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.
In the figure, lines l and k are parallel. If a is an acut
[#permalink]
17 Mar 2019, 02:24
17 Mar 2019, 02:24
Expert Reply
00:00
Question Stats:
83% (01:36) correct
16% (00:56) wrong based on 6 sessions
Hide Show timer Statistics
Attachment:
#GREpracticequestion In the figure, lines l and k are parallel.jpg [ 18.37 KiB | Viewed 4443 times ]
In the figure, lines \(l\) and \(k\) are parallel. If a is an acute angle, then which one of the following must be true?
(A) \(b > 10\)
(B) \(b > 15\)
(C) \(b < 20\)
(D) \(b < 30\)
(E) \(b > 45\)
Re: In the figure, lines l and k are parallel. If a is an acut
[#permalink]
20 Mar 2019, 11:24
20 Mar 2019, 11:24
Expert Reply
I drew an imaginary line passing through point O and forming two right triangles, as seen in the attached image.
The angles at O must all add up to 180, so:
60 - b + 90 - b + a = 180
Combine like terms:
150 - 2b + a = 180
Add 2b to both sides:
150 + a = 180 + 2b
Subtract 180:
a - 30 = 2b
Now, if a is acute, less than 90, then (a - 30) must be less than 60. This means that 2b must be less than 60, and hence that b must be less than 30.
The angles at O must all add up to 180, so:
60 - b + 90 - b + a = 180
Combine like terms:
150 - 2b + a = 180
Add 2b to both sides:
150 + a = 180 + 2b
Subtract 180:
a - 30 = 2b
Now, if a is acute, less than 90, then (a - 30) must be less than 60. This means that 2b must be less than 60, and hence that b must be less than 30.
Attachments
In the figure, lines l and k are parallel. If a is an acut.png [ 14.51 KiB | Viewed 4358 times ]
gmatclubot
Re: In the figure, lines l and k are parallel. If a is an acut [#permalink]
20 Mar 2019, 11:24
Moderators:
