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# In the above figure, which one of the following COULD

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In the above figure, which one of the following COULD [#permalink]  13 Jan 2019, 11:10
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52% (02:10) correct 47% (02:46) wrong based on 21 sessions

In the above figure, which one of the following COULD be the value of b ?

(A) 20
(B) 30
(C) 60
(D) 75
(E) 90
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com

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Joined: 01 Nov 2017
Posts: 370
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Re: In the above figure, which one of the following COULD [#permalink]  13 Jan 2019, 19:02
Expert's post
GreenlightTestPrep wrote:

In the above figure, which one of the following COULD be the value of b ?

(A) 20
(B) 30
(C) 60
(D) 75
(E) 90

The sum of all angles must be 369°, so add all of them..
$$a+b-\frac{a}{2}+\frac{a}{2}+2b+2a-2b+2a-b=360....5a=360...a=72$$..
Now a is 60 and all angles given should be non-negative..

1) $$b-\frac{a}{2}\geq{0}...b\geq{36}$$
2)$$2a-2b\geq{0}.....b\leq{a}.....b \leq{72}$$

So $$36\leq{b}\leq{72}$$

Only, 60 fits in the range..

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
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5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

GRE Instructor
Joined: 10 Apr 2015
Posts: 2386
Followers: 77

Kudos [?]: 2352 [2] , given: 33

Re: In the above figure, which one of the following COULD [#permalink]  14 Jan 2019, 06:37
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GreenlightTestPrep wrote:

In the above figure, which one of the following COULD be the value of b ?

(A) 20
(B) 30
(C) 60
(D) 75
(E) 90

We know that all 5 angles in the circle must add to 360 degrees.
So, we can write: (a) + (b - a/2) + (a/2 + 2b) + (2a - 2b) + (2a - b) = 360
Simplify left side: 5a = 360
Solve: a = 72

So, we know the value of a BUT we don't know the value of b.
However, one thing we do know is that each angle must be greater than 0 degrees

So, for example, angle b cannot equal 20°, because we're told that one of the five angles is (b - a/2)
Since a = 72, this angle simplifies to be (b - 36)°
So, if b = 20, then that particular angle = (20 - 36)° = -16°, which is impossible. ELIMINATE A
Also, if b = 30, then that same angle = (30 - 36)° = -6°, which is impossible. ELIMINATE B

We also know that one of the angles = (2a - 2b)°
Since a = 72, this angle simplifies to be (144 - 2b)°
If b = 75, then this particular angle =(144 - 150)° = -6°, which is impossible. ELIMINATE D
Also, if b = 90, then this particular angle =(144 - 180)° = -36°, which is impossible. ELIMINATE E

By the process of elimination, the correct answer is C

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: In the above figure, which one of the following COULD [#permalink]  06 Sep 2019, 11:24
If I plug in a=72 for each of the expressions and set them >= 0, I get:
b>=36
b>=-18
b<=72
b<=144

So, I have a lowest possible value of -18 and a highest possible value of 144.
I assume that range is incorrect.

How am I to know that range is incorrect? How am I to know that of those numbers that I should only use 36 and 72 to calculate a range?

Or can I only use the check and eliminate method?
Re: In the above figure, which one of the following COULD   [#permalink] 06 Sep 2019, 11:24
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