In a school election, Joan and Peter were the only candidates for

Question

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

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

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

Luckisnoexcuse · Answer

I will go with B

(1) gives us the total senior class count...which cannot tell how many votes Joan got from junior class

(2) tells us the total of junior class and votes of Joan can then be derived..hence sufficient

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amanvermagmat · Answer

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 .

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 .

Hence  B answer

quantumliner · Answer

Joan - 390 Senior votes
Peter - 336 Junior votes

Statement 1: Joan received 40% of the votes cast by seniors

This means the 390 of the votes cast by seniors received by Joan represents 40% of the votes cast by seniors. So the rest of the 60% of the votes cast by seniors was received by Peter.

So

Number of Votes cast by Seniors received by Peter = 60 * 390/40 = 585

So by this statement we know

Joan - 390 Senior votes , don't know??
Peter - 585 Senior votes , 336 Junior votes

Since, this statement does not give how votes cast by junior were received by Joan. This statement is not sufficient.

Statement 2: Peter received 60% of the votes cast by juniors

This means the 336 of the votes cast by juniors received by Peter represents 60% of the votes cast by juniors. So the rest of the 40% of the votes cast by juniors was received by Joan.

So

Number of Votes cast by juniors received by Joan = 40 * 336/60 = 224

So by this statement we know

Joan - 390 Senior votes , 224 Junior votes

Since, this statement gives how votes cast by junior and seniors were received by Joan. This statement is sufficient.

Answer is B

henriquenkg · Answer

I'm sorry but where are the alternatives? I only see the statements.

mohshu · Answer

to find the total votes joan received,, we need number of votes cast by juniors to joan..

stat1: no info about juniors vote

stat2: suff

ans B

amanvermagmat · Answer

Hi

In GMAT, data sufficiency questions always have the following five alternatives:

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. 
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 
(D) EACH statement ALONE is sufficient. 
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

This is known and understood by almost everyone here, that's why people who post here don't specify these five alternatives with a DS question.

fskilnik · Answer

\left. \begin{gathered}
 {	ext{seniors}}\,\,\,\left\{ \begin{gathered}
 \,390\,\,\,\, 	o \,\,\,\,{	ext{Joan}} \hfill \
 S - 390\,\,\,\, 	o \,\,\,\,{	ext{Peter}} \hfill \ 
\end{gathered} ight. \hfill \
 {	ext{juniors}}\,\,\,\left\{ \begin{gathered}
 \,J - 336\,\,\,\, 	o \,\,{	ext{Joan}} \hfill \
 \,336\,\,\,\, 	o \,\,{	ext{Peter}} \hfill \ 
\end{gathered} ight.\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \ 
\end{gathered} ight\}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 390 + \left( {J - 336} ight)\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{\,\,\,? = J\,\,}

\left( 1 ight)\,\,\,\,S - 390 = \frac{6}{10}\left( S ight)\,\,\,\,\, \Rightarrow \,\,\,\,\,S\,\,\,{	ext{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,J\,\,{	ext{bifurcates}}\,\,{	ext{trivially}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{	ext{INSUFF}}.

\left( 2 ight)\,\,\,J - 336 = \frac{4}{10}\left( J ight)\,\,\,\, \Rightarrow \,\,\,\,\,J\,\,\,{	ext{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{	ext{SUFF}}.

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

Regards, 
Fabio.

bumpbot · Answer

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