SajjadAhmad wrote:

At Perry High School, the ratio of students who participate in either the band program or the choral program to students who participate in neither program is 3 to 8. If 220 students attend Perry High School, how many of them do NOT participate in either program?

(A) 40

(B) 60

(C) 100

(D) 160

(E) 180

Trivial application of the

k technique and

Venn diagrams ("overlapping sets"):

\(\frac{{B \cup C}}{{{\text{none}}}} = \frac{3}{8}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered}

\,B \cup C\,\,{\text{ = }}\,\,{\text{3}}k \hfill \\

\,{\text{none}}\,\, = \,\,8k \hfill \\

\end{gathered} \right.\,\,\,\,\,\,\,(k > 0)\,\,\,\,\,\,\,\,\,\left( * \right)\)

\(? = {\text{none}}\,\, = \,\,8k\)

\(220 = {\text{Total}}\,\,{\text{ = }}\,\,B \cup C\,\,{\text{ + }}\,\,{\text{none}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,220\,\, = \,\,\,11k\)

\(?\,\,\, = \,\,\,\left( {\frac{8}{{11}}} \right) \cdot 11k\,\,\, = \,\,\,\left( {\frac{8}{{11}}} \right) \cdot 220\,\,\, = \,\,\,160\)

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

Regards,

Fábio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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