Twelve buildings are arranged in two parallel rows, each containing six buildings. Row 1 has buildings A, B, C, D, E, and F facing east, while Row 2 has buildings J, K, L, M, N, and O facing west. Each building faces the building directly opposite it in the other row. The number of offices in each building varies, with none having fewer than 5 or more than 28 offices. Given the following clues:

- M is second to the right of the building with 15 offices.
- The number of buildings to the right of M is one less than the number of buildings to the left of L.
- L has a prime number of offices.
- The building facing M is second to the left of the building immediately right of D.
- F has 22 offices and is second from either end.
- The difference between the number of offices in F and L is 5.
- The number of buildings between D and F equals the number between J and L.
- K has 12 offices and is second to the left of J.
- The difference between the offices in K and L equals the number of offices in B.
- C is third to the right of B, which does not face M.
- C has 16 offices.
- O has two fewer offices than N.
- N has fewer offices than L.
- The number of offices in E is a multiple of 11.
- E is to the right of the building with 18 offices.
- The difference between the offices in O and A equals the number of offices in M.
- J has a perfect square number of offices and more than D.
- M has 15 fewer offices than J.

Which of the following statements is true?

Question

Twelve buildings are arranged in two parallel rows, each containing six buildings. Row 1 has buildings A, B, C, D, E, and F facing east, while Row 2 has buildings J, K, L, M, N, and O facing west. Each building faces the building directly opposite it in the other row. The number of offices in each building varies, with none having fewer than 5 or more than 28 offices. Given the following clues:

- M is second to the right of the building with 15 offices.
- The number of buildings to the right of M is one less than the number of buildings to the left of L.
- L has a prime number of offices.
- The building facing M is second to the left of the building immediately right of D.
- F has 22 offices and is second from either end.
- The difference between the number of offices in F and L is 5.
- The number of buildings between D and F equals the number between J and L.
- K has 12 offices and is second to the left of J.
- The difference between the offices in K and L equals the number of offices in B.
- C is third to the right of B, which does not face M.
- C has 16 offices.
- O has two fewer offices than N.
- N has fewer offices than L.
- The number of offices in E is a multiple of 11.
- E is to the right of the building with 18 offices.
- The difference between the offices in O and A equals the number of offices in M.
- J has a perfect square number of offices and more than D.
- M has 15 fewer offices than J.

Which of the following statements is true?

Accepted Answer

**Solution:**

1. **Identify positions of F:** F is second from either end in Row 1, so F is either at position 2 or 5.

2. **Offices in F:** F has 22 offices.

3. **Positions of M and L:** M is second to the right of the building with 15 offices. The number of buildings to the right of M is one less than the number to the left of L.

4. **Prime offices in L:** L has a prime number of offices.

5. **Difference between offices of F and L:** The difference is 5, so if F has 22 offices, L can have either 17 or 27 offices. Since maximum is 28, L likely has 17 offices (which is prime).

6. **K and J:** K has 12 offices and is second to the left of J. J has a perfect square number of offices and more than D. M has 15 fewer offices than J.

7. **Offices in C:** C has 16 offices and is third to the right of B, which does not face M.

8. **Offices in E:** Multiple of 11, so possible values are 11 or 22 (22 already taken by F), so E has 11 offices.

9. **Offices in O and N:** O has two fewer offices than N, and N has fewer offices than L (which has 17). So N < 17 and O = N - 2.

10. **Offices in B:** The difference between offices in K (12) and L (17) is 5, which equals offices in B.

11. **Offices in J:** J has a perfect square number of offices greater than D.

12. **From the above, N has more offices than B (5 offices).**

Thus, the statement "N has more offices than B" is true.

**Answer:** N has more offices than B

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