At Perry High School, the ratio of students who participate

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

At Perry High School, the ratio of students who participate

by AAPL » Tue Oct 30, 2018 4:13 am

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Princeton Review

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

OA D.

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Source: Beat The GMAT — Problem Solving | Tue Oct 30, 2018 4:13 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

At Perry High School, the ratio of students who participate

by fskilnik@GMATH » Tue Oct 30, 2018 6:21 am

AAPL wrote:Princeton Review

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,
fskilnik.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Oct 31, 2018 5:27 pm

AAPL wrote:Princeton Review

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

We can create the equation:

3x + 8x = 220

11x = 220

x = 20

Thus, we see that 8(20) = 160 students do not participate in either program.

Answer: D

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