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If points A and B are 5 units apart, which of the following
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31 Mar 2012, 02:29
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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
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Re: If points A and B are 5 units apart, which of the following
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31 Mar 2012, 02:42
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
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31 Mar 2012, 02:46
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
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04 Dec 2014, 06:47
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.



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Re: If points A and B are 5 units apart, which of the following
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04 Dec 2014, 06:52
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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Re: If points A and B are 5 units apart, which of the following
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04 Dec 2014, 06:57
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 Dday, hence, a little freaked out. thanks for the confirmation bunuel, kudos to you.



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Re: If points A and B are 5 units apart, which of the following
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02 Nov 2016, 06:51
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 345. since we are not 100% sure of that, we can't have a definite answer. E is out. A is the answer.



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