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

[fskilnik@GMATH]

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 Lilly´s seat?

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

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

[fskilnik@GMATH]

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 Lilly´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.