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GRE Math Challenge #20- Which is greater a+b or c+d
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07 Sep 2014, 06:59
07 Sep 2014, 06:59
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Question Stats:
74% (00:47) correct
25% (00:56) wrong based on 181 sessions
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Quantity A |
Quantity B |
\(a+b\) |
\(c+d\) |
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
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Re: GRE Math Challenge #20- Geometry Triangle a + b or c + d
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16 Dec 2017, 06:53
16 Dec 2017, 06:53
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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.
Answer: B
Cheers,
Brent
Re: GRE Math Challenge #20- Which is greater a+b or c+d
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03 Jul 2020, 18:57
03 Jul 2020, 18:57
2
The question asks for a comparison between a+b and c+d.
There's a property of triangles (Exterior angle theorem) that says that the sum of two interior angles is equal to the non-adjacent external angle.
Consequently, a+b=d.
Just with this condition, even with if c's value is the least different that 0 (It's known that in triangles there are no negative quantities), the sum c+d will always be greater than a+b.
Answer: B
There's a property of triangles (Exterior angle theorem) that says that the sum of two interior angles is equal to the non-adjacent external angle.
Consequently, a+b=d.
Just with this condition, even with if c's value is the least different that 0 (It's known that in triangles there are no negative quantities), the sum c+d will always be greater than a+b.
Answer: B
