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TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 3535
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Kudos [?]: 4020  , given: 65

Which of the following must be true of the angles marke [#permalink]
1
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Expert's post 00:00

Question Stats: 82% (00:55) correct 17% (00:52) wrong based on 29 sessions Which of the following must be true of the angles marked in the figure above?

I. a + b = d + e
II. b + e = c + f
III. a + c + e = b + d + f

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 167 , given: 4

Re: Which of the following must be true of the angles marke [#permalink]
Expert's post
GreenlightTestPrep wrote: Which of the following must be true of the angles marked in the figure above?

I. a + b = d + e
II. b + e = c + f
III. a + c + e = b + d + f

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

property - Opposite angles are equal
So, a=d, b=e and c=f.

I. a + b = d + e
Since a=d and b=e, their sum a+b=d+e
Hence true..

II. b + e = c + f
we can write this as b+b=c+c....b=c
But we do not know the relation between b and c..
Hence need not be true

III. a + c + e = b + d + f
Since a=d, b=e and c=f, both sides are equal.

I and III are true..

C
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 134

Kudos [?]: 4020 , given: 65

Re: Which of the following must be true of the angles marke [#permalink]
Expert's post
GreenlightTestPrep wrote: Which of the following must be true of the angles marked in the figure above?

I. a + b = d + e
II. b + e = c + f
III. a + c + e = b + d + f

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Since opposite angles are equal, let's first denote pairs of equal angles with the same symbols. Now, we'll check the statements...

I. a + b = d + e
We can rewrite this as: (red dot) + (blue star) = (blue star) + (red dot)
Definitely TRUE (always!)
Since statement I is true, we can ELIMINATE answer choice D

II. b + e = c + f
We can rewrite this as: (blue star) + (blue star) = (green square) + (green square)
This need not be true
Since statement II is false, we can ELIMINATE answer choices B and E

III. a + c + e = b + d + f
We can rewrite this as: (red dot) + (green square) + (blue star) = (blue star) + (red dot) + (green square)
Definitely TRUE (always!)
Since statement III is true, we can ELIMINATE answer choice A

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Brent Hanneson – Creator of greenlighttestprep.com  Re: Which of the following must be true of the angles marke   [#permalink] 02 Jan 2019, 06:26
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