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

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Oneyde and Jorge must make two reservations for an airplane trip, in w  [#permalink]

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New post 01 Mar 2019, 09:07
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Question Stats:

63% (01:56) correct 37% (02:01) wrong based on 19 sessions

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GMATH practice exercise (Quant Class 18)

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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 Lilly´s seat?

(A) 9
(B) 11
(C) 13
(D) 15
(E) 17

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Re: Oneyde and Jorge must make two reservations for an airplane trip, in w  [#permalink]

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New post 01 Mar 2019, 09:49
Oneyde and Jorge can sit only 1 way in which lilly is sitting.
In the first compartment, both can sit in 6 ways.
In the middle compartment, both can sit in 2 ways.
Total = 6+2+1 = 9

A is the answer.
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Re: Oneyde and Jorge must make two reservations for an airplane trip, in w  [#permalink]

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New post 01 Mar 2019, 11:13
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Image

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 Lilly´s seat?

(A) 9
(B) 11
(C) 13
(D) 15
(E) 17

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


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

\({\rm{2 - seats}}\,\,{\rm{group}}\,\,{\rm{:}}\,\,{\rm{2}}\,\,{\rm{possibilities}}\,\,\,\left\{ \matrix{
\,\left( {O,J} \right) \hfill \cr
\,\left( {J,O} \right) \hfill \cr} \right.\)

\({\rm{4 - seats}}\,\,{\rm{group}}\,\,{\rm{(right)}}\,\,{\rm{:}}\,\,{\rm{1}}\,\,{\rm{possibility}}\,\left( {O,J,L,e} \right)\,\,\,\,\,\,\left[ {L = {\rm{Lilly}}} \right]\,\,\,\)


\(? = 6 + 2 + 1 = 9\)


The correct answer is (A).


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

Regards,
Fabio.
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Oneyde and Jorge must make two reservations for an airplane trip, in w  [#permalink]

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New post 01 Mar 2019, 14:37
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fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Image

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 Lilly´s seat?

(A) 9
(B) 11
(C) 13
(D) 15
(E) 17


Hi,
Considering Onedye & Jorge as one. Similarly consider two seats as 1.
possibilities in first column = choose 1 from 3 * 2(Onedye & Jorge can switch seats, since they are considered as 1) = 3C2 * 2 = 6
Similarly in second column = choose 1 from 1 * 2 = 1C1 * 2 = 2
When it comes to third column, there is only one way to sit = 1
total combinations = 6 + 2 + 1 = 9

Option A

Thanks.
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Oneyde and Jorge must make two reservations for an airplane trip, in w   [#permalink] 01 Mar 2019, 14:37
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