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CAT 2017 Slot 2 · DILR · Easy · Logical Reasoning

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Passage / data set

In an 8 X 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 is given by the combination of column and row labels. For example, position c5 means that the piece is in cthc^{th} column and 5th5^{th} row.

Question 1 of 4

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.

  1. A.

    2

  2. B.

    3

  3. C.

    4

  4. D.

    5

Answer

C

Explanation

Queen at c5 attacks:

  • Column c: c2
  • Row 5: g5
  • Diagonal: a3 (c5 to a3 along diagonal)
  • Diagonal: g1 (c5-d4-e3-f2-g1) Total pieces under attack = 4.

Question 2 of 4

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?

  1. A.

    f8

  2. B.

    a7

  3. C.

    c1

  4. D.

    d3

Answer

D

Explanation

Testing d3:

  • Row 3: a3
  • Column d: d7
  • Diagonals: a6? No. d3 to a1? No (d3-c2-b1). d3 to h7 (d3-e4-f5-g6-h7) -> Yes.
  • d3 to b4? No. d3 to b1? Checking each option shows d3 attacks maximum number of pieces.

Question 3 of 4

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?

  1. A.

    0

  2. B.

    3

  3. C.

    4

  4. D.

    6

Answer

C

Explanation

Counting positions on the 8x8 board from which no line of sight exists to any of the 6 given pieces yields 4 positions.

Question 4 of 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?

  1. A.

    32

  2. B.

    35

  3. C.

    36

  4. D.

    37

Answer

C

Explanation

Queen at d5 controls:

  • Row 5: 7 squares
  • Column d: 7 squares
  • Diagonal 1 (a2 to g8): 6 squares
  • Diagonal 2 (a8 to h1): 7 squares Total squares under attack including queen's square = 1+7+7+6+7=281 + 7 + 7 + 6 + 7 = 28. Safe squares = 64−28=3664 - 28 = 36.

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