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# GRE Math Challenge #20- Geometry Triangle a + b or c + d

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GRE Math Challenge #20- Geometry Triangle a + b or c + d [#permalink]  07 Sep 2014, 06:59
Expert's post
00:00

Question Stats:

66% (01:14) correct 33% (01:38) wrong based on 15 sessions

Quantity A: a + b
Quantity B: c + d

A)The quantity in Column A is greater
B)The quantity in Column B is greater
C)Both are Equal.
D)The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #20- Geometry Triangle a + b or c + d [#permalink]  16 Dec 2017, 06:53
Expert's post
sandy wrote:

Quantity A: a + b
Quantity B: c + d

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

Let's let x = the 3rd angle in the left-side triangle (with angles a and b)

Since angles in a triangle must add to 180 degrees, we can write: a + b + x = 180
Also, notice that angles x and d are on the same line. As such, they must add to 180 degrees. So, we can write: d + x = 180

Since, both equations are set equal to 180, we can write: a + b + x = d + x
Subtract x from both sides to get: a + b = d

Given:
Quantity A: a + b
Quantity B: c + d

Replace a + b with d to get:
Quantity A: d
Quantity B: c + d

Subtract d from both quantities to get:
Quantity A: 0
Quantity B: c

On the GRE, we can assume that all angles in a diagram are greater than 0 degrees.

So, it must be the case that quantity B is greater.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: GRE Math Challenge #20- Geometry Triangle a + b or c + d   [#permalink] 16 Dec 2017, 06:53
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