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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?
We need to find the total number of votes that Candidate X received.
To find X's total votes, we need to know:
Think of it this way: X's total = 624 + (X's votes from women)
So we need to find that missing piece.
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:
But here's the critical point: This tells us nothing about:
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.
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:
[STOP - Sufficient!] We now have everything we need:
Statement 2 is sufficient.
This eliminates choices C and E.
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."