Oneyde and Jorge must make two reservations for a trip, in w

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

by fskilnik@GMATH » Fri Mar 01, 2019 8:03 am

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GMATH practice exercise (Quant Class 18)

Oneyde and Jorge must make two reservations for a trip, in which only 9 seats are still available, all of them in row F (see figure). If they want to sit next to each other, without being separated by central corridors, in how many ways this could be done if Oneyde refuses to sit in any of the two places next to LillyÂ´s seat?

(A) 9
(B) 11
(C) 12
(D) 13
(E) 15

Answer: [spoiler]____(A)__[/spoiler]

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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Source: Beat The GMAT — Problem Solving | Fri Mar 01, 2019 8:03 am

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

Oneyde and Jorge must make two reservations for a trip, in w

by fskilnik@GMATH » Fri Mar 01, 2019 10:02 am

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 18)

Oneyde and Jorge must make two reservations for a trip, in which only 9 seats are still available, all of them in row F (see figure). If they want to sit next to each other, without being separated by central corridors, in how many ways this could be done if Oneyde refuses to sit in any of the two places next to LillyÂ´s seat?

(A) 9
(B) 11
(C) 12
(D) 13
(E) 15

$$?\,\,\,\,:\,\,\,\# \,\,\,O,J\,\,{\rm{positions}}\,\,{\rm{with}}\,\,{\rm{restrictions}}$$

$${\rm{4 - seats}}\,\,{\rm{group}}\,\,{\rm{(left)}}\,\,{\rm{:}}\,\,{\rm{6}}\,\,{\rm{possibilities}}\,\,\,\left\{ \matrix{
\,\left( {O,J,e,e} \right)\,\,{\rm{or}}\,\,\left( {J,O,e,e} \right) \hfill \cr
\,\left( {e,O,J,e} \right)\,\,{\rm{or}}\,\,\left( {e,J,O,e} \right) \hfill \cr
\left( {e,e,O,J} \right)\,\,{\rm{or}}\,\,\left( {e,e,J,O} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\left[ {e = {\rm{empty}}\,{\rm{seat}}} \right]$$
$${\rm{2 - seats}}\,\,{\rm{group}}\,\,{\rm{:}}\,\,{\rm{2}}\,\,{\rm{possibilities}}\,\,\,\left\{ \matrix{
\,\left( {O,J} \right) \hfill \cr
\,\left( {J,O} \right) \hfill \cr} \right.$$
$${\rm{4 - seats}}\,\,{\rm{group}}\,\,{\rm{(right)}}\,\,{\rm{:}}\,\,{\rm{1}}\,\,{\rm{possibility}}\,\left( {O,J,L,e} \right)\,\,\,\,\,\,\left[ {L = {\rm{Lilly}}} \right]\,\,\,$$

$$? = 6 + 2 + 1 = 9$$

The correct answer is (A).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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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