Question 1 · Analytical Aptitude · 2026_Set2
MCQ
‘When it is raining, peacocks dance.’
Based only on this sentence, which one of the following options is necessarily true?
- A.
Peacocks dance only when it is raining.
- B.
When peacocks dance, it is raining.
- C.
When peacocks are not dancing, it is not raining.
- D.
When it is not raining, peacocks do not dance.
Step-by-Step Solution
Insight: "When P, Q" translates to P⟹Q. The contrapositive ¬Q⟹¬P is logically equivalent and must be true.
Exam route: Identify P (raining) and Q (peacocks dance). The contrapositive is "If peacocks are not dancing, it is not raining." Match with Option C.
Learning route:
- Translate the statement: "When it is raining (P), peacocks dance (Q)" means P⟹Q.
- Recall logical equivalences: The contrapositive ¬Q⟹¬P is always true if P⟹Q is true.
- Form the contrapositive: "When peacocks are not dancing (¬Q), it is not raining (¬P)."
- Evaluate options:
- Option A & B represent the converse (Q⟹P), which is not necessarily true.
- Option D represents the inverse (¬P⟹¬Q), which is not necessarily true.
- Option C represents the contrapositive (¬Q⟹¬P), which must be true.
Answer is C.
Question 2 · Analytical Aptitude · 2026_Set1
MCQ
‘When the teacher is in the room, all students stand silently.’
If the above statement is true, which one of the following statements is not necessarily true?
- A.
If any student is not standing silently, then the teacher is not in the room.
- B.
When the teacher is in the room, all students are silent.
- C.
If all students are standing, then the teacher is in the room.
- D.
When the teacher is in the room, all students are standing.
Step-by-Step Solution
Insight: The question asks for what is NOT necessarily true. "When P, Q" means P⟹Q. The converse Q⟹P is not necessarily true.
Exam route: Identify P (teacher in room) and Q (students stand silently). The question asks for the invalid inference. Option C is the converse ("If students are standing, teacher is in room"), which is not necessarily true.
Learning route:
- Formalize the statement: "When the teacher is in the room (P), all students stand silently (Q)" means P⟹Q.
- Understand the question: We need to find the statement that is NOT necessarily true (i.e., the invalid inference).
- Evaluate options:
- Option A is the contrapositive (¬Q⟹¬P), which is necessarily true.
- Option B is a restatement of P⟹Q (standing silently implies standing), necessarily true.
- Option C is the converse (Q⟹P). Just because students are standing doesn't mean the teacher is in the room. Not necessarily true.
- Option D is a restatement of P⟹Q, necessarily true.
Answer is C.
Question 3 · Analytical Aptitude · 2025_Set2
MCQ
Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to see you”, Ramya told Josephine.
- A.
Ramya knew that Josephine was in the hospital.
- B.
Ramya did not know that Josephine was in the hospital.
- C.
Ramya and Josephine were once close friends; but now, they are not.
- D.
Josephine was in the hospital due to an injury to her leg.
Step-by-Step Solution
Insight: "Even if I had known" is a past counterfactual conditional, which grammatically implies the condition was not met in reality.
Exam route: Identify the counterfactual structure "had known". This implies the speaker did not know. Select Option B.
Learning route: The phrase "Even if I had known" uses the past perfect tense in a conditional clause, which in English grammar marks a counterfactual situation—a situation that is contrary to the actual facts of the past. By saying "If I had known," Ramya implies that she did not, in fact, know. While the core of her statement is about her firm intent not to visit regardless of the condition, the grammatical structure logically entails that the condition (knowing) was false. Options C and D introduce outside information not present in the text. Option A directly contradicts the counterfactual implication.
Wrong path: A student might focus on the emotional tone and infer they were once friends but are not now (Option C), or assume the reason for the hospital visit (Option D). This breaks because these are subjective interpretations and outside information not supported by the text. Another wrong path is taking the conditional literally as a real possibility (Option A), ignoring the counterfactual grammar. Generalization: "If I had X" grammatically means "I did not X"; do not infer emotional or historical context not explicitly stated. Verification: The counterfactual "had known" strictly implies she did not know, matching Option B.
Question 4 · Analytical Aptitude · 2023
MCQ
The country of Zombieland is in distress since more than 75% of its working population is suffering from serious health issues. Studies conducted by competent health experts concluded that a complete lack of physical exercise among its working population was one of the leading causes of their health issues. As one of the measures to address the problem, the Government of Zombieland has decided to provide monetary incentives to those who ride bicycles to work.
Based only on the information provided above, which one of the following statements can be logically inferred with certainty?
- A.
All the working population of Zombieland will henceforth ride bicycles to work.
- B.
Riding bicycles will ensure that all of the working population of Zombieland is free of health issues.
- C.
The health experts suggested to the Government of Zombieland to declare riding bicycles as mandatory.
- D.
The Government of Zombieland believes that riding bicycles is a form of physical exercise.
Step-by-Step Solution
Insight: The government's action (incentivizing cycling) to solve a specific problem (lack of exercise) reveals their underlying belief (cycling is exercise).
Exam route: Match the problem (lack of exercise) with the solution (incentivize cycling). The logical bridge is that the government believes cycling addresses the lack of exercise. Option D states exactly this.
Learning route: The passage establishes that lack of physical exercise is a leading cause of health issues. The government responds by providing monetary incentives for riding bicycles to work. For this action to make logical sense as a remedy for the stated problem, the government must believe that riding bicycles constitutes physical exercise. We cannot infer that everyone will ride bicycles (Option A), that it will cure all issues (Option B), or that experts suggested making it mandatory (Option C), as these introduce extreme claims or unstated information.
Wrong path: A student might see the government taking action and assume it will definitely solve the problem, leading to Option B. This breaks because the passage states lack of exercise is only "one of the leading causes", so cycling cannot guarantee a complete cure. Another wrong path is assuming experts suggested the specific policy (Option C), which is outside information. Generalization: An action taken to solve a problem implies a belief in the solution's efficacy, but does not guarantee the outcome or imply unstated suggestions. Verification: Option D perfectly bridges the problem and the action without overreaching.
Question 5 · Analytical Aptitude · 2023
MCQ
A survey for a certain year found that 90% of pregnant women received medical care at least once before giving birth. Of these women, 60% received medical care from doctors, while 40% received medical care from other healthcare providers.
Given this information, which one of the following statements can be inferred with certainty?
- A.
More than half of the pregnant women received medical care at least once from a doctor.
- B.
Less than half of the pregnant women received medical care at least once from a doctor.
- C.
More than half of the pregnant women received medical care at most once from a doctor.
- D.
Less than half of the pregnant women received medical care at most once from a doctor.
Step-by-Step Solution
Insight: 60% of the 90% who received care is 54% of the total, which is strictly more than half.
Exam route: Calculate 0.60×0.90=0.54. Since 54%>50%, Option A is directly verified without needing to assume anything about overlap.
Learning route: Let the total number of pregnant women be 100. The passage states 90 received care. Of these 90, 60% received care from doctors. 60% of 90 is 54. Thus, 54 out of 100 women (54%) received care from a doctor. Since 54% is strictly greater than 50%, it is certain that more than half received care from a doctor. The trap is to assume the 60% and 40% must overlap or be disjoint in a way that changes the total, but the question only asks about the doctor subset, which is firmly 54%.
Wrong path: A student might add 60% and 40% to get 100% and assume they are disjoint, or try to find the overlap. This leads to confusion about the "at most once" options (C and D), which introduce frequency data not present in the passage. The exact line where it breaks is assuming the passage provides data on visit frequency. Generalization: Always calculate the true base for nested percentages and ignore unstated variables. Verification: 54% of total is indeed more than half, matching Option A.
Question 6 · Analytical Aptitude · 2022
MCQ
Some people believe that “what gets measured, improves”. Some others believe that “what gets measured, gets gamed”. One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes. However, the same metrics are counterproductive in organizations with poor work culture.
Which one of the following is the CORRECT logical inference based on the information in the above passage?
- A.
Metrics are useful in organizations with poor work culture
- B.
Metrics are useful in organizations with good work culture
- C.
Metrics are always counterproductive in organizations with good work culture
- D.
Metrics are never useful in organizations with good work culture
Step-by-Step Solution
Insight: The passage explicitly states the effect of metrics in good work cultures. Deductive inference requires selecting what must be true based strictly on the text.
Exam route: Scan for "good work culture". The text says "metrics help improve outcomes". This directly means metrics are useful. Match with Option B.
Learning route:
- Analyze the passage: The text states, "In organizations with good work culture, metrics help improve outcomes."
- Apply the Golden Rule of Deductive Inference: Accept the passage as absolute truth and look for what must be true without adding outside assumptions.
- Evaluate options:
- Option A claims metrics are useful in poor work culture, but the text says they are "counterproductive".
- Option B claims metrics are useful in good work culture, which perfectly matches "help improve outcomes".
- Options C and D claim metrics are counterproductive or never useful in good work culture, directly contradicting the text.
Answer is B.
Question 7 · Analytical Aptitude · 2022
MCQ
Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.
- A.
Statement 1 and Statement 3
- B.
Statement 1 and Statement 2
- C.
Statement 2 and Statement 4
- D.
Statement 3 and Statement 4
Step-by-Step Solution
Insight: "All S are P" and "No S is P" are mutually exclusive; they cannot both be true for a non-empty set.
Exam route: Statement 1 is Type A (All), Statement 3 is Type E (No). A and E are contraries. Select Option A.
Learning route: In categorical logic, assuming the subject class is not empty, the universal affirmative (All students are inquisitive) and the universal negative (No student is inquisitive) cannot both be true. If all are inquisitive, it is false that none are. Statement 2 (Some are) and Statement 4 (Some are not) can both be true simultaneously if only a portion are inquisitive. Therefore, Statements 1 and 3 are the pair that cannot be true simultaneously.
Wrong path: A student might think "Some" means "Some but not all" (everyday language trap), leading them to believe Statements 2 and 4 cannot both be true (Option C). This breaks because in formal logic, "Some" means "at least one" and does not exclude "All". If all are inquisitive, both "Some are" and "Some are not" (wait, if all are, "Some are not" is false. But if some are, then some are not can also be true. The pair 2 and 4 can both be true if the set is partially inquisitive). Generalization: Never assume "Some S are P" implies "Some S are not P" in formal logic. Verification: Statements 1 and 3 directly contradict each other for any non-empty set.
Question 8 · Analytical Aptitude · 2021_Set1
MCQ
Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All bacteria are microorganisms.
Statement 2: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
- A.
Only conclusion I is correct
- B.
Only conclusion II is correct
- C.
Either conclusion I or II is correct.
- D.
Neither conclusion I nor II is correct.
Step-by-Step Solution
Insight: Two subsets of a larger set may or may not overlap; without explicit information, neither overlap nor disjointness can be definitively concluded.
Exam route: Draw Venn diagram with Bacteria and Pathogens inside Microorganisms. They can be disjoint or overlapping. Since neither is a definite conclusion, select Option D.
Learning route: Let Microorganisms be the universal set. Bacteria and Pathogens are both subsets. The premises do not specify the relationship between Bacteria and Pathogens. If they overlap, Conclusion I (Some pathogens are bacteria) is true, and Conclusion II (All pathogens are not bacteria / No pathogens are bacteria) is false. If they are disjoint, Conclusion I is false, and Conclusion II is true. Because we cannot determine which scenario is the actual case from the premises alone, neither conclusion is logically correct as a definite deduction. Option C is a trap for those who recognize they are contradictory, but in strict syllogism, we only accept conclusions that are definitively true in all valid diagrams.
Wrong path: A student might see that I and II are contradictory and select Option C (Either I or II). This breaks because in strict syllogism, a conclusion must be definitely true based on the premises. Since we cannot deduce which one is true from the given statements, neither is a valid definite conclusion. Generalization: A conclusion must hold in every valid Venn diagram to be correct; do not fall for the "Either/Or" trap when neither is definitively provable. Verification: Both disjoint and overlapping diagrams satisfy the premises, proving neither conclusion is definite.