CAT 2024 Slot 2 — DILR Question 6
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. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.
Answer & solution
- A
Only II
- B
Neither I nor II
- C
Only I
Both I and II
Medium
Use the fixed positions of the extreme values. 10 is forced to R1C4 and 1 to R4C4, so both statements are necessarily true.
Solved grid (R2C2, R3C3 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 |
Statement I — 10 in Row 1. As the global maximum, 10 must be the rightmost in its row and topmost in its column; the only such slot is R1C4, which is in Row 1.
Statement II — 1 in Row 4. Clue 3 places 1 in Row 1 or Column 4 of 10; being the global minimum it lands at R4C4, which is in Row 4.