XAT 2023 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 14 : A painter draws 64 equal squares of 1 square inch on a square canvas measuring 64 square inches. She chooses two squares (1 square inch each) randomly and then paints them. What is the probability that two painted squares have a common side?

Video Explanation

Explanatory Answer

Since there are 64 squares on 1 cm² each on a canvas of 64 cm² area, The squares should form a lattice just the Chessboard.
The two adjacent squares can be adjacent in the same row or the same column.
In the same row, there can be 7 sets of adjacent pairs of squares.
Since there are 8 rows, It can be done in \( 8 \times 7 \) ways.
Similarly, there will be \( 8 \times 7 \) ways of painting vertically adjacent squares.
So, totally there will be \( 2 \times 8 \times 7 = 112 \) ways of adjacent pairs of squares.
From the 64 squares, 2 squares can be selected in \( { } ^ { 64 } C _ { 2 } = \frac { 64 \times 63 } { 2 \times 1 } = 2016 \) ways
The probability of finding two adjacent squares = \( \frac { 112 } { 2016 } \)

The answer is '\(\frac{112}{2016}\)'

Choice A is the correct answer.

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