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Which is greater r+t+v or s+u+w

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Which is greater r+t+v or s+u+w [#permalink] New post 07 Jun 2017, 00:50
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Quantity A
Quantity B
r + t + v
s + u + w


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: r + t + v [#permalink] New post 07 Jun 2017, 15:19
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Expert's post
We have 3 pairs of opposite angles here, and opposite angles are always equal.

So, we can conclude that:
s = v
r = u
w = t

So, we get:
Quantity A: r + t + v
Quantity B: s + u + w

Since the same three angles appear in each quantity, their sums must be equal.

Answer:
[Reveal] Spoiler:
C


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Re: Which is greater r+t+v or s+u+w [#permalink] New post 11 Feb 2019, 20:22
From your solution, it's obvious we assumed the lines are all equal. As nothing in the question suggests that.
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Re: Which is greater r+t+v or s+u+w [#permalink] New post 21 Feb 2019, 14:19
Expert's post
akingba wrote:
From your solution, it's obvious we assumed the lines are all equal. As nothing in the question suggests that.


Hey there, akingba, we don't actually have to assume that the lines are equal. We only assume that opposite pairs of angles are equal. Whenever two lines cross, they will create two pairs of opposite angles, and these opposite angles are equal. For instance, s and v form one pair of opposite angles. Hence, s = v, no matter the length of the lines.
Re: Which is greater r+t+v or s+u+w   [#permalink] 21 Feb 2019, 14:19
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