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Data Sufficiency Question from GMAC Focus

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by aarthyk » Thu Apr 09, 2009 11:09 pm
Hi Folks,

This forum is absolutely great, it's so wonderful to see everyone helping each other to learn :)

I came across this question in a practice GMATFocus test, I'm hoping you can help me understand why they are not sufficient together. The solution shown doesn't really click intuitively.

Thank you!

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by aarthyk » Thu Apr 09, 2009 11:10 pm
I'm sorry the image didn't paste properly. Here is the link to the problem: https://yfrog.com/72gmatfocus1j
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by milqman » Fri Apr 10, 2009 9:51 am
Let's just look at the first statement to start:
-More than half are women
This means that there could be as few as 6 women or as many as 10 women. Let's figure the probability for each of those scenarios and see if we have it solved.
6 Women:
Prob of both being selected = (6/10)*(5/9) = 1/3 (less than 1/2)
10 Women:
Prob of both being selected = 1 (greater than 1/2)
First statement is insufficient.

Second statement: The prob of both being men is less than 1/10.
Let's see how many men this would allow so we can test for sufficiency.
0-Possible (Prob = 0)
1-Possible (Prob = 0)
2-Possible (Prob = (2/10)*(1/9) = .022)
3-Possible (Prob = (3/10)*(2/9) = .066)
4-NOT Possible (Prob = (4/10)*(3/9) = .133)

So let's test the prob of both being women if there are 3 men (the max allowable under this second rule).

Prob = (7/10)*(6/9) = .466 (less than 1/2)

That means that this second rule can allow the prob of both being women to be above or below 1/2. This rule is more restrictive than the first, so even when you put them together, the two rules can still combine for a prob that is either over OR under 1/2.

Does that make more sense?
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by aarthyk » Fri Apr 10, 2009 2:06 pm
That makes sense, thank you so much! :)
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