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.
The center of a circle is (10, –3). The point (10, 9) is out
[#permalink]
06 Oct 2018, 15:08
06 Oct 2018, 15:08
1
Expert Reply
3
Bookmarks
00:00
Question Stats:
65% (01:45) correct
34% (02:06) wrong based on 52 sessions
Hide Show timer Statistics
The center of a circle is (10, –3). The point (10, 9) is outside the circle, and the point (6, –3) is inside the circle; neither point is on the circle. If the radius, r, is an integer, how many possible values are there for r?
(A) Seven
(B) Eight
(C) Nine
(D) Ten
(E) Eleven
(A) Seven
(B) Eight
(C) Nine
(D) Ten
(E) Eleven
Re: The center of a circle is (10, –3). The point (10, 9) is out
[#permalink]
15 Nov 2018, 00:24
15 Nov 2018, 00:24
1
Bookmarks
Can I get an explanation?
Re: The center of a circle is (10, –3). The point (10, 9) is out
[#permalink]
19 Nov 2018, 14:11
19 Nov 2018, 14:11
1
Expert Reply
Explanation
Given that (10,9 ) is out side the circle centered at (10, –3). A distance between these two points are:
\(d1 = \sqrt{(10-10)^2+(9-(-3))^2}=12\). So the radius is less than 12.
Similarly, given that (6,-3) is out side the circle centered at (10, –3). A distance between these two points are:
\(d2 = \sqrt{(10-6)^2+(-3-(-3))^2}=4\). So the radius is more than 4.
So the radius is an integer between 4 and 12 hence there are 7 integers between 4 and 12.
Hence A.
Given that (10,9 ) is out side the circle centered at (10, –3). A distance between these two points are:
\(d1 = \sqrt{(10-10)^2+(9-(-3))^2}=12\). So the radius is less than 12.
Similarly, given that (6,-3) is out side the circle centered at (10, –3). A distance between these two points are:
\(d2 = \sqrt{(10-6)^2+(-3-(-3))^2}=4\). So the radius is more than 4.
So the radius is an integer between 4 and 12 hence there are 7 integers between 4 and 12.
Hence A.
