CAT 2020 Slot 2 DILR Question & Solution

Logical ReasoningMedium

Data Set

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:

1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

Question 1

The total number of possible configurations using beads of only two colours is:

Solution:

Since we are required to use only two colours, these can be either
1. Green + Blue
2. ⁠Blue + Red
3. ⁠Green + Red

But we know that Between any two Red coloured beads in a row or a column, there have to be both a Green and a Blue coloured bead. Hence without both Green and Blue, Red beads cannot be used to fill the grid.Thus if we use only Green and Blue beads, the two configurations that are possible are:

cracku1

There are only 2 configurations possible

cracku2

Question 2

What is the maximum possible number of Red beads that can appear in any configuration?

Solution:

Question Figure

Maximum 9 red beads are possible as shown here

Question 3

What is the minimum number of Blue beads in any configuration?

Solution:

To solve this question we can use the answer of the previous question, since maximum 9 red beads are possible, filling the remaining space with green and blue beads, in such a way that number of blue beads is minimised

Question Figure

Hence number of blue beads is 6

Question 4

Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration?

Solution:

6 more beads can be placed as shown

Question Figure