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

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by vinni.k » Mon Nov 12, 2018 8:12 am

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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

OA is B

The above two statements look confusing. Please tell me how you will analyze the two statements.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Nov 13, 2018 4:40 am
vinni.k wrote: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

OA is B

The above two statements look confusing. Please tell me how you will analyze the two statements.
Say the total number of votes cast by Juniors = J and the total number of votes cast by Seniors = S

# of votes Joan received = 390 + (J - 336)

If we get the value of J, we get the answer.

Let's take each statement one by one.

(1) Joan received 40% of the votes cast by seniors

=> 390 = 40% of S

This will not help us get the value of J. Insufficient.

(2) Peter received 60% of the votes cast by juniors

=> 336 = 60% of J

J = 336/60% = 560

Thus, # of votes Joan received = 390 + (J - 336) = 390 + (560 - 336) = 614. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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by vinni.k » Tue Nov 13, 2018 10:52 am
Jay,

Thanks for your solution. Appreciate it.
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by fskilnik@GMATH » Tue Nov 13, 2018 12:41 pm
vinni.k wrote: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
\[\left. \begin{gathered}
{\text{seniors}}\,\,\,\left\{ \begin{gathered}
\,390\,\,\,\, \to \,\,\,\,{\text{Joan}} \hfill \\
S - 390\,\,\,\, \to \,\,\,\,{\text{Peter}} \hfill \\
\end{gathered} \right. \hfill \\
{\text{juniors}}\,\,\,\left\{ \begin{gathered}
\,J - 336\,\,\,\, \to \,\,{\text{Joan}} \hfill \\
\,336\,\,\,\, \to \,\,{\text{Peter}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 390 + \left( {J - 336} \right)\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{\,\,\,\,? = J\,\,}\]
\[\left( 1 \right)\,\,\,\,S - 390 = \frac{6}{{10}}\left( S \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,S\,\,\,{\text{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,J\,\,{\text{bifurcates}}\,\,{\text{trivially}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.\]
\[\left( 2 \right)\,\,\,J - 336 = \frac{4}{{10}}\left( J \right)\,\,\,\, \Rightarrow \,\,\,\,\,J\,\,\,{\text{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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