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

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Since the highlighted triangle is a RIGHT TRIANGLE, we can apply the Pythagorean Theorem. We get: 1² + x² = (√3)² Evaluate to get: 1 + x² = 3 So, x² = 2, which means x = √2.....

Now focus on the lower triangle (in blue)

Since we're told that DB = BC, we can see that side BC = √2 We'll let the 3rd side have length y

Since the highlighted triangle is a RIGHT TRIANGLE, we can apply the Pythagorean Theorem We get: (√2)² + (√2)² = y² Evaluate to get: 2 + 2 = y² So, 4 = y², which mean y = 2

We need to know the following properties of a right angled triangle.

If the right triangle is isosceles in nature, angle ratio(45:45:90) the sides are in the ratio 1:1:\(\sqrt{2}\)

Coming back to the question, Using Pythagoras theorem, \(AB^2 = AD^2 + BD^2\) From this we can find out that the value of BD = \(\sqrt{2}\)(because BD = \(\sqrt{3-1}\))

In second triangle, using Pythagoras theorem, \(CD^2 = BC^2 + BD^2\) Since BD = \(\sqrt{2}\) and the right angled triangle is isosceles, the hypotenuse(CD) = 2(Option B)
_________________

Given Both the triangles are Right Angles Triangles

So, we can write

\((AB)^2 = (AD)^2 + (DB)^2\)

\({\sqrt{3}}^2 = (1)^2 + (DB)^2\)

\((DB)^2 = 3 - 1 = 2\)

\(DB = \sqrt{2}\)

Now for the other triangle

\((CD)^2 = (DB)^2 + (BC)^2\)

As, \(DB = BC\)

\((CD)^2 = {\sqrt{2}}^2 + {\sqrt{2}}^2\)

\((CD)^2 = 2 + 2\)

\((CD)^2 = 4\)

\(CD= 2\)

Hence, Answer is B _________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Worried About IDIOMS?Here is a Daily Practice List: https://gmatclub.com/forum/idiom-s-ydmuley-s-daily-practice-list-250731.html#p1937393

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

OK to be clear, you cannot use 1: root 3: 2 , because the angles aren't given?

Hi..

The reason is not that angles are not given. BUT the main reason is that in 1:√3:2, the ratio 2 is the hypotenuse. Here √3 is given as hypotenuse so ratio here is 1:__:√3, which is not same as 1:√3:__
_________________

OK to be clear, you cannot use 1: root 3: 2 , because the angles aren't given?

Hi..

The reason is not that angles are not given. BUT the main reason is that in 1:√3:2, the ratio 2 is the hypotenuse. Here √3 is given as hypotenuse so ratio here is 1:__:√3, which is not same as 1:√3:__