The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.
Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.
The following additional facts are known.
- X, U, and Z are standing at the three corners of a triangle formed by three street segments.
- X can see only U and Z.
- Y can see only U and W.
- U sees V standing in the next intersection behind Z.
- W cannot see V or Z.
- No one among the six is standing at intersection d.
Solution
Understanding the set :-
- This set gives us a street map, and there are some people (U, V, W, X, Y, and Z,) standing at some of this interactions.
- . A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections.
This is a set where there will be certain cases that you need to make before you reach the correct answer,
but this is quite normal in CAT sets, where you go with more then one case simultaneously and at the end one of the case contradict any clue, and we reject that and come to the final answer.
Clue 1 says,
X, U, and Z are standing at the three corners of a triangle formed by three street segments.
Since X, U, Z are forming a triangle,
Only possibility - X, U, and Z lie at b, f, and g in any order.
Clue 4 says,
U sees V standing in the next intersection behind Z.
Now, there will be certain cases possible.
So, let's try and analyze all the cases one by one
CASE - 1 :-
In this case,
W cannot see V or Z.
So W can only be at the intersection a.
Since Y can see only U and W, Y can only be at c where X can see him.
Hence this case is rejected.
Case - 2 :-
Y can only see U and W.
Y cannot be placed anywhere.
Hence this case is also rejected.
CASE - 3 :-
Y can only see U and W.
Y cannot be placed anywhere.
Hence this case is also rejected.
CASE - 3:-
W cannot see V or Z.
W can only be placed at i.
Y can see only U and W.
Y can only be placed at j or e, where he can see more people than U and W.
Hence this case is also rejected.
CASE - 4 :-
W cannot see V or Z.
Y can only see U and W.
Hence W and Y can only be placed as shown:
From the diagram we can say that,
V can see U and Z only.