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Which is greater x+y or p+q

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Which is greater x+y or p+q [#permalink] New post 08 May 2018, 16:11
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Quantity A
Quantity B
x+y
p+q



A)The quantity in Column A is greater.
B)The quantity in Column 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: x+y [#permalink] New post 11 May 2018, 07:26
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Carcass wrote:
Attachment:
lines.jpg


Quantity A
Quantity B
x+y
p+q



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Since vertically opposite angles are equal, let's add another angle () to the diagram.
Image

Since angles in a triangle add to 180°, we can write two equations:
w + x + y = 180
w + p + q = 180

Since both equations are equal to 180, we can write: w + x + y = w + p + q
Now subtract w from both sides of the equation to get: x + y = p + q

Answer: C

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Brent
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Re: Which is greater x+y or p+q [#permalink] New post 08 Aug 2020, 19:15
Based on the rule that the larger the angle, the longer the side opposite that angle. Shouldn't angle y be bigger since the side opposite it is longer compared to angle p? Same applies to the remaining angles. At least I was expecting the answer to be a D.
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Re: Which is greater x+y or p+q [#permalink] New post 09 Aug 2020, 00:16
One question. By default is the figure drawn to scale, when nothing is mentioned?
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Re: Which is greater x+y or p+q [#permalink] New post 09 Aug 2020, 17:43
Boom1 wrote:
Based on the rule that the larger the angle, the longer the side opposite that angle. Shouldn't angle y be bigger since the side opposite it is longer compared to angle p? Same applies to the remaining angles. At least I was expecting the answer to be a D.


We don't need to know the values or relative values of any of the angles to solve this problem. We can see that the unlabelled angles in each triangle are opposite/vertical to one another, which means they're equal (to visualize this, I refer you to Brent's explanation, where he labelled both of them "w"). Since the angles of all triangles add up to 180 degrees and the third angle is fixed, x+y must equal p+q.
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Re: Which is greater x+y or p+q [#permalink] New post 10 Aug 2020, 06:08
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Farina wrote:
One question. By default is the figure drawn to scale, when nothing is mentioned?


Geometric diagrams are not necessarily drawn to scale.
The only time we can be certain a diagram is drawn to scale is when we're specifically told so.
For more and what can and cannot be assumed (with regard to diagrams), watch this video: https://www.greenlighttestprep.com/modu ... /video/863
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Re: Which is greater x+y or p+q   [#permalink] 10 Aug 2020, 06:08
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