CAT 2024 Slot 2 — DILR Question 7
Answer the following questions based on the information given below.
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.
| Column 1 | Column 2 | Column 3 | Column 4 | |
|---|---|---|---|---|
| Row 1 | □ | □ | □ | □ |
| Row 2 | □ | □ | □ | |
| Row 3 | □ | □ | ||
| Row 4 | □ |
(Row 1 has 4 slots in Columns 1–4; Row 2 has 3 slots in Columns 2–4; Row 3 has 2 slots in Columns 3–4; Row 4 has 1 slot in Column 4 — ten slots in all.)
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row.
Which of the following statements MUST be true?
I. 2 is placed in a slot in Column 2.
II. 3 is placed in a slot in Column 3.
Answer & solution
- A
Only II
Neither I nor II
- C
Only I
- D
Both I and II
Medium
The numbers 2 and 3 occupy cells R2C2 and R3C3, but the clues never fix which is which. So "2 in Column 2" and "3 in Column 3" are each only sometimes true.
Solved grid (R2C2 = Column 2, R3C3 = Column 3 hold {2,3} in either order):
| Col 1 | Col 2 | Col 3 | Col 4 | |
|---|---|---|---|---|
| Row 1 | 4 | 6 | 9 | 10 |
| Row 2 | 2 or 3 | 5 | 8 | |
| Row 3 | 3 or 2 | 7 | ||
| Row 4 | 1 |
Where 2 and 3 can sit. Clue 4 keeps 2 and 3 out of Row 1 and Column 4, leaving only R2C2 and R3C3; no clue distinguishes them.
Test both statements. If 2 is at R3C3 then "2 in Column 2" fails; if 3 is at R2C2 then "3 in Column 3" fails.