|
|
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.
20 Jul 2017, 01:04
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:57) correct
35%
(02:37)
wrong
based on 83
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
7.20.png [ 2.37 KiB | Viewed 2695 times ]
If ∠B, ∠ADB are \(90^o\), \(A=60^o\), and \(C=30^o\), what is the area of the triangle BDC?
1) The perimeter of the triangle ABD is 3+√3.
2) The perimeter of the triangle BCD is 3+3√3.
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
20 Jul 2017, 01:53
Kudos
Bookmarks
MathRevolution
Attachment:
7.20.png [ 4.01 KiB | Viewed 2623 times ]
Assume that \(AD = x\), so we have \(AB = 2AD = 2x\)
Also, we have \(AC = 2 AB = 4x \implies CD = 3x\)
In triangle ABD, we have \(BD = \sqrt{AB^2 - AD^2} = \sqrt{4x^2 - x^2} = x\sqrt{3}\)
In triangle ABC, we have \(BC = 2BD = 2x\sqrt{3}\)
The area of the triangle BCD is \(\frac{1}{2} \times x\sqrt{3} \times 3x = \frac{3\sqrt{3} x^2}{2}\). Hence we simply need to know the value of \(x\) to know the area of the triangle BCD.
(1) The perimeter of the triangle ABD is \(3+\sqrt{3}\)
so we have \(x + 2x + x\sqrt{3} = 3+\sqrt{3} \implies x(3+\sqrt{3})=3+\sqrt{3} \implies x=1\). Sufficient.
(2) The perimeter of the triangle BCD is \(3+3\sqrt{3}\)
so we have \(x\sqrt{3} + 2x\sqrt{3} + 3x = 3+3\sqrt{3} \implies x(3\sqrt{3} + 3) = 3+3\sqrt{3} \implies x=1\). Sufficient.
The answer is D.
23 Jul 2017, 18:24
Kudos
Bookmarks
==> In the original condition, if AD=x, you get \(BD=\sqrt{3}x, AB=2x\), and from \(BC=2\sqrt{3}x\) and AC=4x, there is 1 variable (x). In order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. By solving con 1) and con 2) separately, you get con 1)=con 2), which is x=1, hence it is unique and sufficient.
The answer is D.
Answer: D
The answer is D.
Answer: D
