If ABCD is a rectangle, what is the value of y+z

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

by fskilnik@GMATH » Wed Feb 13, 2019 5:01 pm

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GMATH practice exercise (Quant Class 15)

If ABCD is a rectangle, what is the value of y+z ?

(1) x = 40
(2) M is the midpoint of line segment BC, and N is the midpoint of line segment CD

Answer: [spoiler]____(A)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Source: Beat The GMAT — Data Sufficiency | Wed Feb 13, 2019 5:01 pm

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

If ABCD is a rectangle, what is the value of y+z ?

by fskilnik@GMATH » Thu Feb 14, 2019 4:42 am

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 15)

If ABCD is a rectangle, what is the value of y+z ?

(1) x = 40
(2) M is the midpoint of line segment BC, and N is the midpoint of line segment CD

Obs.: all angles are measured in degrees.

$$\left( {{\rm{Vertex}}\,A\,,\,\,{\rm{see}}\,\,{\rm{first}}\,\,{\rm{figure}}} \right)\,\,\,\,\,\left( {90 - y} \right) + x + \left( {90 - z} \right) = 90\,\,\,\,\, \Rightarrow \,\,\,\,\,\,y + z = x + 90\,\,\,\,\,\left( * \right)$$

$$? = y + z\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\boxed{\,? = x\,}$$

$$\left( 1 \right)\,\,\,x = 40\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{SUFF}}.$$

$$\left( 2 \right)\,\,{\rm{INSUFF}}.\,\,\,:\,\,\,{\rm{geometric}}\,\,{\rm{bifurcation}}\,\,\left( {{\rm{see}}\,\,{\rm{images}}} \right)$$

The correct answer is (A).

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

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