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SET 1 — 🔍 CAT Level
The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.
The management of a university hockey team was evaluating the performance of four women players—Amla, Bimla, Harita and Sarita—for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.
Only one goal was scored in every even-numbered match.
Harita scored more goals than Bimla.
The highest goal scorer scored goals in exactly 3 matches, including Match 4 and Match 8.
Bimla scored a goal in Match 1 and one each in three other consecutive matches.
An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
The match in which the highest number of goals was scored was unique and it was not Match 5.
Question 1
How many goals were scored in Match 7?
A. 3
B. 2
C. 1
D. Cannot be determined
Question 2
Which of the following is the correct sequence of goals scored in Matches 1, 3, 5 and 7?
A. 5, 1, 0, 1
B. 3, 1, 2, 1
C. 3, 2, 1, 2
D. 4, 1, 2, 1
Question 3
Which of the following statement(s) is/are true?
Statement-1: Amla and Sarita never scored goals in the same match.
Statement-2: Harita and Sarita never scored goals in the same match.
A. Statement-1 only
B. Statement-2 only
C. Both the statements
D. None of the statements
Question 4
Which of the following statement(s) is/are false?
Statement-1: In every match at least one player scored a goal.
Statement-2: No two players scored goals in the same number of matches.
A. None of the statements
B. Statement-1 only
C. Both the statements
D. Statement-2 only
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✅ Answers & Explanations
Total goals = 12
Even matches 2, 4, 6, 8 had 1 goal each.
So, total goals in even matches = 4
Therefore, total goals in odd matches 1, 3, 5, 7 = 12 - 4 = 8
Now, Match 3 and Match 7 had equal goals.
Also, goals in Match 3 and Match 7 were different from Match 1 and Match 5.
From the options in Q26, the only possible sequence for Matches 1, 3, 5, 7 is:
4, 1, 2, 1
Because:
4 + 1 + 2 + 1 = 8
So, match-wise goals are:
Match | Goals |
|---|---|
1 | 4 |
2 | 1 |
3 | 1 |
4 | 1 |
5 | 2 |
6 | 1 |
7 | 1 |
8 | 1 |
The unique highest-scoring match is Match 1 with 4 goals. It is not Match 5, so condition 6 is satisfied.
Now player totals must be distinct and sum to 12.
Bimla scored in Match 1 and in three other consecutive matches. So Bimla scored 4 goals.
Harita scored more than Bimla, so Harita must have 5 goals.
Then remaining two players must have 1 and 2 goals.
So totals are:
Player | Total Goals |
|---|---|
Harita | 5 |
Bimla | 4 |
Amla/Sarita | 1 and 2 |
Harita is the highest scorer. She scored in exactly 3 matches including Match 4 and Match 8.
Since Match 4 and Match 8 each had only 1 goal, Harita scored in both.
To reach 5 goals in exactly 3 matches, Harita must have scored 3 goals in Match 1.
So Harita scored in Matches 1, 4 and 8.
Bimla scored in Match 1 and three consecutive matches. Since Match 4 and Match 8 are already Harita’s goals, Bimla’s three consecutive matches must be Matches 5, 6 and 7.
So Bimla scored in Matches 1, 5, 6 and 7.
A possible table:
Match | Amla | Bimla | Harita | Sarita | Total |
|---|---|---|---|---|---|
1 | 0 | 1 | 3 | 0 | 4 |
2 | 1/S | 0 | 0 | 0/1 | 1 |
3 | 1/S | 0 | 0 | 0/1 | 1 |
4 | 0 | 0 | 1 | 0 | 1 |
5 | remaining | 1 | 0 | remaining | 2 |
6 | 0 | 1 | 0 | 0 | 1 |
7 | 0 | 1 | 0 | 0 | 1 |
8 | 0 | 0 | 1 | 0 | 1 |
Final Answers
Match 7 had 1 goal.
Answer: CSequence for Matches 1, 3, 5 and 7 is 4, 1, 2, 1.
Answer: DAmla and Sarita never scored together. Harita and Sarita also never scored together.
Answer: CEvery match had at least one goal. Also, the players scored in different numbers of matches. So none of the statements is false.
Answer: A
⚡ 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!