Data Sufficiency

Of the 4800 voters who voted for or against Resolution K, 1800 were Democrats and 3000 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.

Target question: What was the total number of female voters who voted for Resolution K?

When solving Data Sufficiency questions, it's important that you don't perform more calculations than are necessary. So, for this question, we need only determine whether or not we have sufficient information to determine the number of female voters who voted for Resolution K.
We NEED NOT determine that actual number.

Given: Of the 4800 voters who voted for or against Resolution K, 1800 were Democrats and 3000 were Republicans.

Statement 1: 3/4 of the Democrats and 2/3 of the Republicans voted for Resolution K.
Since we have no information about the number of females, we CANNOT determine the number of female voters who voted for Resolution K
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 1/3 of the Democrats who voted for Resolution K and 1/2 of the Republicans who voted for Resolution K were females.
We have no information about the total number of Democrats and Republicans who VOTED FOR Resolution K.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
At this point, we should recognize that we do, indeed, have enough information, but we won't go as far as performing any calculations.
First, we know that, of the 1800 Democrats, 3/4 voted for Resolution K, and of those 1/3 were female. So, we COULD use this info to determine the number of female Democrats who voted for Resolution K.
Likewise, we know that, of the 3000 Republicans, 2/3 voted for Resolution K, and of those 1/2 were female. So, we COULD use this info to determine the number of female Republicans who voted for Resolution K.
So, we COULD use all of this info to determine the total number of female voters who voted for Resolution K
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

AAPL wrote:GMAT Prep

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

We have

# of Dems voted (For + Against) = 1800;
# of Reps voted (For + Against) = 3000

Question: What was the total number of female voters who voted for?

Let's take each statement one by one.

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

# of Dems voted for = 3/4*1800 = 1350;
# of Reps voted for = 2/3*3000 = 2000

No split of votes male and female. Insufficient.

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

We have no information about the # of 'Democrats who voted for' and the # of 'Republicans who voted for'. Insufficient.

(1) and (2) together

=> # of females who voted for = 1/3*1350 + 1/2*2000 = 450 + 1000 = 1450. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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