence the right answer is 16.67%

Bunuel please look into the options.
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Edited the typo. Thank you.

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20% of the females at company A are over 50 years old, 50% of the male
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28 Dec 2022, 09:36
If we assume total employees = 100, x = females, y = males
35 employees are 50+ and 65 are below 50

We get the following 2 equations:
0.2x + 0.5y = 35

0.8x + 0.5y = 65

Solving these 2 gives us x = 50 which is the answer - C) 50%
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saynchalk
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20% of the females at company A are over 50 years old, 50% of the male
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16 Mar 2024, 21:34
GMATWhizTeam
Solution:

We can solve this question methodically and also using alligation method.

Methodical way:

Let the number of males in the company be \(X\) and females be \(Y\).

So, number of females over 50 years old \(= \frac{20Y}{100} = \frac{Y}{5}\)

number of males over 50 years old \(= \frac{50X}{100} = \frac{X}{2}\)

Number of over 50 years old in the whole office \(= \frac{45}{100} \times (X+Y)\)

According to the question: \(\frac{X}{2} + \frac{Y}{5} = \frac{45}{100} \times (X+Y)\)

On solving this we will get \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Alligation Method:

Attachment:
aligation.png

So the ration \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Hence the right answer is 16.67%

Bunuel please look into the options.
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­Hi, how did you get 45%? In the question it's mentioned that 35% of all employees are over 50 so I am confused there
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20% of the females at company A are over 50 years old, 50% of the male
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16 Mar 2024, 23:50
saynchalk

GMATWhizTeam
Solution:

We can solve this question methodically and also using alligation method.

Methodical way:

Let the number of males in the company be \(X\) and females be \(Y\).

So, number of females over 50 years old \(= \frac{20Y}{100} = \frac{Y}{5}\)

number of males over 50 years old \(= \frac{50X}{100} = \frac{X}{2}\)

Number of over 50 years old in the whole office \(= \frac{45}{100} \times (X+Y)\)

According to the question: \(\frac{X}{2} + \frac{Y}{5} = \frac{45}{100} \times (X+Y)\)

On solving this we will get \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Alligation Method:

Attachment:
aligation.png

So the ration \(\frac{X}{Y} = \frac{5}{1}\)

Which means percent of females in the company \(= \frac{1}{5+1} \times 100 = \frac{1}{6} \times 100 = 16.67\)%

Hence the right answer is 16.67%

Bunuel please look into the options.
­Hi, how did you get 45%? In the question it's mentioned that 35% of all employees are over 50 so I am confused there
Show more
­
That's clearly a typo. Here is a correct equation: 0.2x + 0.5y = 0.35(x + y)

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