Connection of cities

Probability Level 1

Five cities $P,Q,R,S,T$ are connected by different modes of transport as follows

$P$ and $Q$ connected by boat as well as rail.
$S$ and $R$ connected by bus and boat.
$Q$ and $T$ connected by air only.
$P$ and $R$ connected by boat only.
$T$ and $R$ connected by rail and bus.

If a person visits each of the places starting from $P$ and gets back to $P,$ which of the following places must he visit twice ?

Cannot be determined Q T S R

2 solutions

Chew-Seong Cheong
Jun 2, 2015

From the information given, we find that the cities $P$ , $Q$ , $R$ , $S$ and $T$ are connected as follows.

$\begin{array} {ccccccc} P & \Leftarrow & \Rightarrow & R & \Leftarrow & \Rightarrow & S \\ \Uparrow & & & \Uparrow \\ \Downarrow & & & \Downarrow \\ Q & \Leftarrow & \Rightarrow & T \end{array}$

To go to $S$ and back to $P$ , $\boxed{R}$ must be visited twice.

What will happen if you go to T, you will take the following Route: P => Q => T and back from T==>Q==>P , here we can see that Q is also visited, Now if person visit just Q it will be :: P <==>Q ,, Therefore Q is ALSO visited twice.

Syed Baqir - 5 years, 11 months ago

The question is which city MUST be visited twice. All cities can be visited twice, trice and all that. Because the only way to $S$ is through $R$ , therefore, $R$ must be visited twice.

Chew-Seong Cheong - 5 years, 11 months ago

I thought that you must follow the same transport modes. I mean, when you go from P to Q, it can only be done via boat or rail. So how can I leave Q to T if the only transport mode is by air and I arrive via either boat or rail?

Rogerio De Souza - 3 years, 6 months ago

Oops! You assumed wrongly.

Chew-Seong Cheong - 3 years, 6 months ago

Same here, why do you even write down what mode of transport it uses? It is totally irrelevant! They are simply connected. Period

Bjarne Speer - 3 years, 2 months ago

exactly, useless, so why add, to confuse us?

KC Yao - 2 years, 7 months ago

Jackson Hobbs
Aug 21, 2015

S only connects to R, since you have to get to S, R must be passed on the way there and back. So R.

Connection of cities

2 solutions

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