Question

1,024 trees are planted in a farm such that the number of rows is equal to the number of columns. If one row and one column of trees are removed, then find the number of trees that were removed.

• 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, the trees form 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 removing 1 row and one column, number of rows/columns = 32-1 = 31.
Remaining trees = ${31}^2$.
Therefore, number of trees removed = ${32}^2-{31}^2$ = (32+31) (32-31) = 63 $\times$ 1 = 63.