in Logical Reasoning edited by
167 views
0 votes
0 votes

Four cars need to travel from Akala $\text{(A)}$ to Bakala $\text{(B)}$. Two routes are available, one via Mamur $\text{(M)}$ and the other via Nanur $\text{(N)}$. The roads from $\text{A}$ to $\text{M}$, and from $\text{N}$ to $\text{B}$, are both short and narrow. In each case, one car takes $6$ minutes to cover the distance, and each additional car increases the travel time per car by $3$ minutes because of congestion. (For example, if only two cars drive from $\text{A}$ to $\text{M}$, each car takes $9$ minutes.) On the road from $\text{A}$ to $\text{N}$, one car takes $20$ minutes, and each additional car increases the travel time per car by $1$ minute. On the road from $\text{M}$ to $\text{B}$, one car takes $20$ minutes, and each additional car increases the travel time per car by $0.9$ minute.

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.

A new one-way road is built from $\text{M}$ to $\text{N}$. Each car now has three possible routes to travel from $\text{A}$ to $\text{B}$: $\text{A-M-B, A-N-B}$ and $\text{A-M-N-B}$. On the road from $\text{M}$ to $\text{N}$, one car takes $7$ minutes and each additional car increases the travel time per car by $1$ minute. Assume that any car taking the $\text{A- M-N-B}$ route travels the $\text{A-M}$ portion at the same time as other cars taking the $\text{A-M-B}$ route, and the $\text{N-B}$ portion at the same time as other cars taking the $\text{A-N-B}$ route.

How many cars would the police department order to take the $\text{A-M-N-B}$ route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.)

  1. $4$
  2. $0$
  3. $1$
  4. $2$
in Logical Reasoning edited by
13.4k points
167 views

Please log in or register to answer this question.

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true