CAT 1995 — QA Question 36
Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
A, B, C and D are four towns, any three of which are non-collinear. Then the number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is
Answer & solution
- A
7
- B
8
- C
9
24
Let us choose a town, say A.
If I were to consider this as the base town and construct two roads such that I connect any pair of towns, I get
the following combinations:
1. AB – BC, 2. AB – BD, 3. AC – CB, 4. AC – CD,
5. AD – DB and 6. AD – DC.
From any of these combinations, if I were to construct a road such that it again comes back to A, then it would form a triangle.
To avoid a triangle, the third road that I construct should not be connected to A but to the third town.
Hence, the combination would be:
1. AB – BC – CD, 2. AB – BD – DC, 3. AC – CB – BD,
4. AC – CD – DB, 5. AD – DB – BC and 6. AD – DC – CB.
Thus, from each town, we can construct 6 such combinations.
Hence, total number of combinations that we can have from four towns = (6 × 4) = 24.