Bunuel wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?
A) 60
B) 70
C) 80
D) 90
E) 100
From the fact that 60% = 3/5 and 50% = 1/2, let´s call 10M the number of games played in the first half.
Besides that, do not forget (in the table below) that half (10M+20) equals 5M+10. Therefore:
\(\begin{array}{*{20}{c}}
{} \\
{{1^{{\text{st}}}}\,{\text{half}}} \\
{{2^{{\text{nd}}}}\,{\text{half}}} \\
{{\text{Total}}}
\end{array}\,\,\,\,\begin{array}{*{20}{c}}
{{\text{won}}} \\
{\frac{3}{5}\left( {10M} \right) = \boxed{6M}} \\
{\boxed3} \\
{\boxed{5M + 10}}
\end{array}\,\,\,\,\,\begin{array}{*{20}{c}}
{{\text{lost}}} \\
{\frac{2}{5}\left( {10M} \right) = 4M} \\
{17} \\
{5M + 10}
\end{array}\,\,\,\,\,\begin{array}{*{20}{c}}
{{\text{Total}}} \\
{10M} \\
{20} \\
{10M + 20}
\end{array}\)
\(? = 10M + 20\)
\(6M + 3 = 5M + 10\,\,\,\,\, \Rightarrow \,\,\,\,\,M = 7\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 90\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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