NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 13:42 It is currently 28 Apr 2024, 13:42
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

ABC and AED are triangles with BC parallel to ED. Find the a

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
obs23
Intern
Intern
Joined: 06 Feb 2013
Posts: 35
Own Kudos [?]: 207 [2]
Given Kudos: 35
Send PM
ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   Updated on: 11 Oct 2013, 03:43
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

73% (01:26) correct 27% (01:49) wrong based on 129 sessions
Hide Show timer Statistics
ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.
Attachment:
Triangle_Barrons.png
Triangle_Barrons.png [ 45.21 KiB | Viewed 7739 times ]


(1) BC = 8
(2) ED = 5
ShowHide Answer
Official Answer
C

Originally posted by obs23 on 11 Oct 2013, 03:42.
Last edited by Bunuel on 11 Oct 2013, 03:43, edited 1 time in total.
Renamed the topic and edited the question.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92977
Own Kudos [?]: 619703 [3]
Given Kudos: 81613
Send PM
CAT Tests Forum Quiz Mode
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   11 Oct 2013, 03:56
1
Kudos
2
Bookmarks
Expert Reply
ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.


(1) BC = 8. We don't know where is ED positioned. Not sufficient.
(2) ED = 5. We don't know the other sides. Not sufficient.

(1)+(2) Notice that angles of triangles ABC and AED are equal, which means that the triangles are similar.

Property:
If two similar triangles have sides in the ratio \(\frac{x}{y}\), then their areas are in the ratio \(\frac{x^2}{y^2}\).
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \(\frac{AREA}{area}=\frac{SIDE^2}{side^2}\).

Since BC/ED=8/5, then \(\frac{AREA_{ABC}}{area_{AED}}=\frac{8^2}{5^2}=\frac{64}{25}\). As given that the area of ABS is 16, then we can find the area of AED and then find the area of BCDE. Sufficient.

Answer: C.

Hope it's clear.
User avatar
obs23
Intern
Intern
Joined: 06 Feb 2013
Posts: 35
Own Kudos [?]: 207 [0]
Given Kudos: 35
Send PM
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   14 Oct 2013, 04:41
Bunuel wrote:
ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.


(1) BC = 8. We don't know where is ED positioned. Not sufficient.
(2) ED = 5. We don't know the other sides. Not sufficient.

(1)+(2) Notice that angles of triangles ABC and AED are equal, which means that the triangles are similar.

Property:
If two similar triangles have sides in the ratio \(\frac{x}{y}\), then their areas are in the ratio \(\frac{x^2}{y^2}\).
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \(\frac{AREA}{area}=\frac{SIDE^2}{side^2}\).

Since BC/ED=8/5, then \(\frac{AREA_{ABC}}{area_{AED}}=\frac{8^2}{5^2}=\frac{64}{25}\). As given that the area of ABS is 16, then we can find the area of AED and then find the area of BCDE. Sufficient.

Answer: C.

Hope it's clear.


Wonderfully done - one question please: "the area of ABC is 16" (in the stimulus) - is there anything we can infer from this information? Or does this information help us in any way before looking at S1 and S2?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92977
Own Kudos [?]: 619703 [1]
Given Kudos: 81613
Send PM
CAT Tests Forum Quiz Mode
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   14 Oct 2013, 04:44
1
Kudos
Expert Reply
obs23 wrote:
Bunuel wrote:
ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.


(1) BC = 8. We don't know where is ED positioned. Not sufficient.
(2) ED = 5. We don't know the other sides. Not sufficient.

(1)+(2) Notice that angles of triangles ABC and AED are equal, which means that the triangles are similar.

Property:
If two similar triangles have sides in the ratio \(\frac{x}{y}\), then their areas are in the ratio \(\frac{x^2}{y^2}\).
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \(\frac{AREA}{area}=\frac{SIDE^2}{side^2}\).

Since BC/ED=8/5, then \(\frac{AREA_{ABC}}{area_{AED}}=\frac{8^2}{5^2}=\frac{64}{25}\). As given that the area of ABS is 16, then we can find the area of AED and then find the area of BCDE. Sufficient.

Answer: C.

Hope it's clear.


Wonderfully done - one question please: "the area of ABC is 16" (in the stimulus) - is there anything we can infer from this information? Or does this information help us in any way before looking at S1 and S2?


We just know that the area is 16, we can get nothing more from it.
User avatar
L
HKD1710
Retired Moderator
Joined: 22 Jun 2014
Posts: 971
Own Kudos [?]: 3805 [0]
Given Kudos: 182
Location: India
Concentration: General Management, Technology
Schools: IIMB IIMA ISB PGP Pro '19
GMAT 1: 540 Q45 V20
GPA: 2.49
WE:Information Technology (Computer Software)
Send PM
GMAT ToolKit User
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   09 Dec 2014, 10:11
Hi Bunuel,

Without combining (1) and (2), can't we say both the triangles are similar? i am asking this because i did not understand the reason for insufficiency "We don't know where is ED positioned. Not sufficient."

I marked the answer D because i thought two triangles are similar. Hence, knowing BC=8 will give me the height of the triangle ABC because the area is given. As we know, for similar triangles their ratios of heights and bases are equal i will be able to find the area of triangle AED.

Please explain.

Thanks
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92977
Own Kudos [?]: 619703 [0]
Given Kudos: 81613
Send PM
CAT Tests Forum Quiz Mode
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   09 Dec 2014, 10:36
Expert Reply
HKD1710 wrote:
Hi Bunuel,

Without combining (1) and (2), can't we say both the triangles are similar? i am asking this because i did not understand the reason for insufficiency "We don't know where is ED positioned. Not sufficient."

I marked the answer D because i thought two triangles are similar. Hence, knowing BC=8 will give me the height of the triangle ABC because the area is given. As we know, for similar triangles their ratios of heights and bases are equal i will be able to find the area of triangle AED.

Please explain.

Thanks


Yes, we know that they are similar from the stem but this does not help. Check the image below:
Attachment:
Untitled.png
Untitled.png [ 49.29 KiB | Viewed 5721 times ]
User avatar
L
HKD1710
Retired Moderator
Joined: 22 Jun 2014
Posts: 971
Own Kudos [?]: 3805 [0]
Given Kudos: 182
Location: India
Concentration: General Management, Technology
Schools: IIMB IIMA ISB PGP Pro '19
GMAT 1: 540 Q45 V20
GPA: 2.49
WE:Information Technology (Computer Software)
Send PM
GMAT ToolKit User
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   09 Dec 2014, 11:12
Bunuel wrote:
HKD1710 wrote:
Hi Bunuel,

Without combining (1) and (2), can't we say both the triangles are similar? i am asking this because i did not understand the reason for insufficiency "We don't know where is ED positioned. Not sufficient."

I marked the answer D because i thought two triangles are similar. Hence, knowing BC=8 will give me the height of the triangle ABC because the area is given. As we know, for similar triangles their ratios of heights and bases are equal i will be able to find the area of triangle AED.

Please explain.

Thanks


Yes, we know that they are similar from the stem but this does not help. Check the image below:
Attachment:
Untitled.png


By looking at the image attached, i understood what you meant by "We don't know where is ED positioned. Not sufficient."

I conclude that in case of similar triangles when the figure is not drawn to scale and value of base for both the triangles is not known then knowing the value of base for only one triangle will always lead to this situation and will be insufficient. Please confirm!

Thank you :)
User avatar
S
Nunuboy1994
Director
Director
Joined: 12 Nov 2016
Posts: 569
Own Kudos [?]: 118 [0]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Send PM
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   06 Sep 2017, 23:57
@Bunuel- just making sure- we cannot actually infer that both triangles are 90 necessarily right triangles right? In other words- we know it's C because of the property you explained not because we can make the assumption that both triangles are right triangles in which case it also makes sense that the answer is C? The fact that I did not think both triangles were right triangles was the reason I second guessed and picked E
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92977
Own Kudos [?]: 619703 [0]
Given Kudos: 81613
Send PM
CAT Tests Forum Quiz Mode
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   07 Sep 2017, 00:02
Expert Reply
Nunuboy1994 wrote:
@Bunuel- just making sure- we cannot actually infer that both triangles are 90 necessarily right triangles right? In other words- we know it's C because of the property you explained not because we can make the assumption that both triangles are right triangles in which case it also makes sense that the answer is C? The fact that I did not think both triangles were right triangles was the reason I second guessed and picked E


Yes, we don't know that the triangles are right.
User avatar
S
Nunuboy1994
Director
Director
Joined: 12 Nov 2016
Posts: 569
Own Kudos [?]: 118 [0]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Send PM
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink] New post   08 Sep 2017, 18:18
obs23 wrote:
ABC and AED are triangles with BC parallel to ED. Find the area of BCDE if the area of ABC is 16.
Attachment:
Triangle_Barrons.png


(1) BC = 8
(2) ED = 5


The proportion of the areas would simply be

8^2/5^2

C
GMAT Club Bot
gmatclubot
Re: ABC and AED are triangles with BC parallel to ED. Find the a [#permalink]
08 Sep 2017, 18:18
Moderator:
Bunuel
Math Expert
92977 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions