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Cabbages [#permalink] New post 11 Jun 2011, 09:22
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A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?

A. 11236
B. 11025
C. 14400
D. 12696
E. Cannot be determined
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Re: Cabbages [#permalink] New post 11 Jun 2011, 09:36
shashankp27 wrote:
A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?

A. 11236
B. 11025
C. 14400
D. 12696
E. Cannot be determined


Its A

Let the side for growing cabbages this year be X ft. thus area = X^2

Le the side for growing cabbages last year be Y ft.
Therefore, the area = Y^2

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.

X^2 - Y^2 = 211
(X + Y)(X - Y) = 211.
211 is a prime number and thus it will be (106 + 105)*(106-105).

(X + Y)(X - Y) = (106 + 105)(106 - 105).
thus X = 106 and Y = 105.

X^2 = 106^2 = 11236
Re: Cabbages   [#permalink] 11 Jun 2011, 09:36
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