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 350,000 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:

Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]
09 Oct 2007, 21:21

ggarr wrote:

Quote:

area of middle part (quad) = B * h (6 - 2√3) * 2 = 12 - 4√3

aren't we solving what's inside the parentheses first? 6 - 2√3 = 4√3 4√3 * 2 = 8√3 should we be using the distributive property here?

6 - 2√3 does not = to 4√3!!
6√3 - 2√3 = 4√3
use a calculator and you will see the difference
and i did use distributive property
(6 - 2√3) * 2 =
6*2 - 2√3*2 =
12 - 4√3

Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]
11 Sep 2010, 13:27

beckee529 wrote:

this is how i got 12 by finding the 3 subparts (by drawing two lines to create two triangles and quadrilateral):

30:60:90 x: √3: 2x 2: 2√3: 4

Is it mandatory to mug up this rule regarding 30:60:90 triangle? No other ways of solving this problem? Isn't it correct that opposite sides of angles 30 and 60 are in ratio 1:2?

Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]
11 Sep 2010, 13:49

3

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

Orange08 wrote:

beckee529 wrote:

this is how i got 12 by finding the 3 subparts (by drawing two lines to create two triangles and quadrilateral):

30:60:90 x: √3: 2x 2: 2√3: 4

Is it mandatory to mug up this rule regarding 30:60:90 triangle? No other ways of solving this problem? Isn't it correct that opposite sides of angles 30 and 60 are in ratio 1:2?

Any help is appreciated.

• A right triangle where the angles are 30°, 60°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio 1 : \sqrt{3}: 2. Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

BACK TO THE ORIGINAL QUESTION:

Now, as hypotenuse PQ (the largest side) equals to 4 then the side opposite 30 degrees (smallest side, which is also the height of the parallelogram) equals to 4/2=2. Thus area of parallelogram is height*base=2*6=12.

Answer: B.

For more on this issues check Triangles chapter of Math Book (link in my signature).

Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]
13 Sep 2010, 07:33

Expert's post

prashantbacchewar wrote:

Bunuel

Are we supposed to remeber the corelations for the standard triangles

Yes, I think it's good to know below 2 cases:

• A right triangle where the angles are 30°, 60°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio 1 : \sqrt{3}: 2. Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

• A right triangle where the angles are 45°, 45°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should also commit to memory is: The sides are always in the ratio 1 : 1 : \sqrt{2}. With the \sqrt{2} being the hypotenuse (longest side). This can be derived from Pythagoras' Theorem. Because the base angles are the same (both 45°) the two legs are equal and so the triangle is also isosceles. • Area of a 45-45-90 triangle. As you see from the figure above, two 45-45-90 triangles together make a square, so the area of one of them is half the area of the square. As a formula A=\frac{S^2}{2}. Where S is the length of either short side.

For more on this issues check Triangles chapter of Math Book (link in my signature).

Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]
19 Nov 2014, 01:18

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Wow...I'm still reeling from my HBS admit . Thank you once again to everyone who has helped me through this process. Every year, USNews releases their rankings of...

I had an interesting conversation with a friend this morning, and I realized I need to add a last word on the series of posts on my application process. Five key words:...