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

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

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?

OA is B

The above two statements look confusing. Please tell me how you will analyze the two statements.

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by [email protected] » Tue Nov 13, 2018 4:40 am

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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?

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

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

Let's take each statement one by one.

=> 390 = 40% of S

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

=> 336 = 60% of J

J = 336/60% = 560

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

Hope this helps!

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

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Jay,

Thanks for your solution. Appreciate it.

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by [email protected] » Tue Nov 13, 2018 12:41 pm

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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?

$\left. \begin{gathered} {\text{seniors}}\,\,\,\left\{ \begin{gathered} \,390\,\,\,\, \to \,\,\,\,{\text{Joan}} \hfill \\ S - 390\,\,\,\, \to \,\,\,\,{\text{Peter}} \hfill \\ \end{gathered} \right. \hfill \\ {\text{juniors}}\,\,\,\left\{ \begin{gathered} \,J - 336\,\,\,\, \to \,\,{\text{Joan}} \hfill \\ \,336\,\,\,\, \to \,\,{\text{Peter}} \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \\ \end{gathered} \right\}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 390 + \left( {J - 336} \right)\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{\,\,\,\,? = J\,\,}$
$\left( 1 \right)\,\,\,\,S - 390 = \frac{6}{{10}}\left( S \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,S\,\,\,{\text{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,J\,\,{\text{bifurcates}}\,\,{\text{trivially}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.$
$\left( 2 \right)\,\,\,J - 336 = \frac{4}{{10}}\left( J \right)\,\,\,\, \Rightarrow \,\,\,\,\,J\,\,\,{\text{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.$