While this question does not state it, we're meant to assume that every square foot of garden space is used to produce cabbage. This question can either be solved with Algebra (as sudhir18n showed) or it can be solved with a bit or Arithmetic and some "brute force."
We're told that the garden is a square; since 1 cabbage takes up 1 square foot of space, it's not hard to figure out how many cabbages can be grown in a square garden (if you know the dimensions of the garden).
For example, if the garden is 100 square feet, then (100)(100) = 10,000 square feet = 10,000 cabbages.
From the prompt, we know that we're dealing with 2 square gardens (one is bigger than the other) and that the difference in cabbages is 211. So, we're looking for an answer that's a perfect square AND that when you subtract 211, you get ANOTHER perfect square. We can use the answer choices to our advantage here - the unit's digit of each answer can be used to help us find the perfect squares faster.
Let's start with Answer A: 11,236
Since this number ends in a 6, IF the square-root is an integer, then it ends in either a 4 or a 6. The math that follows is not that difficult, but it does take some practice to get these skills back.
(104)(104) = 10,816 This is TOO SMALL
(106)(106) = 11,236 This is A MATCH!!!!
Subtracting 211, we have 11,236 - 211 = 11, 025
It's interesting that this number ends in a 5....IF its square-root is an integer, then it ends in a 5....and there's only one number between 104 and 106.....
(105)(105) = 11,025 This is A MATCH!!!
The question asks for the number of cabbages grown THIS YEAR.
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