Last visit was: 24 Apr 2026, 00:30 It is currently 24 Apr 2026, 00:30
Home
Messages
Tests
Schools
Events
Close
GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,882
 [4]
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,882
 [4]
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 11 Sep 2018, 06:45
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

61% (01:51) correct 39% (01:52) wrong based on 87 sessions

History

Date
Time
Result
Not Attempted Yet
[GMATH practice question]

Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two points which are p units apart. What is the value of p?

(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,006
 [6]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,006
 [6]
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 11 Sep 2018, 07:01
3
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
fskilnik
[GMATH practice question]

Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two points which are p units apart. What is the value of p?

(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4
Show more


when any line or curve intersects vertical or Y-axis, the value of x is 0..
so substitute x as 0
\((x-3)^2 + (y-1)^2 = 13.......(0-3)^2 + (y-1)^2 = 13......(y-1)^2=13-9=4\)
so two cases
1. \(y-1=2....y=3\)
2. \(y-1=-2...y=-1\)

distance = \(p = 3-(-1)=3+1=4\)

E
General Discussion
User avatar
PKN
User avatar
Joined: 01 Oct 2017
Last visit: 11 Oct 2025
Posts: 809
Own Kudos:
1,636
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 809
Kudos: 1,636
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 11 Sep 2018, 07:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fskilnik
[GMATH practice question]

Circle \((x-3)^2 + (y-1)^2 = 13\) ntersects the vertical axis in two points which are p units apart. What is the value of p?

(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4
Show more

On the vertical axis, x=0.
So, the intersection points of the circle with vertical axis are (0,\(y_{1}\)) and (0,\(y_{2}\))

Now, put x=0 in the equation of the given circle to get the values of \(y_{1}\) and ,\(y_{2\)

Hence, \((0-3)^2+(y-1)^2=13\)
or, \(9+(y-1)^2=13\)
or, \((y-1)^2=4\)
Or, y-1=2, y-1=-2
Or, \(y_{1}\)=3, \(y_{2}\)=-1

p=3-(-1)=4

Ans.(E)
User avatar
Princ
User avatar
Joined: 22 Feb 2018
Last visit: 04 May 2025
Posts: 351
Own Kudos:
924
Given Kudos: 34
Posts: 351
Kudos: 924
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 11 Sep 2018, 08:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
OA: E

The equation of circle : \((x-3)^2 + (y-1)^2 = 13\)

Centre of circle :\((3,1)\)

\({Radius}^2 \quad=13\)
Attachment:
Circle.PNG
Circle.PNG [ 14.81 KiB | Viewed 2643 times ]

Using Pythagoras theorem, we get

Required Chord length \(= 2* \sqrt{{{Radius}^2-3^2}}= 2* \sqrt{{13-9}}=2* \sqrt{{4}}=4\)
avatar
Harikamini
avatar
Joined: 11 Mar 2018
Last visit: 22 Nov 2020
Posts: 3
Given Kudos: 283
Posts: 3
Kudos: 0
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 11 Sep 2018, 19:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
fskilnik
[GMATH practice question]

Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two points which are p units apart. What is the value of p?

(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4


when any line or curve intersects vertical or Y-axis, the value of x is 0..
so substitute x as 0
\((x-3)^2 + (y-1)^2 = 13.......(0-3)^2 + (y-1)^2 = 13......(y-1)^2=13-9=4\)
so two cases
1. \(y-1=2....y=3\)
2. \(y-1=-2...y=-1\)

distance = \(p = 3-(-1)=3+1=4\)

E
Show more

In cases like these, to find distance, how will we choose coordinates as Y1 and Y2? Like in this problem, while taking the difference b/w y-coordinates, how have you chosen the y coordinates? Cant it be -1-3=-4?
User avatar
PKN
User avatar
Joined: 01 Oct 2017
Last visit: 11 Oct 2025
Posts: 809
Own Kudos:
1,636
 [1]
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 809
Kudos: 1,636
 [1]
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 11 Sep 2018, 19:59
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Harikamini
Show more

In cases like these, to find distance, how will we choose coordinates as Y1 and Y2? Like in this problem, while taking the difference b/w y-coordinates, how have you chosen the y coordinates? Cant it be -1-3=-4?[/quote]

Hi Harikamini,

Here two point are (0,-1) and (0,3).

Apply distance formula,

1) \(p=\sqrt{(3-(-1))^2+(0-0)^2}\)=4

2) \(p=\sqrt{(-1-3)^2+(0-0)^2}\)=4

Either way , distance is the same.

Hope it helps.
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,882
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,882
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 12 Sep 2018, 06:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fskilnik
[GMATH practice question]

Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two points which are p units apart. What is the value of p?

(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4
Show more

\(? = p\)

\(\left\{ \begin{gathered}\\
{\left( {x - 3} \right)^2} + {\left( {y - 1} \right)^2} = 13 \hfill \\\\
x = 0 \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {y - 1} \right)^2} = 4\,\,\,\,\, \Rightarrow \,\,\,\left\{ \begin{gathered}\\
y - 1 = - 2 \hfill \\\\
\,\,\,\,\,{\text{OR}} \hfill \\\\
y - 1 = 2 \hfill \\ \\
\end{gathered} \right.\)

\(\left\{ \begin{gathered}\\
x = 0\,\,\,;\,\,\,y - 1 = - 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{point}}\,\,\,A = \,\,\left( {0, - 1} \right) \hfill \\\\
\,\,\,\,\,{\text{OR}} \hfill \\\\
x = 0\,\,\,;\,\,\,y - 1 = 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{point}}\,\,B = \left( {0,3} \right) \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\)

\(? = p = {\text{dist}}\left( {A,B} \right) = 4\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two poin 05 Apr 2025, 15:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109802 posts
Krunaal
Tuck School Moderator
853 posts