CAT 2017 Slot 2 DILR Question & Solution

Logical ReasoningMedium

Data Set

In an 8 X 8 chess board a queen placed any where 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 is given by the combination of column and row labels. For example, position c5 means that the piece is in $c^{th}$ column and $5^{th}$ row.

Question 1

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.

2

3

4

5

Solution:

Let us draw the diagram and mark position of various pieces as given in the question.

Question Figure

Attack line is shown by the yellow color. All the pieces on this line will be under attack.

Question Figure

From the diagram we can see that a3, g1, c2 and g5 are under attack. Hence, option C is the correct answer.

Question 2

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?

f8

a7

c1

d3

Solution:

Option (a): When queen is at f8. In this case h8 and b4 will be under attack.

Question Figure

Option (b): When queen is at a7. In this case a3 and d7 will be under attack.

Question Figure

Option (c): When queen is at c1. In this case a1 and a3 will be under attack.

Question Figure

Option (d): When queen is at d3. In this case a3, d7 and h3 will be under attack.

Question Figure

Therefore, we can say that option D is the correct answer.

Question 3

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?

0

3

4

6

Solution:

From the diagram we can see that except positions e2, f2, g2 and g5 queen can attack at least one among the given pieces.

Question Figure

Hence, we can say that there are exactly for position from where queen can’t attack any of the given pieces. Therefore, option C is the correct answer.

Question 4

Suppose the queen is the only piece on the board and it is at position d5. In how many positions can another piece be placed on the board such that it is safe from attack from the queen?

32

35

36

37

Solution:

Question Figure

From the diagram we can see that the number of positions those are safe from queen’s attack = 6 + 5 + 5 + 5 + 5 + 5 + 5 = 36. Therefore, option C is the correct answer.