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Question

1024 plants are planted in a grid such that the number of rows is equal to the number of columns. One row and one column of plants are then sold to a customer. Find the number of plants that were sold.

A
61
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B
65
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C
63
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D
67
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Solution

The correct option is C 63
Number of trees =1024
Since the number of rows is equal to the number of columns, it implies that the number of plants is a perfect square.
Therefore, number of rows (or number of columns) = square root of 1024 (number of plants)
=1024
=2×2×2×2×2×2×2×2×2×2
=2×2×2×2×2
=32
Therefore, initial number of rows (or columns) =32
After 1 row and 1 column of plants are sold,
Number of rows (or columns) =321=31
Number of plants remaining =312
Therefore, the number of plants sold =322312
=1024961
=63

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