LR - Board Games - Previous Year CAT/MBA Questions
You can practice all previous year CAT questions from the topic LR - Board Games. This will help you understand the type of questions asked in CAT. It would be best if you clear your concepts before you practice previous year CAT questions.
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:
Solution
Discuss
ReportWhat is the maximum possible number of Red beads that can appear in any configuration?
What is the minimum number of Blue beads in any configuration?
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 maximize the number of Red beads used in the configuration?
Answer the following questions based on the information given below.
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.
What is the total amount of money (in rupees) in the three pouches kept in the first column of the second row?
How many pouches contain exactly one coin?
What is the number of slots for which the average amount (in rupees) of its three pouches is an integer?
The number of slots for which the total amount in its three pouches strictly exceeds Rs. 10 is
Answer the following question based on the information given below.
You are given an n × n square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.
What is the minimum number of different numerals needed to fill a 3×3 square matrix?
What is the minimum number of different numerals needed to fill a 5 × 5 square matrix?
Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?
- A.
9
- B.
16
- C.
25
- D.
4
Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5×5 square matrix?
- A.
25
- B.
16
- C.
9
- D.
4
Answer the following question based on the information given below.
In an 8 × 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
The columns are labelled a to h (left to right) and the rows are numbered 1 to 8 (bottom to top). The position of a piece given by the combination of column and row labels. For example, position c5 means that the piece is cth column and 5th row.
If the queen is at c5, and the other pieces at positions c2, g1, g3, g5 and a3, how many are under attack by the queen? There are no other pieces on the board.
- A.
2
- B.
3
- C.
4
- D.
5
If the other pieces are only at positions a1, a3, b4, d7, h7 and h8, then which of the following positions of the queen results in the maximum number of pieces being under attack?
- A.
f8
- B.
a7
- C.
c1
- D.
d3
If the other pieces are only at positions a1, a3, b4, d7, h7 and h8, then from how many positions the queen cannot attack any of the pieces?
- A.
0
- B.
3
- C.
4
- D.
6
Suppose the queen is the only piece on the board and it is at position d5.
In how many positons can another piece be placed on the board such that it is safe from attack from the queen?
- A.
32
- B.
35
- C.
36
- D.
37
