 It is currently 24 Jan 2020, 05:08 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # BD is parallel to AE.  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 9396
Followers: 195

Kudos [?]: 2288 , given: 8892

BD is parallel to AE. [#permalink]
Expert's post 00:00

Question Stats: 70% (00:44) correct 29% (00:34) wrong based on 124 sessions

Attachment: #GREpracticequestion BD is parallel to AE..jpg [ 17.41 KiB | Viewed 3206 times ]

BD is parallel to AE.

 Quantity A Quantity B xz wy

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Intern Joined: 28 Feb 2017
Posts: 6
Followers: 0

Kudos [?]: 2 , given: 3

Re: BD is parallel to AE. [#permalink] VP Joined: 20 Apr 2016
Posts: 1118
WE: Engineering (Energy and Utilities)
Followers: 17

Kudos [?]: 1008  , given: 229

Re: BD is parallel to AE. [#permalink]
3
KUDOS
Pria wrote:

Here given BD is parallel to AE,

so angle CBD = angle CAE, and angle BDC = angle AEC.

Therefore the triangles BCD and ACE are similar (Angle C is common to both triangles and by AAA triangle BCD and triangle ACE are similar)

Now it is given side BC = x , AB = y and AC =x+w.

side CD = y, DE = z and CE = y+Z

Now as both triangles BCD and ACE are similar

therfore we have

$$\frac{CB}{CA}$$ = $$\frac{CD}{CE}$$

substitute the values we get

$$\frac{x}{(x+w)}$$= $$\frac{y}{(y+z)}$$

or x(y+z) = y(x+w)

or xy + xz = xy + wy

or xz = wy. So option C.
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Intern Joined: 28 Feb 2017
Posts: 6
Followers: 0

Kudos [?]: 2 , given: 3

Re: BD is parallel to AE. [#permalink]
Thank you.
Intern Joined: 22 Sep 2017
Posts: 2
Followers: 0

Kudos [?]: 0 , given: 5

Re: BD is parallel to AE. [#permalink]
I don't understand.
CA could be different length than CE

Can anyone explain? Thank you VP Joined: 20 Apr 2016
Posts: 1118
WE: Engineering (Energy and Utilities)
Followers: 17

Kudos [?]: 1008  , given: 229

Re: BD is parallel to AE. [#permalink]
1
KUDOS
pclawong wrote:
I don't understand.
CA could be different length than CE

Can anyone explain? Thank you

$$\frac{{CB}}{{CA}} = \frac{{CD}}{{CE}}$$ because they are similar and the ratio's of there length has to be equal.

CA= x+w (total length of CA, x & w are given)

CE = y+z (total length of CE, y & z are given)
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Director Joined: 09 Nov 2018
Posts: 508
Followers: 0

Kudos [?]: 50 , given: 1

Re: BD is parallel to AE. [#permalink]
pranab01 wrote:
Pria wrote:

Here given BD is parallel to AE,

so angle CBD = angle CAE, and angle BDC = angle AEC.

Therefore the triangles BCD and ACE are similar (Angle C is common to both triangles and by AAA triangle BCD and triangle ACE are similar)

Now it is given side BC = x , AB = y and AC =x+w.

side CD = y, DE = z and CE = y+Z

Now as both triangles BCD and ACE are similar

therfore we have

$$\frac{CB}{CA}$$ = $$\frac{CD}{CE}$$

substitute the values we get

$$\frac{x}{(x+w)}$$= $$\frac{y}{(y+z)}$$

or x(y+z) = y(x+w)

or xy + xz = xy + wy

or xz = wy. So option C.

If you put the reason, it will be better---

If two triangles are similar, the ratio of their corresponding sides are equal.

---------------------------------------------------------------------------------------------------------
Please let me know, if I am wrong.
Intern Joined: 07 Jan 2019
Posts: 30
Followers: 0

Kudos [?]: 2 , given: 0

Re: BD is parallel to AE. [#permalink]
thank you
Director Joined: 09 Nov 2018
Posts: 508
Followers: 0

Kudos [?]: 50 , given: 1

Re: BD is parallel to AE. [#permalink]
pclawong wrote:
I don't understand.
CA could be different length than CE

Can anyone explain? Thank you

By maintaining ratio, any length is possible. Intern Joined: 27 Jan 2019
Posts: 30
Followers: 0

Kudos [?]: 24  , given: 3

Re: BD is parallel to AE. [#permalink]
1
KUDOS
A line drawn parallel to a side of the triangle divides the two other sides proportionally. So x/w and y/z have the same ratio. Hence xz and wy are equal Intern Joined: 14 May 2019
Posts: 9
Followers: 0

Kudos [?]: 9  , given: 0

Re: BD is parallel to AE. [#permalink]
2
KUDOS
Hi,

This is a question of proportionality of sides of two triangles that are similar. The larger and the smaller triangles are similar due to two common angles.

Here, x/w=y/z

So, xz=wy.

Hence, option (C) is the right answer. GRE Forum Moderator Joined: 27 Aug 2019
Posts: 59
Followers: 0

Kudos [?]: 42  , given: 41

Re: BD is parallel to AE. [#permalink]
1
KUDOS
Let's say x = a*w where 'a' is the constant term of proportionality between a side of the little triangle and the corresponding side of the larger triangle.
Then, it must be also that: y = a*z.

Therefore:
x*z = (a*w)*z
w*y = w*(a*z)

The two are equal, hence C.
_________________

GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Re: BD is parallel to AE.   [#permalink] 30 Sep 2019, 06:16
Display posts from previous: Sort by

# BD is parallel to AE.  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.