📌 Section 1 is Logical reasoning specially designed for CAT

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Six teams, A through F, participated in an inter-college football tournament. The tournament was played in two stages. In the first stage, each team played one match each against exactly three of the other teams. In the second stage, each team played one match each against the remaining two teams (against which it did not play any match in the first stage).

In each match, for a win, a team gets 3 points and for a loss, it gets no points. If a match ended in a draw, then each team gets 1 point each.

The following two tables give the Goals For (total goals scored by the team), Goals Against (total goals conceded by the team) and the total points scored by each of the six teams in the first stage and in the second stage matches respectively:

Each of the six teams scored at least one goal in each match that it played.

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From the given information, we can say that nine matches took place in the first stage and six matches took place in the second stage.

From the details of the second-stage matches, we can say that a match between B and C was drawn, B lost a match with a goal difference of 2, and C lost a match with a goal difference of 1.

Also, in the second-stage matches, in either of the matches that F played, its opponent scored exactly one goal. In either of the matches that E played, it scored exactly one goal.

Also, A, D and F won 2, 1 and 2 matches respectively. B, C, D and E lost 1, 1, 1 and 2 matches respectively.

Therefore, E lost to exactly two teams among A, D and F in the second stage.

Hence, E could not have played B and C in the second stage. Therefore, E played against B and C in the first stage.

Also, the match between D and E was drawn in the first stage.

Therefore, E played against A and F in the second stage.

In the second stage, A and F did not play against each other since neither team lost any match in the second stage.

Therefore, A and F played against each other in the first stage.

B and D did not play against each other in the first stage since B lost all its matches while D did not win any match in the first stage.

Therefore, B and D played against each other in the second stage.

From the second table, Team A scored one goal more than its opponent in each of its two second-stage matches.

Therefore, in the match between A and E:

A 2–1 E

Hence, E lost to F:

E 1–4 F

Therefore, A scored 4 goals in its other match.

As D conceded a total of 4 goals in its two second-stage matches and each team scored at least one goal in each match, A and D could not have played against each other in the second stage.

Therefore, A and D played against each other in the first stage.

Thus, A–C and D–F were the remaining second-stage matches.

The second-stage results are:

B played against A, E and F, while D played against A, C and E. Therefore, C played against F.

C won against D, E and F by 2–1 in each match.

Since D–E was drawn and E won one match by a goal difference of 2, while D scored one goal in each of its first-stage matches:

Now B lost to A and F with goal differences of 1 and 2 in some order. F similarly defeated A and B with goal differences of 1 and 2.

The only possible results satisfying the aggregate goals are:

✅ Final Match Results

1. F
2. 3 goals
3. 1 goal
4. 3 goals

⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.

Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.

See you in tomorrow’s challenge!