Question

The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one person sitting in each box. It is known that
(i) Meritorius' daughter and his brother are seated in the same column.
(ii) His son is seated diagonally across from the sibling of the worst orator.
(iii) The best and worst orators are seated in the same row.
Who is the best orator?

	Column 1	Column 2
Row 1
Row 2

• A. Meritorius
• B. Meritorius' brother
• C. Meritorius' son
• D. Meritorius' daughter

Hint:

Split the four people into two columns using clue (i), then use the diagonal rule to see who shares a row with the worst orator.

Answer 1

The Correct Option is B

Step 1: List the people and the sibling pairs.
The four seated people are Meritorius (M), his brother (Br), his son (S), and his daughter (D).
There are two sibling pairs here: M and Br are siblings of each other, and S and D are siblings of each other, since they are M's two children.

Step 2: Use clue (i) to split the people into columns.
The grid has 2 rows and 2 columns, one person per box. Clue (i) says D and Br sit in the same column.
Since each column holds exactly 2 people, the other column must hold the remaining two people, M and S.
So Column 1 holds D and Br in some order across the two rows, and Column 2 holds M and S in some order across the two rows.

Step 3: Use clue (ii) to locate the son's diagonal partner.
In a 2x2 grid, the box diagonally across from a seat is in the other row and the other column.
The son S sits in Column 2, so his diagonal partner sits in Column 1, in the row opposite to S. Column 1 only contains D and Br, so this diagonal partner is either D or Br.
Clue (ii) says this diagonal partner is the sibling of the worst orator, so the worst orator's sibling is seated in Column 1, in the row opposite to S.

Step 4: Work out who sits in the same row as the son.
Column 1 has two people split across the two rows; one of them is diagonal to S (opposite row), so the other Column 1 person sits in the SAME row as S.
Also, since M and S are the only two people in Column 2, M must sit in the row that is not S's row, that is, the same row as the diagonal partner from Column 1.

Step 5: Identify the best orator using clue (iii).
Case 1: the diagonal partner is Br. Then the worst orator is Br's sibling, which is M. Since M sits in the same row as Br (Step 4), the worst orator M and Br share a row. By clue (iii), the best orator is also in that row, and since only 2 seats exist per row, the best orator must be Br.
Case 2: the diagonal partner is D. Then the worst orator is D's sibling, which is S. From Step 4, the person sharing S's row is the other Column 1 occupant, namely Br. So the worst orator S sits in the same row as Br, and by clue (iii) the best orator is again Br.
Both logically possible cases point to the same person.

Step 6: Why the other options are wrong.
Meritorius can only be the worst orator (Case 1), never the best, since clue (iii) always places the best orator as Br in that scenario.
The son can only be the worst orator (Case 2), so he cannot be the best orator either.
The daughter is always either the diagonal partner or sharing a column with Br, and clues (ii)-(iii) never place her in the best-orator role in either case.

Final Answer:
The best orator is Meritorius' brother.