Overlapping Sets Question from GMATPrep

[leighton.d.powell]

Source: GMATPrep software

Of the 4,800 voters who voted for or against Resolution K, 1,800 were Democrats, and 3,000 were Republicans. What was the total number of female voters who voted for Resolution K?

(1) 3/4 of the Democrats and 2/3 of the Republicans voted for resolution K.

(2) 1/3 of the Democrats who voted for Resolution K and 1/2 of the Republicans who voted for Resolution K were females.

OA: C

Can someone please explain the answer to me? I was trying to set up a double (maybe triple?) set matrix in order to ascertain the different categorizations, but just didn't know how to do it. Are there 3 different categorizations -- for or against Resolution K, Republican or Democrats, and male or female -- in this question?

Thanks in advance!

[jnelson0612]

Actually, you can do this without the traditional matrix. Remember, we want to obtain the number of females who voted for Resolution K. Let's take a look:

Statement 1: no information about females, so insufficient.
Statement 2: no information about how many voted for, so insufficient.

Together they are sufficient. Let's see how:

Statement 1 says that 3/4 of Democrats and 2/3 of Republicans voted for Resolution K. Given that 1800 voters are Democrats and 3000 Republicans, we know that 1350 Democrats and 2000 Republicans voted for.

Statement 2 says that 1/3 of the Democrats who voted for Resolution K and 1/2 of the Republicans who voted for Resolution K were females.

So 1/3 of 1350 Democrats and 1/2 of the 2000 Republicans who voted for are female. That is 450 Democrats and 1000 Republicans who are female, or 1450 total. Thus, C is sufficient.

[leighton.d.powell]

Great explanation. Thanks!

[jnelson0612]

Great, thanks!