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A circular patch is placed on a square piece of fabric. What

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by BTGmoderatorDC » Wed Oct 16, 2019 6:30 pm
A circular patch is placed on a square piece of fabric. What is the perimeter of the square piece of fabric?

(1) The radius of the patch is 4 centimeters.

(2) Each side of the square piece of fabric is tangent to the patch.


OA C

Source: Princeton Review
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Oct 16, 2019 10:29 pm
BTGmoderatorDC wrote:A circular patch is placed on a square piece of fabric. What is the perimeter of the square piece of fabric?

(1) The radius of the patch is 4 centimeters.

(2) Each side of the square piece of fabric is tangent to the patch.

OA C

Source: Princeton Review
Needless to state that each statement itself is insufficient as with Statement 1, we do not have any information of the square piece of fabric, and with Statement 2, we do not have any information about dimensions of the patch and the square piece of fabric.

Taking Statement 1 and 2 together, we have

Since each side of the square piece of fabric is tangent to the patch, side of the square fabric = diameter of the patch = 2*4 = 8 cm.

Thus, the perimeter of the square piece of fabric = 4*side = 4*8 = 32 cm.

The correct answer: C

Hope this helps!

-Jay
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by swerve » Thu Oct 17, 2019 11:04 am
BTGmoderatorDC wrote:A circular patch is placed on a square piece of fabric. What is the perimeter of the square piece of fabric?

(1) The radius of the patch is 4 centimeters.

(2) Each side of the square piece of fabric is tangent to the patch.


OA C

Source: Princeton Review
Perimeter of the square= 4(length of each side)= \(4a\)

Notice the language: it does not say where the circle is place.. it just says on...

There are three cases

Case 1) the circle could meet the square at exactly at one point i.e the sides of the square becomes a tangent

Case 2) the circle could not touch the square at all. it could be at the center of the square.

case 3) the circle could touch at two points on each side

1) The radius of the patch is 4 centimeters.
If the circle is on the square we could find the perimeter, if not then no.

Not sufficient \(\Large{\color{red}\chi}\)

2) Each side of the square piece of fabric is tangent to the patch.
The measurement of any side is not given

Not sufficient \(\Large{\color{red}\chi}\)

Combining both 1 and 2

Only case 1 is possible \(\Large{\color{green}\checkmark}\)

Therefore, the correct answer is C
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