CAT 2025 Lesson : Numerical Reasoning - Case 9

Read the following and answer the questions that follow



Three pouches (each represented by a filled circle) are kept in each of the nine slots in a 3 × 3 grid, as shown in the figure. 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.

[CAT 2019 S2]

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

Answer:

31) How many pouches contain exactly one coin?

Answer:

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

Answer:

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

Answer:

Solution

There are 3 pouches in each cell, one should be the minimum, one should be maximum. Now we left to find the 3^rd possible value between the maximum and the minimum value.

As the average amount of money in pouches in any column or any row is an integer, and we have 9 pouches, we shall conclude that amount of money in any row or any column is multiple of 9.

From the 2^nd paragraph it is given the total amount of money in C¹R³is 4, then the distribution of money in 3 pouches will be 1, 2 and 2.

In C²R²the minimum and maximum amount of money 1, then all the 3 pouches have 1, 1 and 1.



Let us find the amount of money which are in their range(between maximum and minimum) by adding the respective columns and rows and finding out which possible multiple of 9 satisfying the condition.

Sum of all the pouches in column 2.

14 + a + 3 + 3 + b = 9/18/27 (Multiple of 9)
20+ a + b = 27 (9, 18 and >27 are not possible)
a + b = 7
The only possibility is a = 6 and b = 1.

Sum of all the pouches in column 1.
6 + c + d + 8 + 4 = 9/18/27
18 + c + d = 27
c + d = 9
The only possibility is c = 4 and d = 5.

Sum of all the pouches in row 1.
6 + c + 14 + a + 4 + e = 9/18/27
Substitute a, c in the equation
6 + 4 + 14 + 6 + 4 + e = 9/18/27/36
34 + e = 36
e = 2

Sum of all the pouches in row 3.
4 + 3 + b + 7 + f = 9/18/27
14 + b + f = 9/18/27
15 + f = 18
f = 3

Sum of all the pouches in column 3.
4 + e + 26 + g + 7 + f = 36/45/54
37 + e + g + f = 36/45/54
42 + g = 54
g = 12



30) Sum of the amount of money in C¹R² is 13

Answer: 13

31)
In row 1 column 3 has 1 pouch with exactly one coin, in row 2 column 2 has 3 pouch with exactly one coin and in row 3 column 1 has 2 pouch with exactly one coin and column 3 has 2 pouch with exactly one coin.

Total number of pouch with exactly one coin = 1 + 3 + 2 + 2 = 8

Answer: 8

32)
we need to find the cells with multiple of 3,



Answer: 2

33) Total amount in its three pouches strictly exceeds Rs. 10 are R¹C², R²C¹and R²C³

Answer:
30) 13
31) 8
32) 2
33) 3