It is currently 19 Nov 2017, 09:24

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ

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

Hide Tags

Expert Post
3 KUDOS received
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4488

Kudos [?]: 8741 [3], given: 105

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 11 Mar 2013, 12:27
3
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (01:21) correct 43% (01:20) wrong based on 207 sessions

HideShow timer Statistics

Attachment:
similar triangles on a line.JPG
similar triangles on a line.JPG [ 21.66 KiB | Viewed 2538 times ]

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ. If the area of triangle VWX is 5, what is the area of triangle XYZ?
(A) 25
(B) 40
(C) 50
(D) 80
(E) 125


For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog:
http://magoosh.com/gmat/2013/gmat-math-similar-shapes/

Experts --- anything you would like to say about similar shapes on the GMAT?

Mike :-)
[Reveal] Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

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

Kudos [?]: 8741 [3], given: 105

Magoosh Discount CodesJamboree Discount CodesEMPOWERgmat Discount Codes
1 KUDOS received
Manager
Manager
User avatar
Joined: 24 Jan 2013
Posts: 77

Kudos [?]: 154 [1], given: 6

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 11 Mar 2013, 15:04
1
This post received
KUDOS
We are told that angle VWX (also called angle W) is equal to angle XYZ (also called angle Y). Then, is easy to know that angles in point X are the same (i.e. angles WXV and YXZ are the same). Therefore, we can easily derive that angle WVX (also called angle V) and angle XZY (also called angle Z) are the same.

This means both triangles are similar.

And for similar triangles, if the side of the big triangle is 4 times the side of the smaller... this means the area of the bigger is \(4^2\) times the area of the smaller.

See the explanation of this typical GMAT rule here: GMAT Maths Triangles theory

So, the area is 5*16=80

Answer D

Last edited by johnwesley on 11 Mar 2013, 17:08, edited 1 time in total.

Kudos [?]: 154 [1], given: 6

Expert Post
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4488

Kudos [?]: 8741 [0], given: 105

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 11 Mar 2013, 15:36
johnwesley wrote:
And for similar triangles, if the side of the big triangle is 5 times the side of the smaller... this means the area of the bigger is \(5^2\) times the area of the smaller.

Dear JohnWesley,
My friend with the Methodist name, I want to point out a slight misreading. The text of the problem states:
VX is one fifth of VZ
VZ is the whole and VX is the part, and as such, VZ is not the side of either triangle. Does this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

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

Kudos [?]: 8741 [0], given: 105

Manager
Manager
User avatar
Joined: 24 Jan 2013
Posts: 77

Kudos [?]: 154 [0], given: 6

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 11 Mar 2013, 17:10
Got it, I updated my response: so just put a 4 where there was a 5.

Kudos [?]: 154 [0], given: 6

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15658

Kudos [?]: 282 [0], given: 0

Premium Member
Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 28 Jul 2014, 06:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 282 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15658

Kudos [?]: 282 [0], given: 0

Premium Member
Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 03 Oct 2015, 01:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 282 [0], given: 0

Board of Directors
User avatar
G
Joined: 17 Jul 2014
Posts: 2672

Kudos [?]: 431 [0], given: 200

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 23 Mar 2016, 19:37
mikemcgarry wrote:
Attachment:
similar triangles on a line.JPG

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ. If the area of triangle VWX is 5, what is the area of triangle XYZ?
(A) 25
(B) 40
(C) 50
(D) 80
(E) 125



i used the concepts taught in the Magoosh lessons...
in similar triangles, if the sides of one triangles is greater by a X factor, then the area of the triangle is greater than that of the smaller one by area*X^2. I even have a sticky note on my monitor at work with this concept :D

ok...so we are told that angle W= angle Y. since VZ is a straight line, and we CAN assume that it is a straight line, and since WY intersects VZ, we CAN assume that the formed angles at point X are equal. if we have at least 2 equal angles in 2 triangles, then the two triangles are similar.
we then are told the scale factor.
VX is 1/5th of VZ. suppose VZ is 5k(k is a constant). 1k is VX, and 4k is XZ. we see that XZ is 4 times greater than VX. we can conclude that the scale factor for the big triangle is 4.
now we are given the area of the small one - 5. the area of the greater one must be 5*4*4 = 80.

C

Kudos [?]: 431 [0], given: 200

Retired Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 869 [0], given: 602

GMAT ToolKit User Premium Member
Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 04 Apr 2016, 15:22
Excellent Question mikemcgarry
Here the two triangles are similar using the AAA property
Hence the ratio of their areas =>x^2/16 * x^2 => 1/16 hence Area of the required triangle = 16*5 => 80 units
hence D is correct.
Any more Questions will be really helpful..
Regards
Stone Cold
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 869 [0], given: 602

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 07 Sep 2017, 02:54
mikemcgarry wrote:
Attachment:
similar triangles on a line.JPG

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ. If the area of triangle VWX is 5, what is the area of triangle XYZ?
(A) 25
(B) 40
(C) 50
(D) 80
(E) 125


For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog:
http://magoosh.com/gmat/2013/gmat-math-similar-shapes/

Experts --- anything you would like to say about similar shapes on the GMAT?

Mike :-)



Bunuel Something seems off about this

If you have two similar triangles

Triangle A
3-4-5

Triangle B
12-16-20

Then the hypotenuse of B is 300% percent greater than A

20-5/5 = 3

However

3^2 = 9

And in this case the area of A and B is

3(4)/2 = 6

12(16)/2= 96

If we multiply 6 by 3^2 we would get 54 which is not the area of B; instead, if we multiply 6 by 16 then we would get 96. The intuition for 16 comes from 4^2 because 20 is 4 times larger than 5?

Kudos [?]: 36 [0], given: 165

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 07 Sep 2017, 02:57
Nunuboy1994 wrote:
mikemcgarry wrote:
Attachment:
similar triangles on a line.JPG

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ. If the area of triangle VWX is 5, what is the area of triangle XYZ?
(A) 25
(B) 40
(C) 50
(D) 80
(E) 125


For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog:
http://magoosh.com/gmat/2013/gmat-math-similar-shapes/

Experts --- anything you would like to say about similar shapes on the GMAT?

Mike :-)



Bunuel Something seems off about this

If you have two similar triangles

Triangle A
3-4-5

Triangle B
12-16-20

Then the hypotenuse of B is 300% percent greater than A

20-5/5 = 3

However

3^2 = 9

And in this case the area of A and B is

3(4)/2 = 6

12(16)/2= 96

If we multiply 6 by 3^2 we would get 54 which is not the area of B; instead, if we multiply 6 by 16 then we would get 96. The intuition for 16 comes from 4^2 because 20 is 4 times larger than 5?


Bunuel nevermind I see the small trap

Kudos [?]: 36 [0], given: 165

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

Show Tags

New post 07 Sep 2017, 03:01
mikemcgarry wrote:
Attachment:
similar triangles on a line.JPG

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ. If the area of triangle VWX is 5, what is the area of triangle XYZ?
(A) 25
(B) 40
(C) 50
(D) 80
(E) 125


For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog:
http://magoosh.com/gmat/2013/gmat-math-similar-shapes/

Experts --- anything you would like to say about similar shapes on the GMAT?

Mike :-)



So the subtle trap in this question is simply getting the test-taker to think that VX is one fifth of XZ. VZ is made up of BOTH XZ and VX so if VX is 5 then XZ is 20. So actually XZ is 4 times larger so the multiplier is simply 4^2

Kudos [?]: 36 [0], given: 165

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ   [#permalink] 07 Sep 2017, 03:01
Display posts from previous: Sort by

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.