Logical Reasoning · Statements & Arguments
Statement and Conclusion — Questions & Answers
Statement and conclusion questions ask which conclusions follow from the given statements. A conclusion follows only if the statements establish it, not if it is merely likely.
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Accept the statement as completely true and add nothing to it. A conclusion follows only if it must be true from the statement alone: a restatement, a direct consequence, or simple arithmetic.
Exactly one option must be true if the statement is true. Test each option: could the statement be true while this option is false? If so, reject it.
Check I, II and III one at a time: does each have to be true? Work out any numbers, then choose the option that lists exactly the conclusions that follow.
Four options follow from the statement (often by simple arithmetic or restatement). Find the one that adds something the statement never says.
5 solved Statement and Conclusion questions
Statement: All the students in Class 8 passed the science exam. Priya is in Class 8.
Conclusions:
I. Priya passed the science exam.
II. No Class 8 student failed the science exam.
Which of the conclusions follow from the statement?Solution — answer E
Both follow. Priya is in Class 8, so she passed (I), and if all Class 8 students passed, none failed (II).
4 steps · reveal one at a timeStep 1: Understand the Statement
The statement provides two key pieces of information. First, it tells us that every student in Class 8 was successful in the science exam. Second, it specifies that Priya is a member of Class 8.
Step 2: Evaluate Conclusion I
Conclusion I states: "Priya passed the science exam." Based on the statement, we know that all students in Class 8 passed, and Priya is in Class 8. Therefore, it logically follows that Priya passed the exam. Conclusion I is valid.
Step 3: Evaluate Conclusion II
Conclusion II states: "No Class 8 student failed the science exam." If "All the students in Class 8 passed the science exam," it directly implies that there are no students in Class 8 who failed. This is simply a rephrasing of the first part of the statement. Conclusion II is also valid.
Step 4: The answer
So the answer is (E) Both I and II can be concluded. Both conclusions are direct and logical consequences of the information provided in the statement.
Statement: All the members of the school chess club are in Class 9, and some Class 9 students play cricket.
Which conclusion definitely follows from the statement?Solution — answer C
Every member is in Class 9, so no member of the chess club is in Class 10. The cricket players among Class 9 may or may not be chess club members, and the other options reverse or overstate the facts.
4 steps · reveal one at a timeStep 1: Identify Key Facts
The statement gives two main facts. First, all members of the school chess club are in Class 9. This means the chess club is entirely contained within Class 9.
Step 2: Deduce Class Membership
If every member of the chess club is in Class 9, then by definition, no member of the chess club can be in any other class. This includes Class 10, or Class 8, etc.
Step 3: Consider Cricket Players
The second fact is that some Class 9 students play cricket. This tells us there's an overlap between Class 9 and cricket players, but it doesn't specify if these cricket players are also in the chess club.
Step 4: The answer
So the answer is (C) No member of the chess club is in Class 10. Since all chess club members are in Class 9, they cannot be in Class 10.
Statement: In a class of 30, 18 students like cricket and the rest like football; each student likes only one of the two.
Conclusions:
I. 12 students like football.
II. More students like cricket than football.
III. Football is unpopular across the whole school.
Which of the conclusions follow from the statement?Solution — answer A
I and II only. 30 − 18 = 12 like football (I), and 18 > 12 (II). One class tells us nothing about the whole school (III).
4 steps · reveal one at a timeStep 1: Calculate Football Fans
The statement tells us there are 30 students in total, and 18 like cricket. Since each student likes only one sport, we can find the number of students who like football by subtracting: 30−18=12 students.
Step 2: Evaluate Conclusions I & II
Conclusion I states that 12 students like football. Our calculation confirms this. Conclusion II states that more students like cricket than football. We know 18 like cricket and 12 like football, and 18>12. So, both conclusions I and II are correct.
Step 3: Evaluate Conclusion III
Conclusion III claims football is unpopular across the whole school. The statement only provides information about one class of 30 students. We cannot make a generalisation about the entire school based on data from a single class. Therefore, conclusion III does not follow.
Step 4: The answer
So the answer is (A) I and II only. Conclusions I and II are directly supported by the information given in the statement, while conclusion III makes an unsupported generalisation.
Statement: Every student in the hostel must be back by 9 p.m. Arun lives in the hostel.
Which of these does NOT follow from the statement?Solution — answer D
The rule says Arun must be back by 9 p.m.; it doesn't tell us that Arun always returns at 8 p.m. The other four follow directly from the rule and from Arun living in the hostel.
5 steps · reveal one at a timeStep 1: Understand the Rule
The statement gives us two key pieces of information: a rule that every student in the hostel must follow, and the fact that Arun lives in the hostel.
Step 2: Apply the Rule
Since Arun lives in the hostel, the rule applies to him. This means Arun must be back by 9 p.m., just like all other hostel students.
Step 3: Check for Direct Consequences
From this, we can deduce several things. For example, a student returning at 10 p.m. would break the rule, and the hostel definitely has a fixed return time for its students.
Step 4: Identify Unproven Facts
The statement tells us what Arun must do (be back by 9 p.m.). It does not provide any information about what time Arun actually returns, only the latest he can be.
Step 5: The answer
So the answer is (D) Arun always returns at 8 p.m. The statement only sets a deadline of 9 p.m.; it doesn't tell us Arun's usual return time.
Statement: Of the 40 students in the class, 30 are girls.
Conclusions:
I. There are 10 boys in the class.
II. The girls in the class score better than the boys.
Taking the statement as true, which conclusion(s) can be drawn?Solution — answer A
Only I can be concluded. 40 − 30 = 10 boys (I). Nothing is said about marks (II).
4 steps · reveal one at a timeStep 1: Understand the Statement
First, let's carefully read the given statement. It tells us that there are a total of 40 students in the class, and 30 of these students are girls. This is all the factual information we have.
Step 2: Evaluate Conclusion I
Conclusion I states: 'There are 10 boys in the class.' Since we know the total number of students is 40 and 30 are girls, we can calculate the number of boys: 40−30=10. This conclusion can be drawn directly from the statement.
Step 3: Evaluate Conclusion II
Conclusion II states: 'The girls in the class score better than the boys.' The original statement provides absolutely no information about student scores, academic performance, or any comparison between boys and girls in terms of marks. Therefore, this conclusion cannot be drawn.
Step 4: The answer
So the answer is (A) Only I can be concluded. We established that Conclusion I is directly supported by the statement, while Conclusion II is not supported by any given information.
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