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# In the figure above, square PQRS is divided into four smaller squares.

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Math Expert
Joined: 02 Sep 2009
Posts: 46128
In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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19 Sep 2017, 23:29
00:00

Difficulty:

25% (medium)

Question Stats:

91% (00:48) correct 9% (01:03) wrong based on 45 sessions

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In the figure above, square PQRS is divided into four smaller squares. If the area of the shaded region is 3, what is the area of PQRS?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 1

Attachment:

2017-09-20_1018.png [ 5.24 KiB | Viewed 962 times ]

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Re: In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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19 Sep 2017, 23:33
4 smaller Equal squares?

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Posts: 46128
Re: In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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19 Sep 2017, 23:35
whuannou wrote:
4 smaller Equal squares?

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If a square is divided into 4 smaller squares as shown above, could these four squares not be equal?
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In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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Updated on: 20 Sep 2017, 00:21
If yes I would say answer A

Originally posted by Octobre on 19 Sep 2017, 23:35.
Last edited by Octobre on 20 Sep 2017, 00:21, edited 1 time in total.
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In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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Updated on: 20 Sep 2017, 00:22
Bunuel wrote:
whuannou wrote:
4 smaller Equal squares?

If a square is divided into 4 smaller squares as shown above, could these four squares not be equal?

True they have to

Originally posted by Octobre on 19 Sep 2017, 23:39.
Last edited by Octobre on 20 Sep 2017, 00:22, edited 1 time in total.
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Joined: 02 Jul 2017
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GMAT 1: 730 Q50 V38
In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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19 Sep 2017, 23:48
In the figure, square PQRS is divided into four smaller squares.
=> Considering all the 4 smaller squares are equal in size.

If the area of the shaded region is 3, what is the area of PQRS?

= > In figure, 2 sides of shaded region : PR is diagonal and other end is center of 2 sides. If we check shaded region consist of 3 triangles. And Square can be divided into kind of 8 triangles out of which shaded region is 3 triangles.

So if area of square is 8x than of shaded region is 3x.

Given Area of shaded reason is 3 => Area of square = 8

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Re: In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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20 Sep 2017, 11:42
Bunuel wrote:

In the figure above, square PQRS is divided into four smaller squares. If the area of the shaded region is 3, what is the area of PQRS?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 1

Attachment:
2017-09-20_1018.png

Area of the shaded region is 3
The shaded region consists of 3 triangles
Hence area of each triangle is 1, since all triangles are similar.
Now, considering the entire square, it consists of 8 such triangles,
hence area of square PQRS = 8

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In the figure above, square PQRS is divided into four smaller squares. [#permalink]

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23 Sep 2017, 13:12
Bunuel wrote:

In the figure above, square PQRS is divided into four smaller squares. If the area of the shaded region is 3, what is the area of PQRS?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 1

Attachment:
2017-09-20_1018.png

A simple ratio can be used.

Divide the fourth small square (with vertex S) in half like the other small squares.

The large square has 8 triangles. Three of the 8 triangles are shaded.

So $$\frac{3}{8}$$ of PQRS is shaded, or

The shaded region = $$\frac{3}{8}A$$ of PQRS

The shaded region also = area of 3

Set them equal

$$\frac{3}{8}A$$ = 3

$$A = 8$$

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In the figure above, square PQRS is divided into four smaller squares.   [#permalink] 23 Sep 2017, 13:12
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