Crossover Aptitude Test Logical Reasoning 4 — Questions and Answers
Question 1: Some doctors are researchers. All researchers publish papers. Which statement must be true?
- All doctors publish papers
- No doctors publish papers
- Some doctors publish papers (Correct answer)
- All publishers are doctors
Correct answer: Some doctors publish papers
The doctors who are researchers must publish papers, so at least some doctors publish papers.
Question 2: If you rearrange the letters 'SILENT', which word can you form?
- TINSEL
- LISTEN
- ENLIST
- All of the above (Correct answer)
Correct answer: All of the above
SILENT, TINSEL, LISTEN, and ENLIST are all anagrams of each other.
Question 3: A train travels 120 miles in 2 hours, then 180 miles in 3 hours. What is its average speed for the entire trip?
- 55 mph
- 60 mph (Correct answer)
- 65 mph
- 70 mph
Correct answer: 60 mph
Total distance = 300 miles, total time = 5 hours; average speed = 300/5 = 60 mph.
Question 4: Odd one out: 144, 169, 196, 216, 225
- 144
- 169
- 196
- 216 (Correct answer)
Correct answer: 216
144=12², 169=13², 196=14², 225=15² are all perfect squares; 216=6³ is a perfect cube, not a perfect square.
Question 5: Statement: 'Only employees with badges can enter.' Tom entered the building. What can you conclude?
- Tom is an employee
- Tom has a badge (Correct answer)
- Tom is not an employee
- Tom entered illegally
Correct answer: Tom has a badge
The rule states having a badge is a necessary condition for entry, so Tom must have a badge.
Question 6: A logical argument: P1: No A is B. P2: All C is B. Conclusion: No C is A. Is this valid?
- Valid (Correct answer)
- Invalid — the conclusion reverses P1
- Invalid — C could be A
- Invalid — B is not defined
Correct answer: Valid
If all C is B and no A is B, then no C can be A — the argument is valid by set disjointness.
Question 7: In a class of 30 students, 18 play soccer and 14 play basketball. If 5 play neither, how many play both?
- 5
- 7 (Correct answer)
- 9
- 11
Correct answer: 7
Students playing at least one sport = 30−5=25; by inclusion-exclusion, both = 18+14−25 = 7.
Crossover Aptitude Test Logical Reasoning 4
Some doctors are researchers.
All researchers publish papers.
Which statement must be true?