Question

1,024 trees are planted in a grid fashion such that the number of rows is equal to the number of columns. One row and one column of trees are cut such that the number of rows and columns after cutting remain equal. Find the number of trees that were cut?

• A. 61
• B. 63
• C. 65
• D. 67

Answer 1

The correct option is B

63

Number of trees = 1024. Since number of rows = number of columns, this means that the number of trees is a perfect square. Therefore number of rows/columns = square root of 1024 (number of trees).
$\sqrt{1024}$= $\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}=32$
Therefore, the initial number of rows/columns = 32. After cutting 1 row and one column, number of rows/columns = 32-1 = 31.
The remaining number of trees = ${31}^2$.
Therefore, number of trees that were cut = ${32}^2-{31}^2$ = (32+31) (32-31) = 63 $\times$ 1 = 63.