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A lady grows cabbages in her garden that is in the shape of a square.

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A lady grows cabbages in her garden that is in the shape of a square. [#permalink] New post 11 Jun 2011, 08:22
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A
B
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E

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Question Stats:

20% (05:03) correct 80% (02:34) wrong based on 19 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Jan 2015, 01:54, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: A lady grows cabbages in her garden that is in the shape of a square. [#permalink] New post 11 Jun 2011, 08:36
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
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Re: A lady grows cabbages in her garden that is in the shape of a square. [#permalink] New post 25 Jan 2015, 05:13
How I can answer it quickly under 2 miunte
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Re: A lady grows cabbages in her garden that is in the shape of a square. [#permalink] New post 25 Jan 2015, 07:20
If you understand the question very well, then it can eaasily be solved under two minutes. So I guess, the key here was not to rush through reading the question.
Understand it completely before starting to solve.
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Re: A lady grows cabbages in her garden that is in the shape of a square. [#permalink] New post 25 Jan 2015, 12:49
Expert's post
Hi All,

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.

Final Answer:
[Reveal] Spoiler:
A


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Re: A lady grows cabbages in her garden that is in the shape of a square.   [#permalink] 25 Jan 2015, 12:49
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