BTGmoderatorDC wrote:A state legislature had a total of 96 members. The members who did not vote on a certain bill consisted of 25 who were absent and 3 who abstained. How many of those voting voted for the bill?

(1) Exactly 1/3 of the total membership of the legislature voted against the bill.

(2) The number of Legislators who voted for the bill was 8 more than the total number who were absent or abstained.

Source: GMAT Prep

$$96\,\,\left\{ \matrix{
\,25\,\,:\,\,{\rm{absent}} \hfill \cr
\,{\rm{3}}\,\,:\,\,{\rm{abstained}} \hfill \cr
\,x\,\,:\,\,{\rm{for }} \hfill \cr
\,{\rm{96}} - \left( {28 + x} \right)\,\,:\,\,{\rm{against}}\, \hfill \cr} \right.\,\,\,\,\,;\,\,\,\,\,\,\,\,\,\,\,\,? = x$$
$$\left( 1 \right)\,\,\,96 - \left( {28 + x} \right) = {1 \over 3}\left( {96} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,\,x = \left( {25 + 3} \right) + 8\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$

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

Regards,
Fabio.