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GRE Math Challenge #96- Internal and external angles

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GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
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GRE Math Challenge #96- Internal and external angles [#permalink] New post 09 May 2015, 11:14
Expert's post
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Question Stats:

66% (02:11) correct 33% (01:39) wrong based on 12 sessions
Image

Quantity A
Quantity B
d
e


• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined



[Reveal] Spoiler:
Attachment:
Quant4.jpg
Quant4.jpg [ 17.64 KiB | Viewed 1814 times ]
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #96- Internal and external angles [#permalink] New post 16 Jan 2018, 23:50
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answer is B?
since a>h ; g>b
d= z+b
e= z+g

e is greater than d
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Re: GRE Math Challenge #96- Internal and external angles [#permalink] New post 26 Jan 2018, 10:54
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b+z+c=180 g+z+f=180
b=a and c=d so g=h and f=e so
a+z+d=180 h+z+e=180

We know that a>h and we have z in both equations. ‘e’ must be greater than ‘d’ to be able to complete the equation
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Re: GRE Math Challenge #96- Internal and external angles [#permalink] New post 19 Jan 2019, 18:40
Attachment:
Image.jpg
Image.jpg [ 23.96 KiB | Viewed 109 times ]


Check the image,
a and b opposite angle, a=b
c and d opposite angle, c=d

now

z+a = 180 -d
d = 180-z-a .................i

In the same way,
e and f opposite angle, e = f
g and h opposite angle, g = h

now,

z+e = 180-h
h = 180-z-e.....................ii

Now from i and ii

Quantity A: d = 180-a-z
QuantityB: h = 180-z-h

Adding -180 both side
Quantity A: -a-z
QuantityB: -h-z

adding +z both side
Quantity A: -a
QuantityB: -h

adding +a both side
Quantity A: -a+a
QuantityB: -h+a

Quantity A: 0
Quantity B: -h+a

adding +h to both side
Quantity A: 0+h
Quantity B: -h+a+h

Quantity A: h
Quantity B: a

given a>h

Hence
Quantity A < Quantity B
Ans B
Re: GRE Math Challenge #96- Internal and external angles   [#permalink] 19 Jan 2019, 18:40
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GRE Math Challenge #96- Internal and external angles

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