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1,600 feet of fencing is used to enclose a square plot.

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Joined: 18 Apr 2015
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Kudos [?]: 1033 [0], given: 4655

1,600 feet of fencing is used to enclose a square plot. [#permalink]  19 Oct 2017, 14:49
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Question Stats:

77% (00:47) correct 22% (01:23) wrong based on 27 sessions

1,600 feet of fencing is used to enclose a square plot.

 Quantity A Quantity B The plot's new area if the length were reduced by 4 feet and the width increased by 4 feet The plot's new area if the length were equal to 398 feet and the width were equal to 402 feet

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 330 [0], given: 66

Re: 1,600 feet of fencing is used to enclose a square plot. [#permalink]  20 Oct 2017, 06:45
Since the plot is a square, its side is equal to $$sqrt(1600) = 40$$. Then quantity A is 36*44 = 1584. Quantity B, instead is 402*398 = 159,996.

Intern
Joined: 03 Mar 2018
Posts: 1
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Kudos [?]: 2 [2] , given: 3

Re: 1,600 feet of fencing is used to enclose a square plot. [#permalink]  04 Mar 2018, 06:42
2
KUDOS
As per the question,
1600ft = perimeter of a square plot => length of each side = 1600/4 = 400ft

So,
Quantity A = (len-4)(len+4) = (400-4)(400+4) = 400^2 - 4^2
Quantity B = 398x402 = (400-2)(400+2) = 400^2 - 2^2
=> Quantity B > Quantity A
Hence answer is B.
Re: 1,600 feet of fencing is used to enclose a square plot.   [#permalink] 04 Mar 2018, 06:42
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1,600 feet of fencing is used to enclose a square plot.

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