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In the figure above, a circle is inscribed in square WXYZ. What is the

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In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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New post 06 Jun 2017, 10:27
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A
B
C
D
E

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71% (00:49) correct 29% (01:09) wrong based on 77 sessions

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In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:
InscribedWXYZ.png
InscribedWXYZ.png [ 5.38 KiB | Viewed 1812 times ]

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Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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New post 06 Jun 2017, 16:36
The answer should be D.

We just need to figure out the diameter of the circle, as that will be the same length as the side of the square. Once we have these numbers, we can solve for the areas.

Statement one tells us that the diagonal is 4 inches. We can solve for the side length (and therefore the diameter of the circle) by knowing that the diagonal = side length * sqrt(2). Sufficient.

Statement two allows us to solve for radius, which we then double to get the diameter. Since diameter = side length, we can also solve with this info.

Both statements ALONE are sufficient. D
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Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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New post 06 Sep 2017, 18:50
Bunuel wrote:
[img]https://gmatclub.com/forum/download/file.php?id=35666[img]
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:
InscribedWXYZ.png


You can calculate the area of a square by squaring the diagonal of the square and dividing it by 2.

St 1

This just illustrates the diagonal of wxyz

suff

St 2

From this we can derive the length of the diagonal of wxyz

suff

D
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Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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New post 02 Nov 2018, 01:26
1
Bunuel wrote:
[img]https://gmatclub.com/forum/download/file.php?id=35666[img]
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:
InscribedWXYZ.png


Dear Moderator,
Please can you check this question, the image for the same is not visible .Thank you.
_________________

- Stne

Math Expert
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Joined: 02 Sep 2009
Posts: 50711
Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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New post 02 Nov 2018, 01:31
stne wrote:
Bunuel wrote:
[img]https://gmatclub.com/forum/download/file.php?id=35666[img]
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:
InscribedWXYZ.png


Dear Moderator,
Please can you check this question, the image for the same is not visible .Thank you.


__________________
Fixed that. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: In the figure above, a circle is inscribed in square WXYZ. What is the &nbs [#permalink] 02 Nov 2018, 01:31
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