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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] New post 13 Jan 2019, 11:10
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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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Re: In the above figure, which one of the following COULD [#permalink] New post 13 Jan 2019, 19:02
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GreenlightTestPrep wrote:
Image

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

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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Re: In the above figure, which one of the following COULD [#permalink] New post 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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In the above figure, which one of the following COULD

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