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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
Five National Ice Hockey Teams—Australia, Belgium, Canada, Denmark, and India—played a round-robin tournament, with each team playing one match against each of the other four teams. In every match, a team scored either 2, 3, or 4 goals.
A total of 60 goals were scored across all the matches. Against each team, there was at least one match in which 2 goals, 3 goals, and 4 goals were scored.
The following information is known:
(i) Australia scored a total of 10 goals, and 13 goals were scored against it.
(ii) Australia scored 2 goals each against Canada and Denmark. No team scored 2 goals in more than two matches.
(iii) Denmark and India scored a total of 15 and 13 goals, respectively. Denmark scored 3 goals against Belgium.
(iv) The number of goals scored against Belgium, Denmark, and India was equal.
(v) No team scored the same number of goals against Australia as Australia scored against that team. The same condition applied to India.
(vi) Canada scored 4 goals in at least one match.
Question 1
How many total goals were scored against Canada?
Question 2
How many more total goals were scored by Belgium than by Australia?
Question 3
How many times did any team score 3 goals across all the matches?
6
7
8
9
Question 4
A team scored more goals than its opponent in a match, it won the match. Which of the following two teams won the same number of matches?
Australia and Denmark
Belgium and India
Belgium and Canada
Canada and Denmark
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✅ Answers & Explanations
Team | Aus | Bel | Can | Den | Ind | Total Scored | Goals Against |
|---|---|---|---|---|---|---|---|
Australia | - | 3 | 2 | 2 | 3 | 10 | 13 |
Belgium | 2 | - | 3 | 3 | 2 | 10 | 12 |
Canada | 3 | 2 | - | 4 | 3 | 12 | 11 |
denmark | 4 | 3 | 4 | - | 4 | 15 | 12 |
India | 4 | 4 | 2 | 3 | - | 13 | 12 |
Set 1
We have 5 teams:
Australia, Belgium, Canada, Denmark, India
Each team plays 4 matches. In every match, each team scores either 2, 3, or 4 goals.
Step 1: Use given totals
Given:
Australia scored 10 goals and conceded 13 goals.
Denmark scored 15 goals.
India scored 13 goals.
Total goals in tournament = 60.
So,
Australia + Belgium + Canada + Denmark + India = 60
10 + Belgium + Canada + 15 + 13 = 60
Belgium + Canada = 22
Step 2: Use goals against condition
Goals against Belgium, Denmark, and India are equal.
Australia conceded 13.
Total goals against all teams must also be 60.
Let goals against Belgium = goals against Denmark = goals against India = x.
So,
Goals against Australia + Goals against Belgium + Goals against Canada + Goals against Denmark + Goals against India = 60
13 + x + Goals against Canada + x + x = 60
13 + 3x + Goals against Canada = 60
From the final arrangement, x = 12.
So goals against Belgium = 12
Goals against Denmark = 12
Goals against India = 12
Then,
13 + 12 + Goals against Canada + 12 + 12 = 60
Goals against Canada = 11
So, answer to Q1 = 11
Goals against:
Australia = 2 + 3 + 4 + 4 = 13
Belgium = 3 + 2 + 3 + 4 = 12
Canada = 2 + 3 + 4 + 2 = 11
Denmark = 2 + 3 + 4 + 3 = 12
India = 3 + 2 + 3 + 4 = 12
Question 1
How many total goals were scored against Canada?
Against Canada:
Australia scored 2
Belgium scored 3
Denmark scored 4
India scored 2
Total = 2 + 3 + 4 + 2 = 11
Answer: 11
Question 2
How many more total goals were scored by Belgium than by Australia?
Australia scored = 10
Belgium scored = 10
Difference = 10 - 10 = 0
Answer: 0
Question 3
How many times did any team score 3 goals across all matches?
Count the number of 3s in the table:
Australia: 3 against Belgium, 3 against India → 2 times
Belgium: 3 against Canada, 3 against Denmark → 2 times
Canada: 3 against Australia, 3 against India → 2 times
Denmark: 3 against Belgium → 1 time
India: 3 against Denmark → 1 time
Total = 2 + 2 + 2 + 1 + 1 = 8
Answer: Option 3 – 8
Question 4
Which two teams won the same number of matches?
Compare each match:
Australia vs Belgium: Australia 3, Belgium 2 → Australia wins
Australia vs Canada: Australia 2, Canada 3 → Canada wins
Australia vs Denmark: Australia 2, Denmark 4 → Denmark wins
Australia vs India: Australia 3, India 4 → India wins
Belgium vs Canada: Belgium 3, Canada 2 → Belgium wins
Belgium vs Denmark: Belgium 3, Denmark 3 → Draw
Belgium vs India: Belgium 2, India 4 → India wins
Canada vs Denmark: Canada 4, Denmark 4 → Draw
Canada vs India: Canada 3, India 2 → Canada wins
Denmark vs India: Denmark 4, India 3 → Denmark wins
Wins:
Australia = 1
Belgium = 1
Canada = 2
Denmark = 2
India = 2
From the options:
Canada and Denmark both won 2 matches.
Answer: Option 4 – Canada and Denmark
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Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!