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CAT 2019 Slot 1 DILR · Set 5 of 8Logical ReasoningModerate DifficultyQ17–Q20 · 4 MCQ

CAT 2019 Slot 1 DILR Set 5: Routes & Networks (4 Questions) with Solutions

The Routes & Networks set from the official CAT 2019 Slot 1 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2019 Slot 1 DILR · Questions 17–20
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.
1
X, U, and Z are standing at the three corners of a triangle formed by three street segments.
2
X can see only U and Z.
3
Y can see only U and W.
4
U sees V standing in the next intersection behind Z.
5
W cannot see V or Z.
6
No one among the six is standing at intersection d.
Official Reference Chart - CAT 2019 Slot 1 Official Reference Chart - CAT 2019 Slot 1

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q17. Routes & Networks

MCQ · +3 / −1
Who is standing at intersection a?
  1. A) No one
  2. B) Y
  3. C) V
  4. D) W
Correct Answer
A) No one
Step-by-step solution
📌 Core Concept
Fix the six positions from the sight-line clues, starting with the only triangles the map allows, then read off intersection a.
🔢 Step-by-Step Solution
1
The map has two triangles of street segments: b-c-g (using the diagonal) and b-f-g. Clue 4 needs U, Z, V in one straight line with Z in the middle.
2
Triangle b-c-g fails. U=c, Z=g, V=k leaves Y no spot from which it sees U=c, because c's lines (a, b, d, g, k) are all blocked by clues 2 and 6 or already occupied. U=g, Z=b would need V beyond b on the diagonal, and no intersection lies there.
3
In triangle b-f-g, try X=g, U=b, Z=f, V=j. X=g sees all of b, c, e, f, h, k, so c and e must be empty, and Y can only be at a. Then W would be at e or i. e sees f and i sees j, which breaks clue 5.
4
Try X=b, U=f, Z=g, V=h. Y must be at e to see U=f, but e also sees g and h, which breaks clue 3.
5
Try X=b, U=g, Z=f, V=e. X=b sees only g and f, so a, c, j are empty. Y sees U=g, so Y is at h or k. h also sees f and e, so Y=k. Y=k then sees only g plus W at i or l. i sees e (V), so W=l, and l sees neither e nor f.
6
Final positions: X=b, U=g, Z=f, V=e, Y=k, W=l. Intersection a is empty.
Why Not the Others
Y is at k, W is at l and V is at e, so none of them is at a.
Correct Answer: A

Q18. Routes & Networks

MCQ · +3 / −1
Who can V see?
  1. A) U, W and Z only
  2. B) Z only
  3. C) U and Z only
  4. D) U only
Correct Answer
C) U and Z only
Step-by-step solution
📌 Core Concept
Once the positions are fixed (X=b, U=g, Z=f, V=e, Y=k, W=l), list the people on V's lines of sight.
🔢 Step-by-Step Solution
1
Clue 4 puts V behind Z along the column e-f-g, as U=g, Z=f, V=e. Clues 2, 3 and 5 then fix X=b, Y=k and W=l, with a, c and j empty.
2
V at e sees along the column: f, g and h. It sees along the row: a and i.
3
Occupied intersections among these are f (Z) and g (U). The others, h, a and i, are empty.
4
So V sees only U and Z.
Why Not the Others
W is at l, which is not on e's row or column, so W is not visible. This rules out A.
V also sees U at g, so Z alone is wrong (B).
V also sees Z at f, so U alone is wrong (D).
Correct Answer: C

Q19. Routes & Networks

MCQ · +3 / −1
What is the minimum number of street segments that X must cross to reach Y?
  1. A) 1
  2. B) 4
  3. C) 3
  4. D) 2
Correct Answer
D) 2
Step-by-step solution
📌 Core Concept
With X=b and Y=k fixed, find the shortest street route and count the segments it uses.
🔢 Step-by-Step Solution
1
The arrangement from the clues is X=b, U=g, Z=f, V=e, Y=k, W=l.
2
X at b has the diagonal segment b-g, which is a street segment in the map.
3
From g, the row segment g-k reaches k.
4
Route b → g → k crosses two segments: b-g and g-k.
5
One segment cannot work, because b and k are not directly joined. Any other route is longer, for example b-f-g-k uses three segments.
6
The minimum is 2.
Quick Check
b and k are not adjacent, so 1 is impossible, and b-g-k achieves 2.
Correct Answer: D

Q20. Routes & Networks

MCQ · +3 / −1
Should a new person stand at intersection d, who among the six would she see?
  1. A) U and Z only
  2. B) V and X only
  3. C) W and X only
  4. D) U and W only
Correct Answer
C) W and X only
Step-by-step solution
📌 Core Concept
Place the new person at d and list the occupied intersections on d's lines of sight.
🔢 Step-by-Step Solution
1
The positions are X=b, U=g, Z=f, V=e, Y=k, W=l.
2
d lies on the left column a-b-c-d. It sees c, b and a. The occupied one is b, which holds X.
3
d lies on the bottom row d-h-l. It sees h and l. The occupied one is l, which holds W.
4
No diagonal passes through d.
5
The new person sees X and W only.
Why Not the Others
U is at g, Z is at f and V is at e. None of these is on d's column or row, so A, B and D are wrong.
Correct Answer: C
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CAT 2019 Slot 1 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Kozhikode

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