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If points A and B are 5 units apart, which of the following

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If points A and B are 5 units apart, which of the following [#permalink] New post 31 Mar 2012, 01:29
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If points A and B are 5 units apart, which of the following can have only one possible value?

I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
[Reveal] Spoiler: OA
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Re: If points A and B are 5 units apart, which of the following [#permalink] New post 31 Mar 2012, 01:42
Expert's post
eybrj2 wrote:
If points A and B are 5 units apart, which of the following can have only one possible value?

I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB

A. I only
B. II only
C. III only
D. I and II only
E. I and III only


I. The area of a square region with side AB --> side=AB=5 --> the area of a square is 5^2=25, so only one possible value;

II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;

III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).

Answer: A.
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Re: If points A and B are 5 units apart, which of the following [#permalink] New post 31 Mar 2012, 01:46
eybrj2 wrote:
If points A and B are 5 units apart, which of the following can have only one possible value?

I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB

A. I only
B. II only
C. III only
D. I and II only
E. I and III only




1: Area od square = (Side)^2=(AB)^2=25 ( fixed )
2: radius of circle can be anything as center of circle is pivot.==> radius is not fix ==> 2*pi*r is not fix.
3. As AB as diagonal is fix ==> point A and B are fix ==> Other point C and D of rectangle are not fix ==> Sides are not fix ==> Area is not fix.

Thus Answer = A
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Re: If points A and B are 5 units apart, which of the following [#permalink] New post 28 Jul 2014, 05:59
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Re: If points A and B are 5 units apart, which of the following   [#permalink] 28 Jul 2014, 05:59
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