Correct Option (B)
For the number of rows and columns to be equal, the total number of plants must form a perfect square. This implies that if there are 'n' rows and 'n' columns, the total number of plants will be n × n = n². The gardener currently possesses 1000 plants.
To determine the minimum number of additional plants required, one must identify the smallest perfect square greater than 1000. The relevant perfect squares around 1000 are:
- 31² = 961
- 32² = 1024
The next perfect square immediately succeeding 1000 is 1024. Therefore, to arrange the plants in 32 rows and 32 columns, a total of 1024 plants are needed. The minimum number of additional plants required is the difference between 1024 and 1000, which calculates to 24.
Incorrect Options:
The fundamental requirement for the problem is that the total number of plants must constitute a perfect square. Let's evaluate why the other options are not correct:
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Option (A) 14: Adding 14 plants to the existing 1000 results in a total of 1014 plants. This number is not a perfect square (as 31² = 961 and 32² = 1024). Consequently, the condition of equal rows and columns cannot be satisfied.
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Option (C) 32: If 32 plants are added to 1000, the total becomes 1032. This value is not a perfect square. While 32 is the integer whose square (1024) meets the condition, it is not the quantity of additional plants needed.
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Option (D) 34: Adding 34 plants to 1000 yields a total of 1034 plants. This number is not a perfect square. Therefore, an arrangement with an equal number of rows and columns is not achievable with this increment.