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DC vs AB
[#permalink]
26 Sep 2018, 15:15
26 Sep 2018, 15:15
Expert Reply
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Question Stats:
42% (01:41) correct
57% (01:37) wrong based on 134 sessions
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Quantity A |
Quantity B |
DC |
AB |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
DC vs AB
[#permalink]
30 Sep 2018, 14:12
30 Sep 2018, 14:12
1
2
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sandy wrote:
Attachment:
Capture.JPG
Quantity A |
Quantity B |
DC |
AB |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Since angles on a line must add to 180°, we know that ∠ABD + 2x = 180°
So, ∠ABD = 180° - 2x (see above)
Next, we'll let y = ∠ADB
Since angles in a triangle add to 180°, we can write: x + y + (180 - 2x) = 180°
Simplify: y - x + 180 = 180
Subtract 180 from both sides: y - x = 0
So, it must be the case that y = x
Since we now know that ∆ABD has two equal angles (each measuring x°), we know that side AB = side BD
Finally, since ∆BCD has two equal angles (each measuring 2x°), we know that side BD = side DC
We now know that AB = BD and BD = DC
So, we can write: AB = BD = DC, which means AB = DC
Answer: C
Cheers,
Brent
Re: DC vs AB
[#permalink]
21 May 2024, 16:22
21 May 2024, 16:22
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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