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Manager  Joined: 31 Oct 2011
Posts: 224
If points A and B are 5 units apart, which of the following  [#permalink]

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9 00:00

Difficulty:   65% (hard)

Question Stats: 51% (01:35) correct 49% (01:19) wrong based on 313 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 53831
Re: If points A and B are 5 units apart, which of the following  [#permalink]

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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).

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Intern  Joined: 27 Mar 2012
Posts: 6
Re: If points A and B are 5 units apart, which of the following  [#permalink]

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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
Manager  B
Joined: 06 Aug 2013
Posts: 70
Re: If points A and B are 5 units apart, which of the following  [#permalink]

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bunuel,
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).

because, the diagonal AB = 5, you have assumed the other two sides to be 3 and 4 for the rectangle. this is what i am wanting to clarify.
Math Expert V
Joined: 02 Sep 2009
Posts: 53831
Re: If points A and B are 5 units apart, which of the following  [#permalink]

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1
arnabs wrote:
bunuel,
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).

because, the diagonal AB = 5, you have assumed the other two sides to be 3 and 4 for the rectangle. this is what i am wanting to clarify.

The question asks which of the following can have only one possible value?

III suggests that it's the area of a rectangular region with diagonal AB:

AB could be the diagonal of a square as well as it could be the diagonal of a rectangle with the sides equal to 3 and 4 (of course there are many other cases possible). Those two cases give different areas for a rectangle with diagonal of 5. Therefore, the area of a rectangular region with diagonal of 5 can have more than one value.

Hope it's clear.
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Manager  B
Joined: 06 Aug 2013
Posts: 70
Re: If points A and B are 5 units apart, which of the following  [#permalink]

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Bunuel wrote:
arnabs wrote:
bunuel,
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).

because, the diagonal AB = 5, you have assumed the other two sides to be 3 and 4 for the rectangle. this is what i am wanting to clarify.

The question asks which of the following can have only one possible value?

III suggests that it's the area of a rectangular region with diagonal AB:

AB could be the diagonal of a square as well as it could be the diagonal of a rectangle with the sides equal to 3 and 4 (of course there are many other cases possible). Those two cases give different areas for a rectangle with diagonal of 5. Therefore, the area of a rectangular region with diagonal of 5 can have more than one value.

Hope it's clear.

yeah, exactly... that is what i wanted to confirm. your approach was one of the approaches of solving, just making sure that i am approaching problems like these in the right fashion. 6 days for the D-day, hence, a little freaked out. thanks for the confirmation bunuel, kudos to you. Board of Directors P
Joined: 17 Jul 2014
Posts: 2561
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: If points A and B are 5 units apart, which of the following  [#permalink]

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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. always true. so B, C are out immediately.
2. we can have multiple options...AB might be a chord, or AB might be the diameter. D is out.
we are left with A and E...pretty good odds, hah? 3. diagonal is AB -> since it's a rectangular region, we might have the rectangular formed by 2 triangles 3-4-5. since we are not 100% sure of that, we can't have a definite answer. E is out.

A is the answer.
Non-Human User Joined: 09 Sep 2013
Posts: 10204
Re: If points A and B are 5 units apart, which of the following  [#permalink]

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_________________ Re: If points A and B are 5 units apart, which of the following   [#permalink] 18 Dec 2017, 12:21
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# If points A and B are 5 units apart, which of the following

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