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Of the 4,800 voters who voted for or against Resolution K

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by NandishSS » Tue Oct 11, 2016 6:11 am
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

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Source: — Data Sufficiency |

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by [email protected] » Tue Oct 11, 2016 9:47 am
Hi NandishSS,

This math behind this DS question is relatively easy, but you have to be careful about how you organize your work, take notes, etc.

We're told that there are 1800 Democrats and 3000 Republicans who each cast a vote on a resolution. We're asked for the total number of FEMALES who voted FOR the resolution. At this point, there are 3 'categories' that we have to keep track of: Democrat/Republican, For/Against, Male/Female.

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

This Fact tells us that...
(3/4)(1800) = 1350 Democrats voted FOR the resolution
(2/3)(3000) = 2000 Republicans voted FOR the resolution

However, we don't know how many of those votes were from Females.
Fact 1 is 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.

Unfortunately, this Fact does not tell us how many 'For" votes were actually cast.
Fact 2 is INSUFFICIENT

Combined, we know the number of "For" votes for each political party AND we know what fraction of those votes were cast by females...

1350(1/3) = 450 Female Democrat For votes
2000(1/2) = 1000 Female Republican For votes
1450 total For votes

Final Answer: C

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by Brent@GMATPrepNow » Tue Oct 11, 2016 11:56 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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by fiza gupta » Thu Oct 13, 2016 7:31 am
let Democrats be D and Republicans be R
Total=4,800 => D=1,800 and R=3,000

Female voters who voted for Resolution K

(1) 3/4(D) + 2/3(R) voted for K --(i)
females no info
INSUFFICIENT

(2) 1/3( D voted for K) + 1/2( R voted for K) = females who voted for K --(ii)
but (D or R voted for K) = ? not given
distractor as D will not be 1,800 because its a total value not who voted for K
INSUFFICIENT

combining
3/4(D) + 2/3(R) voted for K
1/3(D voted for K) + 1/2(R voted for K)
=1/3(3/4(D)) + 1/2(2/3(R)) = females who voted for K
AS D and R are given
SUFFICIENT
Fiza Gupta
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