Question (1 to 5) :
The management of a university hockey team was evaluating 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.
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.
1. Only one goal was scored in every even numbered match.
2. Harita scored more goals than Bimla.
3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.
5. 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.
6. The match in which the highest number of goals was scored was unique and it was not Match 5.
Question 1 Q. 1 How many goals were scored in Match 7?
1. 1
2. Cannot be determined
3. 2
4. 3
Explanation
Correct answer- 1
Step 1: Basic information and initial deductions
- From condition (1):
Matches 2, 4, 6, and 8 had only 1 goal each. - From condition (4):
Bimla scored a goal in Match 1.
Bimla scored a total of 4 goals. - From condition (2):
Harita scored more goals than Bimla.
Since Bimla has 4 goals, Harita must have at least 5 goals. - From condition (3):
Harita is the highest goal scorer.
Harita scored in exactly 3 matches, which includes Match 4 and Match 8.
So in those 3 matches, she scored a total of 5 goals (because she scored more than Bimla). - Since Harita and Bimla together scored 5 + 4 = 9 goals, the remaining 3 goals must be scored by Amla and Sarita.
- From condition (4):
Bimla scored 1 goal each in three consecutive matches — Matches 5, 6, and 7.
Intermediate table after Step 1
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 1 / 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | X | X | 5 | ||||||
| Sarita | 2 / 1 | ||||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Step 2: Further conditions
- From condition (5):
The number of goals in Match 3 and Match 7 are equal.
That number is different from goals in Match 1 or Match 5. - From condition (6):
The match with the highest number of goals was unique and not Match 5. - From conditions above:
Since Match 5 had 2 goals (we’ve accounted for Bimla’s 1 goal, so only 1 left for someone else)
Match 1 had the highest number of goals — 4 goals. - Since Harita is the top scorer and scored in 3 matches, including Match 4 and Match 8:
She must have scored 3 goals in Match 1 (because she has to score 5 in total). - Each player scored in at least one match (from the conditions).
- Since Match 3 and Match 7 had equal goals and both are different from 1 or 5:
Both had 1 goal each.
Final table
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | 3 | 1 | 1 | 5 | |||||
| Sarita | 1 | 1 | 2 | ||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Summary of logic
- You used conditions to identify total goals in each match.
- You determined Harita had to score 3 goals in Match 1 to reach her total of 5 goals.
- Bimla’s distribution was fixed by her consecutive matches.
- The remaining goals were distributed to Amla and Sarita, ensuring every player had at least one goal and conditions for match goals were satisfied.
Question 2
Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?
1. 3, 1, 2, 1
2. 5, 1, 0, 1
3. 3, 2, 1, 2
4. 4, 1, 2, 1
Explanation
Correct answer- 4
Step 1: Basic information and initial deductions
- From condition (1):
Matches 2, 4, 6, and 8 had only 1 goal each. - From condition (4):
Bimla scored a goal in Match 1.
Bimla scored a total of 4 goals. - From condition (2):
Harita scored more goals than Bimla.
Since Bimla has 4 goals, Harita must have at least 5 goals. - From condition (3):
Harita is the highest goal scorer.
Harita scored in exactly 3 matches, which includes Match 4 and Match 8.
So in those 3 matches, she scored a total of 5 goals (because she scored more than Bimla). - Since Harita and Bimla together scored 5 + 4 = 9 goals, the remaining 3 goals must be scored by Amla and Sarita.
- From condition (4):
Bimla scored 1 goal each in three consecutive matches — Matches 5, 6, and 7.
Intermediate table after Step 1
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 1 / 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | X | X | 5 | ||||||
| Sarita | 2 / 1 | ||||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Step 2: Further conditions
- From condition (5):
The number of goals in Match 3 and Match 7 are equal.
That number is different from goals in Match 1 or Match 5. - From condition (6):
The match with the highest number of goals was unique and not Match 5. - From conditions above:
Since Match 5 had 2 goals (we’ve accounted for Bimla’s 1 goal, so only 1 left for someone else)
Match 1 had the highest number of goals — 4 goals. - Since Harita is the top scorer and scored in 3 matches, including Match 4 and Match 8:
She must have scored 3 goals in Match 1 (because she has to score 5 in total). - Each player scored in at least one match (from the conditions).
- Since Match 3 and Match 7 had equal goals and both are different from 1 or 5:
Both had 1 goal each.
Final table
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | 3 | 1 | 1 | 5 | |||||
| Sarita | 1 | 1 | 2 | ||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Summary of logic
- You used conditions to identify total goals in each match.
- You determined Harita had to score 3 goals in Match 1 to reach her total of 5 goals.
- Bimla’s distribution was fixed by her consecutive matches.
- The remaining goals were distributed to Amla and Sarita, ensuring every player had at least one goal and conditions for match goals were satisfied.
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.
1. Statement-2 only
2. Both the statements
3. Statement-1 only
4. None of the statements
Explanation
Correct answer – 2
Step 1: Basic information and initial deductions
- From condition (1):
Matches 2, 4, 6, and 8 had only 1 goal each. - From condition (4):
Bimla scored a goal in Match 1.
Bimla scored a total of 4 goals. - From condition (2):
Harita scored more goals than Bimla.
Since Bimla has 4 goals, Harita must have at least 5 goals. - From condition (3):
Harita is the highest goal scorer.
Harita scored in exactly 3 matches, which includes Match 4 and Match 8.
So in those 3 matches, she scored a total of 5 goals (because she scored more than Bimla). - Since Harita and Bimla together scored 5 + 4 = 9 goals, the remaining 3 goals must be scored by Amla and Sarita.
- From condition (4):
Bimla scored 1 goal each in three consecutive matches — Matches 5, 6, and 7.
Intermediate table after Step 1
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 1 / 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | X | X | 5 | ||||||
| Sarita | 2 / 1 | ||||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Step 2: Further conditions
- From condition (5):
The number of goals in Match 3 and Match 7 are equal.
That number is different from goals in Match 1 or Match 5. - From condition (6):
The match with the highest number of goals was unique and not Match 5. - From conditions above:
Since Match 5 had 2 goals (we’ve accounted for Bimla’s 1 goal, so only 1 left for someone else)
Match 1 had the highest number of goals — 4 goals. - Since Harita is the top scorer and scored in 3 matches, including Match 4 and Match 8:
She must have scored 3 goals in Match 1 (because she has to score 5 in total). - Each player scored in at least one match (from the conditions).
- Since Match 3 and Match 7 had equal goals and both are different from 1 or 5:
Both had 1 goal each.
Final table
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | 3 | 1 | 1 | 5 | |||||
| Sarita | 1 | 1 | 2 | ||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Summary of logic
- You used conditions to identify total goals in each match.
- You determined Harita had to score 3 goals in Match 1 to reach her total of 5 goals.
- Bimla’s distribution was fixed by her consecutive matches.
- The remaining goals were distributed to Amla and Sarita, ensuring every player had at least one goal and conditions for match goals were satisfied.
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.
1. Both the statements
2. None of the statements
3. Statement-1 only
4. Statement-2 only
Explanation
Correct answer- 2
Step 1: Basic information and initial deductions
- From condition (1):
Matches 2, 4, 6, and 8 had only 1 goal each. - From condition (4):
Bimla scored a goal in Match 1.
Bimla scored a total of 4 goals. - From condition (2):
Harita scored more goals than Bimla.
Since Bimla has 4 goals, Harita must have at least 5 goals. - From condition (3):
Harita is the highest goal scorer.
Harita scored in exactly 3 matches, which includes Match 4 and Match 8.
So in those 3 matches, she scored a total of 5 goals (because she scored more than Bimla). - Since Harita and Bimla together scored 5 + 4 = 9 goals, the remaining 3 goals must be scored by Amla and Sarita.
- From condition (4):
Bimla scored 1 goal each in three consecutive matches — Matches 5, 6, and 7.
Intermediate table after Step 1
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 1 / 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | X | X | 5 | ||||||
| Sarita | 2 / 1 | ||||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Step 2: Further conditions
- From condition (5):
The number of goals in Match 3 and Match 7 are equal.
That number is different from goals in Match 1 or Match 5. - From condition (6):
The match with the highest number of goals was unique and not Match 5. - From conditions above:
Since Match 5 had 2 goals (we’ve accounted for Bimla’s 1 goal, so only 1 left for someone else)
Match 1 had the highest number of goals — 4 goals. - Since Harita is the top scorer and scored in 3 matches, including Match 4 and Match 8:
She must have scored 3 goals in Match 1 (because she has to score 5 in total). - Each player scored in at least one match (from the conditions).
- Since Match 3 and Match 7 had equal goals and both are different from 1 or 5:
Both had 1 goal each.
Final table
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | 3 | 1 | 1 | 5 | |||||
| Sarita | 1 | 1 | 2 | ||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Summary of logic
- You used conditions to identify total goals in each match.
- You determined Harita had to score 3 goals in Match 1 to reach her total of 5 goals.
- Bimla’s distribution was fixed by her consecutive matches.
- The remaining goals were distributed to Amla and Sarita, ensuring every player had at least one goal and conditions for match goals were satisfied.
Question 5
If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true?
Statement-1: Amla scored goals in consecutive matches.
Statement-2: Sarita scored goals in consecutive matches.
1. Both the statements
2. Statement-2 only
3. None of the statements
4. Statement-1 only
Explanation
Correct answer-3
Step 1: Basic information and initial deductions
- From condition (1):
Matches 2, 4, 6, and 8 had only 1 goal each. - From condition (4):
Bimla scored a goal in Match 1.
Bimla scored a total of 4 goals. - From condition (2):
Harita scored more goals than Bimla.
Since Bimla has 4 goals, Harita must have at least 5 goals. - From condition (3):
Harita is the highest goal scorer.
Harita scored in exactly 3 matches, which includes Match 4 and Match 8.
So in those 3 matches, she scored a total of 5 goals (because she scored more than Bimla). - Since Harita and Bimla together scored 5 + 4 = 9 goals, the remaining 3 goals must be scored by Amla and Sarita.
- From condition (4):
Bimla scored 1 goal each in three consecutive matches — Matches 5, 6, and 7.
Intermediate table after Step 1
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 1 / 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | X | X | 5 | ||||||
| Sarita | 2 / 1 | ||||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Step 2: Further conditions
- From condition (5):
The number of goals in Match 3 and Match 7 are equal.
That number is different from goals in Match 1 or Match 5. - From condition (6):
The match with the highest number of goals was unique and not Match 5. - From conditions above:
Since Match 5 had 2 goals (we’ve accounted for Bimla’s 1 goal, so only 1 left for someone else)
Match 1 had the highest number of goals — 4 goals. - Since Harita is the top scorer and scored in 3 matches, including Match 4 and Match 8:
She must have scored 3 goals in Match 1 (because she has to score 5 in total). - Each player scored in at least one match (from the conditions).
- Since Match 3 and Match 7 had equal goals and both are different from 1 or 5:
Both had 1 goal each.
Final table
| Player | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 | Match 7 | Match 8 | Total Goals |
|---|---|---|---|---|---|---|---|---|---|
| Amla | X | X | 2 | ||||||
| Bimla | 1 | 1 | 1 | 1 | 4 | ||||
| Harita | 3 | 1 | 1 | 5 | |||||
| Sarita | 1 | 1 | 2 | ||||||
| Total Goals | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Summary of logic
- You used conditions to identify total goals in each match.
- You determined Harita had to score 3 goals in Match 1 to reach her total of 5 goals.
- Bimla’s distribution was fixed by her consecutive matches.
- The remaining goals were distributed to Amla and Sarita, ensuring every player had at least one goal and conditions for match goals were satisfied.
