I googled and found the source

http://questionbank.4gmat.com/mba_prep_sample_questions/mensuration/mensuration_121103.shtmlThe correct choice is (A) and the correct answer is 11236.

Explanatory Answer

The shape of the area used for growing cabbages has remained a square in both the years.

Let the side of the square area used for growing cabbages this year be X ft.

Therefore, the area of the ground this year = X² sq.ft.

And let the side of the square area used for growing cabbages last year be Y ft.

Therefore, the area of the ground used last year = Y² sq.ft.

As the number of cabbages grown has increased by 211, the area would have increased by 211 sq ft as each cabbage takes 1 sq ft space.

Hence X² - Y² = 211 => (X + Y)(X – Y) = 211.

211 is a prime number and hence it will have only two factors. i.e., 211 = 211*1.

This can be represented as (106 + 105)*(106-105).

(X + Y)(X – Y) = (106 + 105)(106 – 105).

From this we can deduce that X = 106 and Y = 105.

Therefore, number of cabbages produced this year = X² = 106² = 11236.

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EDIT :

gmatclub user: asdert ... suggested this method (i remembered that this had been discussed on gmatclub before)

x^2 - 211 = (x-1)^2

x^2 - 211 = x^2-2x+1

2x = 212

x = 106

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