Three Pouches in a 3x3 Grid

CAT 2019 Slot 2 · DILR · Hard · Grid & Matrix

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Passage / data set

Three pouches (each represented by a filled circle) are kept in each of the nine slots in a 3×33 \times 3 grid. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8. There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.

Column 1Column 2Column 3
Row 1(2, 4)(6, 8)(1, 3)
Row 2(3, 5)(1, 1)(6, 20)
Row 3(1, 2)(1, 2)(2, 5)

Question 1 of 4

What is the total amount of money (in rupees) in the three pouches kept in the first column of the second row?

Answer

13

Explanation

By solving the grid constraints, row 2 column 1 contains pouches with values (3, 5, 5), giving a total of 13 rupees.

Question 2 of 4

How many pouches contain exactly one coin?

Answer

8

Explanation

Counting the pouches across all slots with value 1 yields 8 pouches.

Question 3 of 4

What is the number of slots for which the average amount (in rupees) of its three pouches is an integer?

Answer

2

Explanation

Only 2 slots have sum divisible by 3, making their average an integer.

Question 4 of 4

The number of slots for which the total amount in its three pouches strictly exceeds Rs. 10 is

Answer

3

Explanation

The slots exceeding Rs. 10 total are Row 1 Col 2, Row 2 Col 1, and Row 2 Col 3 (total 3 slots).

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