Direction: A statement is given followed by two conclusions numbered I and II. Assuming that the given statement is true even if it seems to be at variance from commonly known facts, decide which of the given conclusions logically follow(s) from the given statement. Statement: In a football match between Team-X and Team-Y, the total number of goals scored by Team-Y was 5, out of which 3 goals were scored by the left footed player. Assumption: I. The left-footed player was adept at scoring goals. II. 60% of the players in Team Y are left footed.
Neither I nor II follows.
Analyzing Football Goals Statement and Conclusions
The question presents a statement about a football match between Team-X and Team-Y and asks us to evaluate two conclusions based on this statement.
Understanding the Statement
The given statement provides the following information:
- Total goals scored by Team-Y: 5
- Goals scored by the left-footed player in Team-Y: 3
We must assume this statement is true, even if it seems unusual.
Evaluating Conclusion I: Player's Adeptness
Conclusion I states: "The left-footed player was adept at scoring goals."
- The statement tells us that a left-footed player scored 3 goals in a single match.
- Scoring 3 goals is a good performance for one match.
- However, the term "adept" implies a high level of skill or proficiency over time.
- We cannot definitively conclude that the player is "adept" based on their performance in just one match. They might have been lucky, or the opposing team's defense might have been weak on the day.
- The statement only describes an outcome, not the inherent skill level or consistency of the player.
Therefore, Conclusion I does not logically follow from the statement.
Evaluating Conclusion II: Percentage of Left-Footed Players
Conclusion II states: "60% of the players in Team Y are left footed."
- The statement only provides information about the goals scored and that one of the goal scorers was left-footed.
- It gives no information about the total number of players in Team-Y.
- It gives no information about the number or percentage of left-footed players in the entire team roster.
- We know that at least one player is left-footed because a left-footed player scored goals.
- We cannot calculate or infer the percentage of left-footed players in the team from the goals scored information.
Therefore, Conclusion II does not logically follow from the statement.
Final Deduction
Based on the analysis of each conclusion, neither Conclusion I nor Conclusion II can be logically derived from the given statement.
The correct logical inference is that neither conclusion follows.
| Element | Information from Statement | Analysis against Conclusion |
|---|---|---|
| Statement | Team-Y scored 5 goals; 3 by a left-footed player. | Basis for evaluation. |
| Conclusion I | Left-footed player was adept at scoring goals. | Scoring 3 goals in one match does not guarantee adeptness. Cannot be concluded. |
| Conclusion II | 60% of players in Team Y are left-footed. | Statement provides no data on total players or total left-footed players. Cannot be concluded. |
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Logical Deduction | Drawing conclusions that are certainly true if the premises (statement) are true. |
| Inference | A conclusion reached on the basis of evidence and reasoning. In logic, the inference must be necessary. |
| Assumption | Something taken for granted or accepted as true without proof. The conclusions here are presented as potential assumptions derived from the statement. |
Additional Information: Evaluating Statements and Conclusions
When solving problems involving statements and conclusions, remember these key points:
- Stick to the Statement: Only use the information explicitly given in the statement. Do not use outside knowledge or common sense unless the statement specifically allows it.
- Logical Necessity: A conclusion follows only if it is impossible for the statement to be true and the conclusion to be false.
- Avoid Assumptions: Do not make assumptions or add information that is not present in the statement.
- Analyze Wording: Pay close attention to the exact wording used in both the statement and the conclusions. Words like "all," "some," "only," "likely," "adept," etc., have specific logical implications.
In this case, neither conclusion could be necessarily derived from the limited information about goals scored in a single football match.
Important Questions from Statements and Assumptions
Consider the given statement and decide which of the given assumptions is implicit in the statement.
statement:
P advised Q, "Go to Mumbai via Jaipur ____ the shortest route"
Assumptions: I. P advises everybody.
II. Q wishes to go to Mumbai.
Read the given statement and assumptions carefully. Assuming that the information given in the statement is true, even if it appears to be at variance with commonly known facts, decide which of the given assumptions logically follow(s) from the statement.
Statement:
During exams, invigilators are not supposed to use mobile phones in the examination hall.
Assumptions:
I. Mobile disturbs students during examination.
II. Keeping mobiles switched off helps to improve their vigilance.
Consider the given statements and decide which of the given assumptions is/are implicit in the statement.
Statement:
To expand their business, a budding company now requires more staff.
Assumptions:
I: The current staff is incompetent.
II: Business can only be expanded by always hiring new staff.
Read the given statement and conclusions carefully and decide which of the assumptions is implicit in the statement.
Statement:
"SAVE MONEY - BUY 1 GET 3" — Advertisement by a commercial brand.
Assumptions:
1. Brand sales increased profusely after the offer.
2. People are more attracted to buy if they are offered more than what they are already paying.
Consider the given statement and decide which of the given assumptions is/are implicit in the statement.
Statement: Many farmers are taking up organic farming.
Assumptions:
I. Organic farming is easy to practice.
II. Organic farming is more beneficial to farmers.
