What is the ordinate (y-coordinate) of point C?

This topic has expert replies
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

GMATH practice exercise (Quant Class 20)

Image

Answer: [spoiler]_____(C)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Mon Mar 11, 2019 1:27 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 20)

Image
[/size]
$$? = {y_C}$$

Image

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,OD = 2\sqrt 2 \hfill \cr
\Delta AOB\,\,{\rm{isosceles}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,\Delta ODB\,\,{\rm{isosceles}} \hfill \cr
\,BD = OD\,\,,\,\,OB = 4 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,\Delta BEF\,\,{\rm{isosceles}} \hfill \cr
\,FG = GB = 4 - 3 \hfill \cr} \right.$$
$$\,\, \Rightarrow \,\,\,{\rm{line}}\,\,EC\,\,\,\left\{ \matrix{
\,{\rm{slope}} = 1\,\,\,\left( {{{45}^ \circ }} \right) \hfill \cr
\,F = \left( {2,0} \right) \in \,\,{\rm{line}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{line}}\,\,EC\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,C\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

Image


The correct answer is (C).

We follow the notations and rationale taught in the GMATH method.

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