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x or y-90

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Carcass
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x or y-90 [#permalink] New post   21 Feb 2021, 10:23
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Attachment:
GRE triangle and angles.jpg
GRE triangle and angles.jpg [ 8.66 KiB | Viewed 2731 times ]



Quantity A
Quantity B
x
y-90



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.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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C
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Re: x or y-90 [#permalink] New post   21 Feb 2021, 10:30
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Solution:

Consider the exterior angle Y. As it lies on the straight line, the angle adjacent to Y will be 180-Y
Thus, X+180-Y+90=180 (Sum of all angles of a triangle)
X-Y+90=0
X-Y=90
X=90-Y

Hence, Qty A=Qty B

IMO C

Hope this helps!
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Re: x or y-90 [#permalink] New post   21 Feb 2021, 11:58
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Carcass wrote:
Attachment:
GRE triangle and angles.jpg



Quantity A
Quantity B
x
y-90



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.


Property: Exterior angle in a triangle is equal to the sum of opposite interior angles

\(y = x + 90\)

Col. A: \(x\)
Col. B: \(y - 90 = (x + 90) - 90 = x\)

Col. A = Col. B

Hence, option C
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Re: x or y-90 [#permalink] New post   21 Feb 2021, 12:23
1
Carcass wrote:
Attachment:
GRE triangle and angles.jpg



Quantity A
Quantity B
x
y-90




Here's another approach....

Since angles on a line must add to 180°, we know that the following angle (in red) must be (180 - y)
Image

This point, we can use the fact that angles in a triangle add to 180° to write: x° + 90° + (180 - y)° = 180°
Simplify: x + 270 - y = 180
Add y to both sides: x + 270 = y + 180
Subtract 270 from both sides: x = y - 90

Answer: C
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Re: x or y-90 [#permalink] New post   21 Feb 2021, 12:27
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I think this solution is a perfect fit for those who are adepts of the church of logic and do not remember the rules of the exterior angles or stuff like that

Brilliant in its simplicity :cool:
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x or y-90 [#permalink] New post   21 Feb 2021, 12:28
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PS: for all the guys in this discussion who are replying to the questions of today...these were for tomorrow NOT today :roll: :blushing:
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x or y-90 [#permalink]
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