CAT 2024 Slot 2 — DILR Question 9
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.
What is the sum of the numbers placed in Column 4?
Answer & solution
Answer: 26
Medium
Column 4 is fully determined: it runs 10, 8, 7, 1 from top to bottom. Add them.
Solved grid — Column 4 = 10, 8, 7, 1:
| 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 |
Add Column 4. Top to bottom 10 > 8 > 7 > 1.