Each vote in a certain election went to one of two candidates, X or Y. Candidate X received 624 of...
GMAT Data Sufficiency : (DS) Questions
Each vote in a certain election went to one of two candidates, X or Y. Candidate X received 624 of the votes cast by men, and Candidate Y received 483 of the votes cast by women. How many votes did Candidate X receive?
- Candidate X received \(50\%\) of the votes cast by men.
- Candidate Y received \(60\%\) of the votes cast by women.
Understanding the Question
We need to find the total number of votes that Candidate X received.
Given Information
- Election had exactly two candidates: X and Y
- X received 624 votes from men
- Y received 483 votes from women
- Every vote went to either X or Y (no abstentions)
What We Need to Determine
To find X's total votes, we need to know:
- How many votes X got from men (we already know this: 624)
- How many votes X got from women (this is what we're missing)
Think of it this way: X's total = 624 + (X's votes from women)
So we need to find that missing piece.
Analyzing Statement 1
Statement 1: X received 50% of the votes cast by men.
Since X got 624 votes from men and this represents 50%, we can determine:
- Total votes cast by men = \(624 \div 0.5 = 1{,}248\)
- Y received the other 50% from men = 624 votes
But here's the critical point: This tells us nothing about:
- How many women voted
- How women split their votes between X and Y
- Most importantly: How many votes X received from women
Without knowing X's votes from women, we cannot find X's total votes.
Statement 1 is NOT sufficient.
This eliminates choices A and D.
Analyzing Statement 2
Remember: We must analyze Statement 2 independently, forgetting Statement 1 completely.
Statement 2: Y received 60% of the votes cast by women.
Since Y got 483 votes from women and this represents 60%, we can determine:
- Total votes cast by women = \(483 \div 0.6 = 805\)
- Since only X and Y were candidates, X must have received the remaining 40%
- X's votes from women = \(0.4 \times 805 = 322\) votes
[STOP - Sufficient!] We now have everything we need:
- X's votes from men: 624 (given)
- X's votes from women: 322 (just calculated)
- X's total votes = \(624 + 322 = 946\)
Statement 2 is sufficient.
This eliminates choices C and E.
The Answer: B
Statement 2 alone gives us the missing piece we identified at the start (X's votes from women), allowing us to calculate X's total votes. Statement 1 alone tells us nothing about women's votes, which is the critical missing information.
Answer Choice B: "Statement 2 alone is sufficient, but Statement 1 alone is not sufficient."