Events & Promotions
|
|
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.
Jun 0308:30 AM PDT
-09:30 AM PDT
In Episode 7 of our GMAT Ninja CR series, we are rounding up the oddballs, the misfits, and the format-benders: EXCEPT, Fill-In-The-Blanks, and other unusual Critical Reasoning question types. When you see a question that ends with a literal blank line
May 2910:00 AM IST
-11:00 PM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.- Jun 02
10:00 AM PDT
-11:00 AM PDT
Probability is one of the most important GMAT Quant topics because it often combines logic, counting, set theory, and permutations & combinations. Many students try to solve probability questions by listing every possible case, but GMAT probability... - Jun 04
08:30 AM PDT
-09:30 AM PDT
For most test takers, Data Insights is the most challenging section on the GMAT, with test takers scoring several points lower on average on DI than on Quant or Verbal and completing the section with less time to spare. - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
16 Sep 2014, 01:10
Kudos
Bookmarks
If in triangle \(ABC\) point \(D\) lies on side \(AC\), what is the degree measure of \(\angle BCA\) ?
(1) The degree measure of \(\angle ABD\) is half that of \(\angle BDC\).
(2) The degree measure of \(\angle DBC\) is 10°.
(1) The degree measure of \(\angle ABD\) is half that of \(\angle BDC\).
(2) The degree measure of \(\angle DBC\) is 10°.
16 Sep 2014, 01:10
Kudos
Bookmarks
Official Solution:
If in triangle \(ABC\) point \(D\) lies on side \(AC\), what is the degree measure of \(\angle BCA\) ?
(1) The degree measure of \(\angle ABD\) is half that of \(\angle BDC\).
Let \(\angle ABD = x\) degrees. Then, \(\angle BDC = 2x\) degrees. However, this statement doesn't tell us anything about \(\angle BCA\) directly. Not sufficient.
(2) The degree measure of \(\angle DBC\) is 10°.
But again, this doesn't give us direct information about \(\angle BCA\) directly. Not sufficient.
(1)+(2) Given that \(\angle BDC\) is an exterior angle to triangle \(ABD\), it follows that \(\angle BDC = \angle BAC + \angle ABD\) (the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.). So, we have that \(2x = \angle BAC + x\), from which we it follows that \(\angle BAC = x\). Next, since the angles in a triangle sum to 180°, we get: \(\angle BCA + \angle ABC + \angle BAC = \angle BCA + (x + 10) + x = 180°\). Without knowing the value of \(x\), we cannot determine \(\angle BCA\). Not sufficient.
Answer: E
If in triangle \(ABC\) point \(D\) lies on side \(AC\), what is the degree measure of \(\angle BCA\) ?
(1) The degree measure of \(\angle ABD\) is half that of \(\angle BDC\).
Let \(\angle ABD = x\) degrees. Then, \(\angle BDC = 2x\) degrees. However, this statement doesn't tell us anything about \(\angle BCA\) directly. Not sufficient.
(2) The degree measure of \(\angle DBC\) is 10°.
But again, this doesn't give us direct information about \(\angle BCA\) directly. Not sufficient.
(1)+(2) Given that \(\angle BDC\) is an exterior angle to triangle \(ABD\), it follows that \(\angle BDC = \angle BAC + \angle ABD\) (the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.). So, we have that \(2x = \angle BAC + x\), from which we it follows that \(\angle BAC = x\). Next, since the angles in a triangle sum to 180°, we get: \(\angle BCA + \angle ABC + \angle BAC = \angle BCA + (x + 10) + x = 180°\). Without knowing the value of \(x\), we cannot determine \(\angle BCA\). Not sufficient.
Answer: E
