Multiple choice general knowledge math & puzzles

Three men (Tom, Peter and Jack) and three women (Eliza, Anne and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her own cottage. There are no others staying in the same row of houses.

A.Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row.
B.Eliza and Anne are unwilling to stay besides any occupied cottage..
C.Karen is next to Peter and Jack.
D.Between Anne and Jackâs cottage there is just one vacant house.
E.None of the girls occupy adjacent cottages.
F.The house occupied by Tom is next to an end cottage.

Which of the above statements can be said to have been derived from two other statements ?

  1. A

  2. B

  3. C

  4. E
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement E (none of the girls occupy adjacent cottages) can be derived from statements B and D. Statement B says Eliza and Anne won't stay beside occupied cottages, and statement D places one vacant house between Anne and Jack. Combining these with the gender constraints ensures the three women (Eliza, Anne, Karen) cannot be adjacent to each other.

AI explanation

To solve this question, we need to analyze each statement and determine which statements can be derived from two other statements. Let's go through each statement:

A. Anne, Tom, and Jack do not want to stay in any cottage, which is at the end of the row. B. Eliza and Anne are unwilling to stay beside any occupied cottage. C. Karen is next to Peter and Jack. D. Between Anne and Jack's cottage, there is just one vacant house. E. None of the girls occupy adjacent cottages. F. The house occupied by Tom is next to an end cottage.

We can try to derive each statement using the other statements:

A cannot be derived using the other statements because it is a unique condition mentioned in the problem statement.

B cannot be derived using the other statements because it is also a unique condition mentioned in the problem statement.

C cannot be derived using the other statements because it is also a unique condition mentioned in the problem statement.

D can be derived using statements C and E. If Karen is next to Peter and Jack, and none of the girls occupy adjacent cottages, then there must be exactly one vacant house between Anne and Jack's cottage.

E cannot be derived using the other statements because it is a unique condition mentioned in the problem statement.

F cannot be derived using the other statements because it is a unique condition mentioned in the problem statement.

Therefore, the statement that can be said to have been derived from two other statements is D.

Keep practicing — related questions