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:

In the picture, quadrilateral ABCD is a parallelogram and [#permalink]

Show Tags

07 Feb 2012, 15:32

24

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

22% (01:28) correct 78% (01:39) wrong based on 716 sessions

HideShow timer Statistics

Attachment:

Untitled.png [ 4.89 KiB | Viewed 25785 times ]

In the picture, quadrilateral ABCD is a parallelogram and quadrilateral DEFG is a rectangle. What is the area of parallelogram ABCD (figure not drawn to scale)?

(1) The area of rectangle DEFG is 8√5. (2) Line AH, the altitude of parallelogram ABCD, is 5.

As a geometry geek myself, I found this a very cool geometry problem, but I will say --- it is WAY harder than anything you would be expected to figure out for yourself on the real GMAT.

Statement #1: The area of rectangle DEFG is 8√5.

Well, to cut to the chase, this statement is sufficient because the rectangle and the parallelogram must have equal area. Why do the rectangle and parallelogram have equal area? You will see the complete geometric argument in the pdf attachment to this post. Leaving those details aside for the moment, Statement #1 is sufficient.

Statement #2: Line AH, the altitude of parallelogram ABCD, is 5. Area of a parallelogram = (base)*(altitude). If we know the altitude and not the base, that's not enough. Therefore, Statement #2 is insufficient.

Answer = A.

Does all this (including everything in the pdf) make sense?

Here's another geometry DS, a little closer to the actual level of difficulty of the GMAT itself.

As a geometry geek myself, I found this a very cool geometry problem, but I will say --- it is WAY harder than anything you would be expected to figure out for yourself on the real GMAT.

Statement #1: The area of rectangle DEFG is 8√5.

Well, to cut to the chase, this statement is sufficient because the rectangle and the parallelogram must have equal area. Why do the rectangle and parallelogram have equal area? You will see the complete geometric argument in the pdf attachment to this post. Leaving those details aside for the moment, Statement #1 is sufficient.

Statement #2: Line AH, the altitude of parallelogram ABCD, is 5. Area of a parallelogram = (base)*(altitude). If we know the altitude and not the base, that's not enough. Therefore, Statement #2 is insufficient.

Answer = A.

Does all this (including everything in the pdf) make sense?

Here's another geometry DS, a little closer to the actual level of difficulty of the GMAT itself.

Please let me know if you have any questions on what I've said here.

Mike

Dear Mike.. What is the likelihood of such a question on the GMAT. The more I see Kaplan questions, the more I feel the questions can be extremely hard. Whereas the questions on GMATPREP seem to be much simpler than this, No?
_________________

"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde

Re: In the picture, quadrilateral ABCD is a parallelogram and [#permalink]

Show Tags

11 Feb 2012, 01:20

1

This post received KUDOS

I personal think it would be on GMAT, but will be a 700 or 800 question. Calculation is straight forward. The only thing you need to recognize is that they both share the same triangle and if a triangle has the same height and width as a parallelogram thats not a trapezoid; then the triangle will always be 1/2 the area of the parallelogram. This is due to the simple mathematical equation to calculate the both of them.

I would say a question like this ---- a question that hinges on a relatively obscure geometry theorem that one probably would have to prove from scratch to answer the question ---- is something far harder than what they would put on the GMAT. Any GMAT math question, no matter how challenging, is something that someone facile with math would be able to solve in under a minute. If you've never seen this theorem, there's virtually no way that you will derive the full geometry proof in under a minute, unless you operate at Isaac Newton level. The GMAT doesn't expect that, even on 800 level questions. You don't have to have be Isaac Newton to answer the hardest questions.

That's my take on it. I am not as familiar with Kaplan questions overall, I am not qualified to make a statement about them. I know that Magoosh has a few hundred math questions, all appropriate difficulty for the GMAT, and each followed but its own video solution. The link above will give you a sample.

Mike
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: In the picture, quadrilateral ABCD is a parallelogram and [#permalink]

Show Tags

07 Dec 2012, 01:19

11

This post received KUDOS

1

This post was BOOKMARKED

Hi, mikemcgarry's is good but it uses similar triangles to prove. I think it's doesn't need to be that complicated. I use the same diagram that mikemcgarry provided.

First, we all agree that by considering DC as base and EQ as height, Area DEC = 1/2 * EQ * DC (1). It also equals 1/2 Area ABCD (area of parallelogram is base * height). This is just normal formula, no problem.

The tricky part is how to link it with the rectangle DEFG. Now, from C, draw a line CP that is perpendicular with DE with P is on DE. Now, for triangle DEC, consider ED as base and CP as height, we have Area of DEC = 1/2 CP * DE (2)

From (1) and (2), the 2 area is the same, we have EQ * DC = CP * DE (3). But in rectangle DEFG, CP = EF (since DEFG is rectangle, CP perpendicular with DE, so CP must = EF)

So (3) can be rewritten as EQ * DC = EF * DE. LHS is area of ABCD. RHS is area of DEFG. So (1) Suff.

(2) obviously NS.

So A is correct. I must admit I couldn't get this right, but after reading the explanation of mikemcgarry, I think this way is simpler as you don't have to think and prove similars. You just need to substitute side for side.

Re: In the picture, quadrilateral ABCD is a parallelogram and [#permalink]

Show Tags

09 Nov 2014, 16:37

enigma123 wrote:

Attachment:

Untitled.png

In the picture, quadrilateral ABCD is a parallelogram and quadrilateral DEFG is a rectangle. What is the area of parallelogram ABCD (figure not drawn to scale)?

(1) The area of rectangle DEFG is 8√5. (2) Line AH, the altitude of parallelogram ABCD, is 5.

Just providing my 2 cents on the problem...

Theorem: Triangles between two parallel lines with same base have equal areas.

Even if you're not familiar with the above theorem, it's pretty intuitive from the area formula of the triangle.

In the figure, join EC.

Then from the above theorem, it's clear that area (tri DEC) = area (tri DBC) = \(\frac{1}{2}\)* area (ABCD) ---- (*)

Similarly, area (tri DEC) = area (tri DEF) = \(\frac{1}{2}\)* area (DEFG) ---- (**)

So, from (*) and (**), area (ABCD) = area (DEFG)

Clearly, (1) is sufficient and (2) is not, so answer is A.

This approach takes less than 2 minutes to solve. I think it is quite possible that similar questions are likely to be seen in GMAT at 700 level.

In the picture, quadrilateral ABCD is a parallelogram and [#permalink]

Show Tags

26 Mar 2015, 05:06

enigma123 wrote:

Attachment:

The attachment Untitled.png is no longer available

In the picture, quadrilateral ABCD is a parallelogram and quadrilateral DEFG is a rectangle. What is the area of parallelogram ABCD (figure not drawn to scale)?

(1) The area of rectangle DEFG is 8√5. (2) Line AH, the altitude of parallelogram ABCD, is 5.

hi guys

here is another solution to this hard problem based on a different approach.

i hope you find the solution interesting and easy.

the diagram in the pdf is self explanatory.

Once we understand the diagram, the solution looks so easy.

The attachment Untitled.png is no longer available

In the picture, quadrilateral ABCD is a parallelogram and quadrilateral DEFG is a rectangle. What is the area of parallelogram ABCD (figure not drawn to scale)?

(1) The area of rectangle DEFG is 8√5. (2) Line AH, the altitude of parallelogram ABCD, is 5.

Please find the attached file for explanation

Answer: option A

Attachments

File comment: www.GMATinsight.com

Untitled1.jpg [ 145.42 KiB | Viewed 8147 times ]

_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Re: In the picture, quadrilateral ABCD is a parallelogram and [#permalink]

Show Tags

14 Nov 2017, 18:16

Somehow I came to know that in any parallelogram, if a triangle is formed joining two vertexes of the parallelogram and a point of opposite side of the vertexes, then the area of resulting triangle is half of the area of the parallelogram.Need confirmation from expert.

Draw a line EC.

Now in DEFG rectangle, Area of DEC = Area of \(\frac{1}{2}\) DEFG Again in ABCD parallelogram, Area of DEC = Area of \(\frac{1}{2}\) ABCD

∴ Area of \(\frac{1}{2}\) DEFG = Area of \(\frac{1}{2}\) ABCD => Area of DEFG = Area of ABCD.