Company Y employs c women and d men.

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Company Y employs c women and d men.

by gmat_guy666 » Tue Oct 14, 2014 6:52 am
Company Y employs c women and d men. Do the women at Company Y earn an average (arithmetic mean) annual salary greater than $25,000?

(1) Company Y pays its employees a total of $30,000(c + d) in salaries annually.
(2) The men at Company Y earn an average (arithmetic mean) annual salary of $34,000.


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by [email protected] » Tue Oct 14, 2014 9:52 am
Hi gmat_guy666,

This is a great "concept" question, meaning that you can get most of the way through it without doing too much physical work (as long as you understand the concepts within the question).

We're told that there are C women and D men. We're asked if the women earn an average annual salary > $25,000. This is a YES/NO question.

Fact 1: Total pay for all employees = $30,000(C+D) annually.

This gives us almost no information. Even if we had the values for C and D, we still wouldn't know the average salary for the women.
Fact 1 is INSUFFICIENT.

Fact 2: The men earn an average annual salary of $34,000.

Just like Fact 1, this doesn't give us much information. We know nothing about the number of women or their salaries.
Fact 2 is INSUFFICIENT.

Combined, we know....
Total pay = $30,000(C+D)
Average pay for Men = $34,000

If you're comfortable with the concept behind weighted averages, you might see that this is INSUFFICIENT (as the number of men increases, the average pay for women decreases). Here's how you can prove it though (by TESTing VALUES):

If....
C=1
D=1
Total pay = 30,000(2) = 60,000
Avg. pay for Men = 34,000
Avg. pay for Women = 26,000
The answer to the question is YES

C=1
D=2
Total pay = 30,000(3) = 90,000
Avg. pay for Men = 34,000 x 2 men
Avg. pay for Women = 22,000 x 1 woman
The answer to the question is NO

Combined, INSUFFICIENT

Final Answer: E

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by GMATGuruNY » Tue Oct 14, 2014 11:45 am
gmat_guy666 wrote:Company Y employs c women and d men. Do the women at Company Y earn an average (arithmetic mean) annual salary greater than $25,000?

(1) Company Y pays its employees a total of $30,000(c + d) in salaries annually.
(2) The men at Company Y earn an average (arithmetic mean) annual salary of $34,000.
An alternate way to combine the two statements is to TEST THE THRESHOLD.
Here, the threshold is an average salary of $25,000 for the women.

To test the threshold, we can use ALLIGATION.
For a description of alligation, check my post here:
https://www.beatthegmat.com/mean-t266852.html

Case 1: Average salary for the women = 25,000
Using alligation to determine the ratio of women to men, we get:
W 25,000-----5,000-----30,000-----4,000-----34,000 M
W/M = 4000/5000 = 4/5.
Thus, if there are 4 women for every 5 men, the average salary for the women will be exactly $25,000.

Case 2: Average salary for the women = 29,000
Using alligation to determine the ratio of women to men, we get:
W 29,000-----1,000-----30,000-----4,000-----34,000 M
W/M = 4000/1000 = 4/1.
Thus, if there are 4 women for every 1 man, the average salary for the women will be $29,000.

Since the average salary for the women is EQUAL to $25,000 in Case 1 but GREATER than $25,000 in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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