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655-705 (Hard)|   Geometry|      
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mikemcgarry
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 11 Mar 2013, 12:27
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55% (hard)

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57% (01:57) correct 43% (01:54) wrong based on 275 sessions

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similar triangles on a line.JPG
similar triangles on a line.JPG [ 21.66 KiB | Viewed 7155 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:
https://magoosh.com/gmat/2013/gmat-math-similar-shapes/

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

Mike :-)
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D
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ Updated on: 11 Mar 2013, 17:08
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.
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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

Answer D
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 11 Mar 2013, 15:36
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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.
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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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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 11 Mar 2013, 17:10
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Got it, I updated my response: so just put a 4 where there was a 5.
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 23 Mar 2016, 19:37
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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
Show more

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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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 04 Apr 2016, 15:22
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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
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 07 Sep 2017, 02:54
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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:
https://magoosh.com/gmat/2013/gmat-math-similar-shapes/

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

Mike :-)
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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?
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 07 Sep 2017, 02:57
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mikemcgarry
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:
https://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?
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Bunuel nevermind I see the small trap
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 07 Sep 2017, 03:01
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mikemcgarry
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:
https://magoosh.com/gmat/2013/gmat-math-similar-shapes/

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

Mike :-)
Show more


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
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In the diagram above, ∠W = ∠Y and VX is one fifth of VZ 12 Jul 2023, 13:01
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