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

 It is currently 16 Oct 2019, 17:25 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.  If AB || DE and AB = 10, what is the length of DE?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4006
If AB || DE and AB = 10, what is the length of DE?  [#permalink]

Show Tags

Top Contributor
4 00:00

Difficulty:   65% (hard)

Question Stats: 52% (01:46) correct 48% (01:44) wrong based on 85 sessions

HideShow timer Statistics If AB || DE, and AB = 10, what is the length of DE?

(1) BC = 6 and CE = 4
(2) DC = 3 and CB = 6

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7959
Re: If AB || DE and AB = 10, what is the length of DE?  [#permalink]

Show Tags

1
1
GMATPrepNow wrote: If AB || DE, and AB = 10, what is the length of DE?

(1) BC = 6 and CE = 4
(2) DC = 3 and CB = 6

The information tells us that ABC is similar to EDC..
Angles A=E; B=D (alternate angles)
Angle DEC=angle ACB ( opposite angles)
So ratio of sides is same...$$\frac{AB}{DE}$$=$$\frac{AC}{CE}$$=$$\frac{BC}{CD}$$..
We require to know any one of the ratio..

(1) BC = 6 and CE = 4
BC and CE are in different ratios so insufficient

(2) DC = 3 and CB = 6
.$$\frac{AB}{DE}$$=$$\frac{BC}{CD}$$....
.$$\frac{10}{DE}=[m]\frac{6}{3}$$.....DE=10*3/6=5
Sufficient

B
_________________
Manager  G
Joined: 21 Jun 2017
Posts: 230
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: If AB || DE and AB = 10, what is the length of DE?  [#permalink]

Show Tags

Hi chetan2u
What is the correct way of naming two similar training gles after we have recognized that they are similar.
I got A as I named the triangles
CAB and CDE

Thanks

Posted from my mobile device
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

GMAT 1 - 620 .... Disappointed for 6 months. Im back Im back. Bhai dera tera COMEBACK !!!
Math Expert V
Joined: 02 Aug 2009
Posts: 7959
Re: If AB || DE and AB = 10, what is the length of DE?  [#permalink]

Show Tags

1
ShankSouljaBoi wrote:
Hi chetan2u
What is the correct way of naming two similar training gles after we have recognized that they are similar.
I got A as I named the triangles
CAB and CDE

Thanks

Posted from my mobile device

You have to name as per the angles that is why I mentioned angles A=E, B=D and C=C
So name it in similar way..
ABC and EDC or CAB and CED and so on
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4006
Re: If AB || DE and AB = 10, what is the length of DE?  [#permalink]

Show Tags

Top Contributor
ShankSouljaBoi wrote:
Hi chetan2u
What is the correct way of naming two similar training gles after we have recognized that they are similar.
I got A as I named the triangles
CAB and CDE

Thanks

Posted from my mobile device

Our video on Similar Triangles suggests a way to determine which sides correspond by labeling the angles differently.

Cheers,
Brent
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4006
Re: If AB || DE and AB = 10, what is the length of DE?  [#permalink]

Show Tags

Top Contributor
GMATPrepNow wrote: If AB || DE, and AB = 10, what is the length of DE?

(1) BC = 6 and CE = 4
(2) DC = 3 and CB = 6

Let's first add the given information (and their implications) to the diagram

If AB || DE, we know that ∠BAC = ∠CED and ∠ABC = ∠DCE
Also, since vertically opposite angles are equal, we know that ∠ACB = ∠DCE Now that we've identified 3 pairs of EQUAL angles, we can conclude that the two triangles are SIMILAR
So, we need to determine which sides are corresponding.
Notice that side AB and side DE BOTH lie between the angles denoted by a star and a square.
This means that side AB corresponds with side DE (denoted by BLUE lines) Likewise, side BC and side CD both lie between the angles denoted by a circle and a square.
This means that side BC corresponds with side CD (denoted by RED lines) Finally, side AC and side CE both lie between the angles denoted by a circle and a star.
This means that side AC corresponds with side CE (denoted by GREEN lines) Now onto the question!!!!

Target question: What is the length of DE?

Statement 1: BC = 6 and CE = 4
Add this info to the diagram: Notice that we don't know the lengths of two corresponding sides.
As such, we can't determine the magnification factor of the two similar triangles (see the video below for more information about magnification factor)
As such, there's no way to determine the length of side DE
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: DC = 3 and CB = 6
Add this info to the diagram: Notice that DC and CB are corresponding sides.
So, the magnification factor of the similar triangles = 6/3 = 2
In other words, ∆ABC is 2 times the size of ∆EDC
So, if side AB = 10, then side DE (the side that corresponds with side AB) must have length 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO FROM OUR COURSE

_________________ Re: If AB || DE and AB = 10, what is the length of DE?   [#permalink] 25 Oct 2018, 17:11
Display posts from previous: Sort by

If AB || DE and AB = 10, what is the length of DE?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  