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!

I'm sorry the image didn't paste properly. Here is the link to the problem: https://yfrog.com/72gmatfocus1j

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?