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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If AD = BC, find the value of x
[#permalink]
Updated on: 02 Apr 2022, 10:50
Updated on: 02 Apr 2022, 10:50
5
23
Bookmarks
00:00
Question Stats:
26% (02:42) correct
73% (02:22) wrong based on 45 sessions
Hide Show timer Statistics
AD = BC
∠ABC = 90°
Quantity A |
Quantity B |
x |
30 |
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.
Originally posted by GreenlightTestPrep on 28 Jan 2021, 09:55.
Last edited by Carcass on 02 Apr 2022, 10:50, edited 1 time in total.
Last edited by Carcass on 02 Apr 2022, 10:50, edited 1 time in total.
Fixed timer
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If AD = BC, find the value of x
[#permalink]
28 Jan 2021, 10:02
28 Jan 2021, 10:02
4
4
Bookmarks
GreenlightTestPrep wrote:
AD = BC
∠ABC = 90°
Quantity A |
Quantity B |
x |
30 |
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.
Important: Even though we aren't provided any angles, we can still label many of the angles in the diagram.
Since angles on a line must add to 180°, ∠ADB = (180 - 2x)°
Since angles in ∆ADB must add to 180°, ∠BAD = x°
Since ∆ADB has two equal angles (of x°), the triangle is an isosceles triangle which means side BD = side AD
Since side BD = side BC, we have an isosceles triangle which means ∠DCB = 2x°, and since all angles must add to 180 degrees, we can see that ∠DBC = (180 - 4x)°
Finally, since ∠ABC = 90°, we can write: x + (180 - 4x)° = 90°
Simplify: 180 - 3x = 90
Solve: x = 30
We get:
QUANTITY A: 30
QUANTITY B: 30
Answer: C
Cheers,
Brent
General Discussion
Re: If AD = BC, find the value of x
[#permalink]
28 Jan 2021, 11:24
28 Jan 2021, 11:24
2
Hi, I am a bit confused here, hope you guys can help :
What if I start with angle DBC = 90-x, then
2x+90-x+dcb = 180
dcb = 90-x
this will make DB=DC
and then if i continue, I get x = 60
Please help guys
What if I start with angle DBC = 90-x, then
2x+90-x+dcb = 180
dcb = 90-x
this will make DB=DC
and then if i continue, I get x = 60
Please help guys
