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# A lady grows cabbages in her garden that is in the shape of

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A lady grows cabbages in her garden that is in the shape of [#permalink]  03 Nov 2008, 05:38
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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: PS : Cabbage [#permalink]  03 Nov 2008, 08:34
amitdgr 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. It cannot be as obvious as it is E.

I had to take the help of excel sheet to make the calculation. The clue is here: A lady grows cabbages in her garden that is in the shape of a square
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Re: PS : Cabbage [#permalink]  03 Nov 2008, 08:54
Can you explain this in detail?
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Re: PS : Cabbage [#permalink]  03 Nov 2008, 09:13
well, I'm going with A too, but just because of the hint....
because sqrt 11236 and sqrt (11236-211) is an integer
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Re: PS : Cabbage [#permalink]  03 Nov 2008, 09:20
linau1982 wrote:
well, I'm going with A too, but just because of the hint....
because sqrt 11236 and sqrt (11236-211) is an integer

how did you know that it is an integer ???
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Re: PS : Cabbage [#permalink]  03 Nov 2008, 10:39
What is the source? Question is good, but it requires lots of calculation.

If, x is the side of original square and x+a is the side of new square, then
(x+a)^2 - x^2 = 211
or, a^2 + 2ax = 211
And, x should be an intger.

Looking at the answer choices, C seems to be an obvious answer. In the exam, I would have chosen C.
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Re: PS : Cabbage [#permalink]  03 Nov 2008, 10:53
I googled and found the source

http://questionbank.4gmat.com/mba_prep_sample_questions/mensuration/mensuration_121103.shtml

The correct choice is (A) and the correct answer is 11236.

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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Re: PS : Cabbage [#permalink]  04 Nov 2008, 01:13
Excellent OE. But 211 is a prime number is also tough to determine.
Re: PS : Cabbage   [#permalink] 04 Nov 2008, 01:13
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