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# DS PROBLEM!

Author Message
Intern
Joined: 31 Oct 2019
Posts: 1

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Updated on: 28 Nov 2019, 12:10
00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:35) correct 22% (02:13) wrong based on 9 sessions

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If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
2) P = (A)(^1/2) * 4

Originally posted by 240799 on 28 Nov 2019, 08:45.
Last edited by 240799 on 28 Nov 2019, 12:10, edited 1 time in total.
SVP
Joined: 03 Jun 2019
Posts: 1880
Location: India

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28 Nov 2019, 09:16
240799 wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
2) P = (A)(^12) * 4

For a square
Area A = x^2
Perimeter P = 4x
where x is the side of a square

Asked: If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
4x = (4/3)x^2
x = 3
But P = (4/3)A may be satisfied for other rectangles too.
NOT SUFFICIENT

2) P = (A)(^12) * 4
4x = x^24*4
x = 1 or x = 0
But P = (A)(^12) * 4 may be satisfied for other rectangles too.
NOT SUFFICIENT

(1) + (2)
1) P = (4/3)A
4x = (4/3)x^2
x = 3
2) P = (A)(^12) * 4
4x = x^24*4
x = 1 or x = 0
Since these 2 equations can not be satisfied by a square, the region is NOT square.
SUFFICIENT

IMO C
SVP
Joined: 03 Jun 2019
Posts: 1880
Location: India

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Updated on: 28 Nov 2019, 09:36
240799 wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
2) P = (A)(^12) * 4

For a square
Area A = x^2
Perimeter P = 4x
where x is the side of a square

For a rectangle
Area A = ab
Perimeter P = 2 (a+b)

Asked: If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
2(a+b) =(4/3)ab
If a=b=3; 2(3+3) = (4/3)3*3 = 12; is a square
BUT IF a=6;b=2; 2(6+2) = (4/3)6*2 = 16 but is NOT a square
NOT SUFFICIENT

2) P = (A)(^12) * 4
$$2(a+b) = a^{12}*b^{12}*4$$
$$a+b = 2a^{12}*b^{12}$$
Only a=b=1 satisfy the condition since a=b=0 do not form a rectangle
SUFFICIENT

IMO B

Originally posted by Kinshook on 28 Nov 2019, 09:27.
Last edited by Kinshook on 28 Nov 2019, 09:36, edited 1 time in total.
SVP
Joined: 03 Jun 2019
Posts: 1880
Location: India

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28 Nov 2019, 09:33
240799 wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
2) P = (A)(^12) * 4

For a square
Area A = x^2
Perimeter P = 4x
where x is the side of a square

For a rectangle
Area A = ab
Perimeter P = 2 (a+b)

Asked: If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
2(a+b) =(4/3)ab
If a=b=3; 2(3+3) = (4/3)3*3 = 12; satisfy the conditions and is a square
But if a =6; 12+2b = 8b; b=2 also satisfy the conditions but is NOT a square
NOT SUFFICIENT

2) P = (A)(^12) * 4
$$2(a+b) = a^{12}*b^{12}*4$$
$$a+b = 2a^{12}*b^{12}$$
Only a=b=1 satisfy the condition since a=b=0 do not form a rectangle
SUFFICIENT

IMO B
Math Expert
Joined: 02 Sep 2009
Posts: 59622

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28 Nov 2019, 22:49
240799 wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

1) P = (4/3)A
2) P = (A)(^1/2) * 4

Discussed here: https://gmatclub.com/forum/if-a-rectang ... 60255.html

TOPIC IS LOCKED AND ARCHIVED.
_________________
Re: DS PROBLEM!   [#permalink] 28 Nov 2019, 22:49
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