Author 
Message 
TAGS:

Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4665

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
11 Mar 2013, 12:27
Question Stats:
57% (01:19) correct 43% (01:19) wrong based on 217 sessions
HideShow timer Statistics
Attachment:
similar triangles on a line.JPG [ 21.66 KiB  Viewed 2755 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) 125For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog: http://magoosh.com/gmat/2013/gmatmathsimilarshapes/Experts  anything you would like to say about similar shapes on the GMAT? Mike
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)





Manager
Joined: 24 Jan 2013
Posts: 72

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
Updated on: 11 Mar 2013, 17:08
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 theorySo, the area is 5*16=80 Answer D
Originally posted by johnwesley on 11 Mar 2013, 15:04.
Last edited by johnwesley on 11 Mar 2013, 17:08, edited 1 time in total.



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4665

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
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 VZVZ 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
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Manager
Joined: 24 Jan 2013
Posts: 72

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
11 Mar 2013, 17:10
Got it, I updated my response: so just put a 4 where there was a 5.



Board of Directors
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
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) 125i 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



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2649

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
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
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Director
Joined: 12 Nov 2016
Posts: 772
Location: United States
GPA: 2.66

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
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) 125For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog: http://magoosh.com/gmat/2013/gmatmathsimilarshapes/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 345 Triangle B 121620 Then the hypotenuse of B is 300% percent greater than A 205/5 = 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?



Director
Joined: 12 Nov 2016
Posts: 772
Location: United States
GPA: 2.66

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
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) 125For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog: http://magoosh.com/gmat/2013/gmatmathsimilarshapes/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 345 Triangle B 121620 Then the hypotenuse of B is 300% percent greater than A 205/5 = 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



Director
Joined: 12 Nov 2016
Posts: 772
Location: United States
GPA: 2.66

Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ
[#permalink]
Show Tags
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) 125For a discussion of similar triangles and area, as well as a complete explanation of this question, see this blog: http://magoosh.com/gmat/2013/gmatmathsimilarshapes/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 testtaker 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




Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ &nbs
[#permalink]
07 Sep 2017, 03:01






