In a school election, Joan and Peter were the only candidate

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Source: Veritas Prep

In a school election, Joan and Peter were the only candidates for class president. Only students in the junior and senior class were allowed to vote and all of them voted for exactly one of the two candidates. Joan received 390 of the votes cast by seniors and Peter received 336 of the votes cast by juniors. How many votes did Joan receive?

1) Joan received 40% of the votes cast by seniors.
2) Peter received 60% of the votes cast by juniors.

The OA is B
Source: — Data Sufficiency |

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by swerve » Thu Aug 01, 2019 4:44 pm

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Let the students in junior class be \(J\), out of which Peter received 336
Let the students in senior class be \(S\), out of which Joan received 390

We need to know the total number of votes received by Joan

Statement 1. 390 = 40% of \(S\) = 0.4\(S\) .. Solve to get \(S =\) 975.
So we know the total number of senior votes, but we don't know how many junior votes Joan received. Insufficient. \(\color{red}{\large{\times}}\)

Statement 2. 336 = 60% of \(J\) = 0.6*\(J\).. Solve to get \(J =\) 560
So total junior votes are 560. If out of these Peter received 336, Joan received = 560-336
Now we have total number of junior votes received by Joan, and the question already gives the number of senior votes received by Joan. So we have the value. Sufficient. \(\color{green}\checkmark\)

Hence, __B__ is the correct answer.