Coordinate

Expert replies

Previous Topic Next Topic

N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Thu Dec 16, 2010 12:18 pm

Attachments

Like this post

Source: Beat The GMAT — Problem Solving | Thu Dec 16, 2010 12:18 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Dec 16, 2010 12:58 pm

Hi there,

Any point (x,y) that belongs to the circle given satisfies the equation (x-0)^2 + (y-a)^2 = r^2 where r>0 is the radius, therefore:

b^2 + (c-a)^2 = r^2 = d^2 + (e-a)^2 and simplifying we have:

b^2 + c^2 - 2ac = d^2 +e^2 - 2ea.

That means LS (left side) - RS (right side) = 2a (c-e) .

Therefore SUPPOSING we can "trust" the figure given, we have

(1) a > 0
(2) c < e

and with those in mind, LS - RS < 0 and we are done. (Answer in this scenario: B)

Regards,
Fabio.

P.S.: of course the OA could be [spoiler](D)[/spoiler], if we agree that (d,e) and (b,c) could "change places" and/or a is not necessarily positive... you got the idea... (I would consider this, therefore I would click [spoiler](D)[/spoiler], by the way.)

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Thu Dec 16, 2010 1:58 pm

fskilnik wrote:Hi there,

Any point (x,y) that belongs to the circle given satisfies the equation (x-0)^2 + (y-a)^2 = r^2 where r>0 is the radius, therefore:

b^2 + (c-a)^2 = r^2 = d^2 + (e-a)^2 and simplifying we have:

b^2 + c^2 - 2ac = d^2 +e^2 - 2ea.

That means LS (left side) - RS (right side) = 2a (c-e) .

Therefore SUPPOSING we can "trust" the figure given, we have

(1) a > 0
(2) c < e

and with those in mind, LS - RS < 0 and we are done. (Answer in this scenario: B)

Regards,
Fabio.

P.S.: of course the OA could be [spoiler](D)[/spoiler], if we agree that (d,e) and (b,c) could "change places" and/or a is not necessarily positive... you got the idea... (I would consider this, therefore I would click [spoiler](D)[/spoiler], by the way.)

Thanks Fabio for your reply! I get it right up till "b^2 + c^2 - 2ac = d^2 +e^2 - 2ea.". What I don't get is the LS-RS part = 2a(c-e), how did you get to that?

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Dec 16, 2010 3:48 pm

N:Dure wrote:

To make the situation easier to see, plug in a=1.

Radius = distance from (b,c) to (0,1) = âˆš(b-0)Â² + (c-1)Â²
Radius = distance from (d,e) to (0,1) = âˆš(d-0)Â² + (e-1)Â²

Since all radii are equal:
âˆš(b-0)Â² + (c-1)Â² = âˆš(d-0)Â² + (e-1)Â²
(b-0)Â² + (c-1)Â² = (d-0)Â² + (e-1)Â²
bÂ² + cÂ² -2c + 1 = dÂ² + eÂ² - 2e + 1
bÂ² + cÂ² -2c = dÂ² + eÂ² - 2e

Looking at the equation above, if bÂ² + cÂ² = dÂ² + eÂ², then -2c = -2e and c=e.
But we can tell from the picture that e>c, which means that the value being subtracted from the right side of the equation (2e) is larger than the value being subtracted from the left side of the equation (2c). Thus, in order for the right side to equal the left side, dÂ² + eÂ² > bÂ² + cÂ².

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Thu Dec 16, 2010 5:58 pm

As always, thanks GMATGuru for your help!

to make sure, since e>c, d^2 + e^2 has to be more than b^2+c^2 in order to equalize the 2 equations (the ones= r^2)

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Dec 16, 2010 6:02 pm

N:Dure wrote:As always, thanks GMATGuru for your help!

to make sure, since e>c, d^2 + e^2 has to be more than b^2+c^2 in order to equalize the 2 equations (the ones= r^2)

Correct!

Like this post

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Fri Dec 17, 2010 5:02 am

N:Dure wrote: Thanks Fabio for your reply! I get it right up till "b^2 + c^2 - 2ac = d^2 +e^2 - 2ea.". What I don't get is the LS-RS part = 2a(c-e), how did you get to that?

Hi N:Dure,

Sorry for the delay.

The answer is: (b^2 + c^2) - (d^2 +e^2) = 2ac - 2ea = LS - RS = 2a(c-e) ...

I hope things are clear, now.

Regards,
Fabio.

P.S.: MitchÂ´s solution is a little less general than mine, but exactly the same reasoning. Be sure you realize that, because this will mean you really understood both!

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review