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

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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11 Mar 2013, 11:27
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similar triangles on a line.JPG [ 21.66 KiB | Viewed 2621 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

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Mike McGarry
Magoosh Test Prep

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

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11 Mar 2013, 14:04
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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

Last edited by johnwesley on 11 Mar 2013, 16:08, edited 1 time in total.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680
Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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11 Mar 2013, 14:36
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
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Mike McGarry
Magoosh Test Prep

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

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

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11 Mar 2013, 16:10
Got it, I updated my response: so just put a 4 where there was a 5.
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Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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28 Jul 2014, 05:57
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Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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03 Oct 2015, 00:06
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).

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

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23 Mar 2016, 18:37
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
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Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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04 Apr 2016, 14:22
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..
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Stone Cold
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Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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07 Sep 2017, 01:54
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

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?
Director
Joined: 12 Nov 2016
Posts: 790
Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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07 Sep 2017, 01:57
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

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
Director
Joined: 12 Nov 2016
Posts: 790
Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ [#permalink]

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07 Sep 2017, 02:01
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
Re: In the diagram above, ∠W = ∠Y and VX is one fifth of VZ   [#permalink] 07 Sep 2017, 02:01
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