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# A square with side length 5 has its corner at the center of a square w

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Math Expert
Joined: 02 Sep 2009
Posts: 65785
A square with side length 5 has its corner at the center of a square w  [#permalink]

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16 Jun 2020, 10:11
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Difficulty:

75% (hard)

Question Stats:

62% (02:17) correct 38% (02:41) wrong based on 37 sessions

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A square with side length 5 has its corner at the center of a square with side length 4. The two squares overlap, and the overlapping region has one side equal to 3 as shown in the diagram above. What is the area where the two squares overlap?

A. 3
B. 4
C. 5
D. 6
E. 7

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Joined: 03 Jun 2019
Posts: 3342
Location: India
GMAT 1: 690 Q50 V34
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Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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16 Jun 2020, 10:26
Bunuel wrote:

A square with side length 5 has its corner at the center of a square with side length 4. The two squares overlap, and the overlapping region has one side equal to 3 as shown in the diagram above. What is the area where the two squares overlap?

A. 3
B. 4
C. 5
D. 6
E. 7

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Screenshot 2020-06-16 at 11.54.28 PM.png [ 41.51 KiB | Viewed 455 times ]

Area of shaded region = 1/4* Area of square - x + x = 1/4 * 4*4 = 4

IMO B
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Kinshook Chaturvedi
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Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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16 Jun 2020, 20:40
1
1

In the figure, there's a typo. Correction: CD = 3-1 = 2.

Area of triangle ABC + Area of trapezoid ACDE = 0.5 * 2 * 1 + 0.5 * (2+1) * 2 = 1 + 3 = 4
Ans: 4
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Intern
Joined: 03 Sep 2018
Posts: 8
Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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22 Jun 2020, 20:47
Lipun wrote:

In the figure, there's a typo. Correction: CD = 3-1 = 2.

Area of triangle ABC + Area of trapezoid ACDE = 0.5 * 2 * 1 + 0.5 * (2+1) * 2 = 1 + 3 = 4
Ans: 4

Hi,

Could you please tell how did you deduce DE=1

Posted from my mobile device
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Joined: 05 Jan 2020
Posts: 142
Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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23 Jun 2020, 03:47
2
DrMudassir wrote:
Hi,

Could you please tell how did you deduce DE=1

Posted from my mobile device

Hi DrMudassir,

Since vertex of the larger square is the center of the smaller square, therefore, the sides of the larger square will move equal distance across each corresponding side of the smaller square when rotated about the center.
Side AB has shifted a distance of BC = 1 on the side of the smaller square, so the side AE must also have shifted by a distance of 1 unit towards D.

Hope it helps!

Lipun
Re: A square with side length 5 has its corner at the center of a square w   [#permalink] 23 Jun 2020, 03:47