|
|
GMAT 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.
06 Jul 2020, 03:51
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (02:00) correct
40%
(02:19)
wrong
based on 135
sessions
History
Date
Time
Result
Not Attempted Yet
Points A, B, C, and D are on the circumference of the circle centered at P, and segments BD and AC both pass through P. What is the measure of ∠BPC?
(1) \(∠APB = \frac{1}{2}∠DCP\)
(2) ∠PDC = 72°
Are You Up For the Challenge: 700 Level Questions
Attachment:
1.png [ 3.43 KiB | Viewed 4834 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
06 Jul 2020, 04:28
Kudos
Bookmarks
Both triangles are isosceles, because in each, two sides are radii. If the two equal angles in PDC (the angles at C and D) are both y degrees, the angle at P in that triangle is 180 - 2y degrees.
In Statement 1, because we have an X-pattern at the center of the circle, angle APB and angle CPD are the same. So using the letters as defined above, Statement 1 tells us 180 - 2y = y/2, and solving we find y = 72. The angle at P is half of that from Statement 1, so is 36 degrees, and the angle we want, BPC, completes a straight line with this 36 degree angle, so is 144 degrees, and Statement 1 is sufficient.
Statement 2 tells us the angle at D is 72, so the angle at C is 72, the angle at P is 36, and again the angle we want is 144 degrees.
So the answer is D.
In Statement 1, because we have an X-pattern at the center of the circle, angle APB and angle CPD are the same. So using the letters as defined above, Statement 1 tells us 180 - 2y = y/2, and solving we find y = 72. The angle at P is half of that from Statement 1, so is 36 degrees, and the angle we want, BPC, completes a straight line with this 36 degree angle, so is 144 degrees, and Statement 1 is sufficient.
Statement 2 tells us the angle at D is 72, so the angle at C is 72, the angle at P is 36, and again the angle we want is 144 degrees.
So the answer is D.
06 Jul 2020, 04:45
Kudos
Bookmarks
BPC = 180 - APB
= 180 - CPD
= DCP + CDP
= 2*DCP = 2*CDP
(1) APB = 1/2 * DCP
DCP = 2x = CDP
=> APB = CPD = x
=> BPC = 2*DCP = 2*2x = 4x = 4*(180/5) = 144
(2) PDC = 72 => BPC = 2*PDC = 144
Ans: D
= 180 - CPD
= DCP + CDP
= 2*DCP = 2*CDP
(1) APB = 1/2 * DCP
DCP = 2x = CDP
=> APB = CPD = x
=> BPC = 2*DCP = 2*2x = 4x = 4*(180/5) = 144
(2) PDC = 72 => BPC = 2*PDC = 144
Ans: D
