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# The rectangle above contains two circles, tangent to each other and ea

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
The rectangle above contains two circles, tangent to each other and ea  [#permalink]

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28 Nov 2017, 20:03
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Question Stats:

92% (01:09) correct 8% (00:00) wrong based on 19 sessions

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The rectangle above contains two circles, tangent to each other and each tangent to three sides of the rectangle. Which of the following pairs of numbers CANNOT be the length and width, respectively, of the rectangle?

(A) 2, 1
(B) 12, 6
(C) 16, 10
(D) 22, 11
(E) 32, 16

Attachment:

2017-11-28_1024_003.png [ 4.61 KiB | Viewed 708 times ]

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Re: The rectangle above contains two circles, tangent to each other and ea  [#permalink]

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29 Nov 2017, 01:17
Bunuel wrote:

The rectangle above contains two circles, tangent to each other and each tangent to three sides of the rectangle. Which of the following pairs of numbers CANNOT be the length and width, respectively, of the rectangle?

(A) 2, 1
(B) 12, 6
(C) 16, 10
(D) 22, 11
(E) 32, 16

Attachment:
2017-11-28_1024_003.png

Length = $$4*radius$$ or $$4x$$.
Width = diameter = $$2*radius$$ or $$2x$$.

Ratio length to widht = $$\frac{4x}{2x}$$ = $$\frac{4}{2}$$ = $$\frac{2}{1}$$.

All the answers are in ration 2:1 except C.

Wdyt?
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Re: The rectangle above contains two circles, tangent to each other and ea  [#permalink]

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29 Nov 2017, 07:59
Bunuel wrote:

The rectangle above contains two circles, tangent to each other and each tangent to three sides of the rectangle. Which of the following pairs of numbers CANNOT be the length and width, respectively, of the rectangle?

(A) 2, 1
(B) 12, 6
(C) 16, 10
(D) 22, 11
(E) 32, 16

Attachment:
2017-11-28_1024_003.png

From the figure.. length is twice of Width. So, Option C
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Re: The rectangle above contains two circles, tangent to each other and ea  [#permalink]

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01 Dec 2017, 06:51
Bunuel wrote:

The rectangle above contains two circles, tangent to each other and each tangent to three sides of the rectangle. Which of the following pairs of numbers CANNOT be the length and width, respectively, of the rectangle?

(A) 2, 1
(B) 12, 6
(C) 16, 10
(D) 22, 11
(E) 32, 16

Attachment:
2017-11-28_1024_003.png

We can see that the length of the rectangle is equal to twice the length of the circle’s diameter, whereas the width of the rectangle is equal to the length of the diameter. In other words, the length of the rectangle is twice its width. The only pair of numbers in which one is not twice the other are 16 and 10, so they cannot be the length and width of the rectangle.

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Re: The rectangle above contains two circles, tangent to each other and ea   [#permalink] 01 Dec 2017, 06:51
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