- Step 1: Recall constraints. A not History. B not Math. C not English. Each chooses a different subject.
- Step 2: Use Question 27 solution. A has Science.
- Step 3: Assign History. A cannot have History. Remaining: B, C, D. B can have History, C can have History, D can have History.
- Step 4: Assign remaining subjects. Subjects left: History, Math, English. If B has History, C has Math (not English), D has English. Assignment: A-Science, B-History, C-Math, D-English.
- Step 5: Verify. Constraints: A not History (satisfied), B not Math (satisfied), C not English (satisfied).
- Step 6: Final conclusion. Option (2) B is the correct answer.
Disregard commonly known facts. Which conclusion would follow on the basis of given statements only?
Statement (I): Some bottles are car. Some cars are cycle.
Conclusion: \[\begin{array}{rl} \bullet & \text{[(I)] Some bottles are cycle is a possibility.} \\ \bullet & \text{[(II)] All bottles are cycle.} \\ \end{array}\]
When $10^{100}$ is divided by 7, the remainder is ?