GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Math Challenge #20- Which is greater a+b or c+d
[#permalink]
07 Sep 2014, 06:59
07 Sep 2014, 06:59
Expert Reply
3
Bookmarks
00:00
Question Stats:
74% (00:47) correct
25% (00:56) wrong based on 181 sessions
Hide Show timer Statistics
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
Show: ::
Attachment:
figure 16.jpg [ 13.88 KiB | Viewed 10277 times ]
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #20- Geometry Triangle a + b or c + d
[#permalink]
16 Dec 2017, 06:53
16 Dec 2017, 06:53
2
1
Bookmarks
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
[#permalink]
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
