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Do at least 20 percent of the organization members who are over 40 hav

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Do at least 20 percent of the organization members who are over 40 hav  [#permalink]

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New post 26 Mar 2018, 23:08
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Do at least 20 percent of the organization members who are over 40 have college degrees?

(1) Among the member of the organization who are over 40, 24 percent of the female members and 16 percent of the male members have college degrees.
(2) Female members constitute 55 percent of the organization’s membership.

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Re: Do at least 20 percent of the organization members who are over 40 hav  [#permalink]

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New post 27 Mar 2018, 12:55
Bunuel wrote:
Do at least 20 percent of the organization members who are over 40 have college degrees?

(1) Among the member of the organization who are over 40, 24 percent of the female members and 16 percent of the male members have college degrees.
(2) Female members constitute 55 percent of the organization’s membership.


Statement 1-
Scenario 1-
Lets suppose that the total number of people employed above 40 is 1000
Also lets suppose the ratio of males to females is 3:2
Number of males= 600, male college degree holders = \(600*0.16\) = 96
Number of females= 400, female college degree holders= \(400*0.24\) = 96
Total number of graduates= 192. This is less than 20%(200 graduates)

Scenario 2-
Lets suppose that the total number of people employed above 40 is 1000
Also lets suppose the ratio of males to females is 1:1
Number of males= 500, male college degree holders = \(500*0.16\) = 80
Number of females= 400, female college degree holders= \(500*0.24\) = 120
Total number of graduates= 200. This is exactly 20%.
Hence statement 1 is not decisive

Statement 2-
This tells us nothing about graduates. Not sufficient.

Combining- Statement 1 and Statement 2
In the Scenario 1 and Scenario 2, we can add more number of females to make the number of females 55% of the total and keeping there age less than 40, so that they dont effect the Scenario numbers.

Hence combining the two statements is also insufficient.

Answer is E
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Re: Do at least 20 percent of the organization members who are over 40 hav  [#permalink]

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New post 28 Mar 2018, 12:56
Let x = number of organization members who are over 40
f% of x are female
m% of x are male
f+m=100

Statement 1
number of females over 40 with college degrees: \(\frac{24}{100}*\frac{f}{100}*x\)

number of males over 40 with college degrees: \(\frac{16}{100}*\frac{m}{100}*x\)

total members over 40 with college degrees: \((\frac{24}{100}*\frac{f}{100}*x)+(\frac{16}{100}*\frac{m}{100}*x)\)

We're asked to find if this is true: \((\frac{24}{100}*\frac{f}{100}*x)+(\frac{16}{100}*\frac{m}{100}*x) >= \frac{20}{100}*x\)

Simplifying,
\(24f+16m >= 2000\)

Since f+m=100, we can plug in m=100-f into above,
\(24f+16(100-f) >= 2000\)
\(24f+1600-16f >= 2000\)
\(8f >= 400\)
\(f >= 50\)

So the question boils down to "do women make up at least half of the members over 40?" Since we do not know the percentage of members over 40 that are women, we cannot answer the question.

Not sufficient

Statement 2
Not sufficient

Combining 1 & 2
At first glance, since Statement 1 reduces the question to finding \(f\), we might think that Statement 2 completes the puzzle since it gives us \(f=55\). The trap is in Statement 2's wording, which gives us the female percentage of the entire organization, whereas Statement 1 is interested in the female percentage of those over 40.

Not sufficient

Answer: E
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Re: Do at least 20 percent of the organization members who are over 40 hav &nbs [#permalink] 28 Mar 2018, 12:56
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