GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2018, 15:22

### 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

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

Track

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# ABCD is a parallelogram (see figure). The ratio of DE to EC

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Mar 2012
Posts: 15
ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

Updated on: 24 Feb 2018, 00:41
4
7
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:45) correct 12% (02:32) wrong based on 217 sessions

### HideShow timer Statistics

ABCD is a parallelogram (see figure). The ratio of DE to EC is 1:3. AE has a length of 3. If quadrilateral ABCE has an area of 21, what is the area of ABCD?

A. 18
B. 20
C. 22
D. 24
E. 26

Attachment:

2014-11-18_2051.png [ 8.02 KiB | Viewed 7742 times ]

Originally posted by sugu86 on 26 Apr 2012, 00:57.
Last edited by Bunuel on 24 Feb 2018, 00:41, edited 4 times in total.
Edited the question and the figure
Math Expert
Joined: 02 Sep 2009
Posts: 46035
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

26 Apr 2012, 01:47
2
3
sugu86 wrote:
ABCD (attached as a jpg file ) is a paralleogram. The ratio of DE to EC is 1;3. Ae has a length of 3 . If Quadrilateral ABCE has an area of 21, what is the area of ABCD ?

A) 18 B) 20 C) 22 D) 24 E ) 26
Thanks,

Suganth

ABCD is a parallelogram (see figure). The ratio of DE to EC is 1:3. AE has a length of 3. If quadrilateral ABCE has an area of 21, what is the area of ABCD?

A. 18
B. 20
C. 22
D. 24
E. 26

The area of a parallelogram is base*height --> the area of ABCD=(x+3x)*3=12x;

Now, notice that quadrilateral ABCE is a trapezoid. The area of a trapezoid is the average base length times altitude --> the area ABCE=(4x+3x)/2*3=21 --> 7x=14 --> x=2;

The area of ABCD=12x=24

_________________
Intern
Joined: 22 Dec 2013
Posts: 21
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

26 Apr 2014, 11:18
3
1
time for basics..sometimes it really helps.. .http://www.cliffsnotes.com/math/geometr ... rence-area
Attachments

area formula.jpg [ 45.3 KiB | Viewed 7129 times ]

Intern
Joined: 20 May 2014
Posts: 32
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

25 Aug 2014, 19:11
Bunuel wrote:
sugu86 wrote:
ABCD (attached as a jpg file ) is a paralleogram. The ratio of DE to EC is 1;3. Ae has a length of 3 . If Quadrilateral ABCE has an area of 21, what is the area of ABCD ?

A) 18 B) 20 C) 22 D) 24 E ) 26
Thanks,

Suganth

Attachment:
ABCD.png
ABCD is a parallelogram (see figure). The ratio of DE to EC is 1:3. AE has a length of 3. If quadrilateral ABCE has an area of 21, what is the area of ABCD?

A. 18
B. 20
C. 22
D. 24
E. 26

The area of a parallelogram is base*height --> the area of ABCD=(x+3x)*3=12x;

Now, notice that quadrilateral ABCE is a trapezoid. The area of a trapezoid is the average base length times altitude --> the area ABCE=(4x+3x)/2*3=21 --> 7x=14 --> x=2;

The area of ABCD=12x=24

I am confused on how you got from ABCE=(4x+3x)/2*3=21 --> 7x=14 --> x=2; isn't 4x + 3x = 7x, and this is divided by 6, multiply both sides by 6 get 7x = 126, x = 18?
Director
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

25 Aug 2014, 21:07
sagnik2422 wrote:
Bunuel wrote:
Attachment:
ABCD.png
ABCD is a parallelogram (see figure). The ratio of DE to EC is 1:3. AE has a length of 3. If quadrilateral ABCE has an area of 21, what is the area of ABCD?

A. 18
B. 20
C. 22
D. 24
E. 26

The area of a parallelogram is base*height --> the area of ABCD=(x+3x)*3=12x;

Now, notice that quadrilateral ABCE is a trapezoid. The area of a trapezoid is the average base length times altitude -->

$$the area ABCE=\frac{(4x+3x)}{2}*3=21$$ --> 7x=14 --> x=2;

The area of ABCD=12x=24

I am confused on how you got from ABCE=(4x+3x)/2*3=21 --> 7x=14 --> x=2; isn't 4x + 3x = 7x, and this is divided by 6, multiply both sides by 6 get 7x = 126, x = 18?

Area of Trapezoid is Avg of Parallel Sides $$\frac{(4x+3x)}{2}$$*Height...$$\frac{7x}{2}*3=21$$
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

26 Aug 2014, 00:56
3
Given that area of shaded region = 21

Attachment:

ABCD.png [ 4.96 KiB | Viewed 6572 times ]

Setting up the equation

$$9x + \frac{3x}{2} = 21$$

x = 2

Area of ABCD = 18 + 3 + 3 = 24

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 27 Aug 2014
Posts: 27
GMAT Date: 09-27-2014
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

28 Aug 2014, 04:00
1
Alternative simpler approach:

Note that the pair of triangles in the parallelogram if placed adjacent adjoining it's hypotenuse - will become a rectangle with the height as length and base as breadth.

So try to imagine, that this parallelogram is made of 8 equal triangles. (Triangle ADE + 3 pairs in between + one to the right)

We are given area of 7 triangles = 21

We are asked, area of 8 triangles = 24.

Sorry I am unable to draw the triangles on my phone to explain. Hope his helps.
Intern
Joined: 19 Nov 2012
Posts: 7
Concentration: Finance, Technology
GMAT Date: 11-02-2014
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

02 Sep 2014, 01:24
area of trapezoid ABCE = 21
(b1+b2)*h/2
(3x + 4x)*3/2
x = 2
area of ABCD //gm = b*h
8*3=24.

Intern
Joined: 25 May 2014
Posts: 46
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

18 Nov 2014, 09:17
Bunuel wrote:
sugu86 wrote:
ABCD (attached as a jpg file ) is a paralleogram. The ratio of DE to EC is 1;3. Ae has a length of 3 . If Quadrilateral ABCE has an area of 21, what is the area of ABCD ?

A) 18 B) 20 C) 22 D) 24 E ) 26
Thanks,

Suganth

Attachment:
ABCD.png
ABCD is a parallelogram (see figure). The ratio of DE to EC is 1:3. AE has a length of 3. If quadrilateral ABCE has an area of 21, what is the area of ABCD?

A. 18
B. 20
C. 22
D. 24
E. 26

The area of a parallelogram is base*height --> the area of ABCD=(x+3x)*3=12x;

Now, notice that quadrilateral ABCE is a trapezoid. The area of a trapezoid is the average base length times altitude --> the area ABCE=(4x+3x)/2*3=21 --> 7x=14 --> x=2;

The area of ABCD=12x=24

Hi Bunuel,

How do we make sure whether AE is perpendicular to CD as it is not stated explicitly and we cannot assume it as height.
I solved the same way as you did but my first thought was that one cannot assume AE as height.
Thanks.
_________________

Never Try Quitting, Never Quit Trying

Math Expert
Joined: 02 Sep 2009
Posts: 46035
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

18 Nov 2014, 09:55
Ankur9 wrote:
Bunuel wrote:
sugu86 wrote:
ABCD (attached as a jpg file ) is a paralleogram. The ratio of DE to EC is 1;3. Ae has a length of 3 . If Quadrilateral ABCE has an area of 21, what is the area of ABCD ?

A) 18 B) 20 C) 22 D) 24 E ) 26
Thanks,

Suganth

ABCD is a parallelogram (see figure). The ratio of DE to EC is 1:3. AE has a length of 3. If quadrilateral ABCE has an area of 21, what is the area of ABCD?

A. 18
B. 20
C. 22
D. 24
E. 26

The area of a parallelogram is base*height --> the area of ABCD=(x+3x)*3=12x;

Now, notice that quadrilateral ABCE is a trapezoid. The area of a trapezoid is the average base length times altitude --> the area ABCE=(4x+3x)/2*3=21 --> 7x=14 --> x=2;

The area of ABCD=12x=24

Hi Bunuel,

How do we make sure whether AE is perpendicular to CD as it is not stated explicitly and we cannot assume it as height.
I solved the same way as you did but my first thought was that one cannot assume AE as height.
Thanks.

Original image indicates that AE is perpendicular to CD:

_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

11 Jan 2015, 06:12
I created another perpendicular from angle C to side AB, which created another right triangle, same as the one already created.

Then I added the area of the parallelogram (I named the point where the perpendicular line from angle C crosses AB as "f") that was created if you take the 2 trinagles out and the area of one of the triangles. So, I ended up with:
Aafce + Afbc = 21
21 = b*h + (b*h)/2
21 = 3x(3) + (3x/2)
21 = 9x + (3x/2)
21 = (18 + 3x) / 2
42 = 21x
x = 42/21
x = 2

So, now I have the value f x and can calculate the rest:

Aabcd = b * h = 8 * 3 = 24.

That's also right, right?
Manager
Joined: 17 Nov 2013
Posts: 135
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

27 Apr 2016, 18:01
ABCD is a parallelogram. The area of a parallelogram is B * H => (X+3X) (3) = 12x
ABCE is a trapezoid. the area of a trapezoid is ((b1 + b2)/2) * h => ((4x+3x)/2) * 3 = 21 => x =2

if x =2 => 12x =Area of parallelogram => 12(2) = 24.
Manager
Joined: 14 Oct 2015
Posts: 243
GPA: 3.57
Re: ABCD is a parallelogram (see figure). The ratio of DE to EC [#permalink]

### Show Tags

08 Sep 2017, 08:12
sugu86 wrote:
Attachment:
2014-11-18_2051.png

ABCD is a parallelogram (see figure). The ratio of DE to EC is 1:3. AE has a length of 3. If quadrilateral ABCE has an area of 21, what is the area of ABCD?

A. 18
B. 20
C. 22
D. 24
E. 26

Let h be the height.

Area of $$ABCD = 4x*h$$
Looking at the picture, Area of Quadrilateral $$ABCE$$ is Area of $$ABCD$$ minus area of the $$\triangle ADE$$
Area of Quadrilateral $$ABCE = 4x*h - \frac{1}{2}*xh = 21$$

$$xh*(4-\frac{1}{2}) = 21$$

$$xh*\frac{7}{2} = 21$$
$$xh = 21*\frac{2}{7} = 6$$

Area of $$ABCD = 4xh = 4*6 = 24$$
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Re: ABCD is a parallelogram (see figure). The ratio of DE to EC   [#permalink] 08 Sep 2017, 08:12
Display posts from previous: Sort by