GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
In the above figure, which one of the following COULD
[#permalink]
13 Jan 2019, 11:10
13 Jan 2019, 11:10
2
4
Bookmarks
00:00
Question Stats:
61% (02:17) correct
38% (02:43) wrong based on 68 sessions
Hide Show timer Statistics
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
Re: In the above figure, which one of the following COULD
[#permalink]
13 Jan 2019, 19:02
13 Jan 2019, 19:02
Expert Reply
1
Bookmarks
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the above figure, which one of the following COULD
[#permalink]
14 Jan 2019, 06:37
14 Jan 2019, 06:37
3
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
