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CAT 2020 Slot 2 — DILR Question 5

Mixed PracticeEasy
Passage / Data

Answer the next 4 questions based on the information given below.

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:

  • Two adjacent beads along the same row or column are always of different colors.
  • There is at least one Green bead between any two Blue beads along the same row or column.
  • 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.

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

Answer & solution

Correct answer: 2

Answer: 2

Solution

We can use beads of only two colors.

Since there must be a blue and a green bead between two red beads, we cannot choose one the two colors as red.

Hence, the two colors that can be used are green and blue.

Also, two adjacent beads along the same row or column are always of different colors. Hence, blue and green beads can only be placed alternately.

∴ The following 2 configurations are possible.

Configuration 1:

Configuration 2:

​​​​​​​

Hence, 2.

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CAT 2020 Slot 2 DILR Q5: The total number of possible configurations using beads of only two colors is: — Solution | TheCATExam