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# which one of the following could be the value of b

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Joined: 22 Oct 2016
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which one of the following could be the value of b [#permalink]  11 Dec 2016, 06:03
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Question Stats:

100% (00:48) correct 0% (00:00) wrong based on 3 sessions
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File comment: this is the diagram the question refers.

geometry.png [ 10.53 KiB | Viewed 939 times ]

From the figure, which one of the following could be the value of b ?
(A) 20
(B) 30
(C) 60
(D) 75
(E) 90

thank you
siva
[Reveal] Spoiler: OA

Last edited by Carcass on 11 Dec 2016, 09:50, edited 1 time in total.
Edited the title
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: geometry question [#permalink]  11 Dec 2016, 08:16
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Expert's post
The sum of the angles in a circle is 360.

Now we write down the values one by one:

$$a + b - \frac{a}{2} + \frac{a}{2} + 2b + 2a - 2b + 2a - b$$ $$=360$$
$$a + b + 2a + 2a - b$$ $$=360$$

$$a + 2a + 2a$$ $$=360$$
$$5a$$ $$=360$$ So we can find value of a = 72.

Now we assume that all the values of angles are positive

$$2a - b \geq 0$$ or $$b \leq 144$$

$$b - \frac{a}{2} \geq 0$$ or $$b \geq 36$$

Finally $$2a - 2b \geq 0$$ so $$b \leq 72$$.

So all option with values of b between 36 and 72 are possible.

Hence option C is correct.

_________________

Sandy
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Re: geometry question   [#permalink] 11 Dec 2016, 08:16
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