Hi, there. I'm happy to contribute to this one.
Prompt:
There are 30 managerial positions in company C, 60 percent of which are occupied by women. What percentage of the managers joined company C a trainee?
As sometime happens, this is prompt that is rich in information for the problem. We know that 60% of 30, or 18 of the managers are women. That means 12 are men.
(
Here, I will give apologies to any readers who are transgender, transsexual, or otherwise not aligned with the binary gender roles. GMAT Quantitative questions like this are unthinkingly heteronormative. In the GMAT world, the idea of a manager who is neither male nor female is unthinkable. We need to abide by those narrow assumptions to answer the questions, although clearly a more open mind will be needed to succeed broadly in the business world of the 21st century.)
Statement #1:
The number of female managers who started in company C as trainee is twice the number of male ones who did not start as trainee.
Let x be the number of females who started in the company as trainees.
Let y be the number of males who started in the company as trainees.
This statement tells us: x = 2y. That's one equation with two unknowns, so we can't solve. Statement #1, by itself, is
insufficient.
Statement #2:
The number of female managers who did not start in company C as trainee is twice the number of female managers who did start in company C as trainee.
If x is the number of females who started in the company as trainees, then (18 - x) is the number of females who did not start in the company as trainees. This statement tells us:
18-x = 2x
18 = 3x
x = 6
So, 6 women begin a trainees, and 12 didn't. We know all about the women, but from this statement alone, we know nothing about the men. (This is an example of a DS question where we could get messed up if we don't completely ignore statement #1 when we are considering statement #2.) Statement #2, by itself, is
insufficient.
Combined statements #1 & #2:
From #2, we know x = 6. This means 6 = 2y, so y = 3. Therefore, 6 females and 3 males began as trainees, so overall, 9 of the 30 managers, or 30%, began as trainees. Combined, the statements are
sufficient to answer the prompt.
Answer =
C
Here's another DS question involving percent and proportions.
https://gmat.magoosh.com/questions/995
When you submit your answer to this questions, the following page will have the video explanation.
Does all this make sense? Please let me know if you have remaining questions.
Mike
