Last visit was: 07 Sep 2026, 14:48 It is currently 07 Sep 2026, 14:48
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 06 Sep 2026
Posts: 16,646
Own Kudos:
81,218
 [1]
Given Kudos: 491
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,646
Kudos: 81,218
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
ktjorge
Joined: 31 Mar 2018
Last visit: 23 Sep 2018
Posts: 1
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 07 Sep 2026
Posts: 113,211
Own Kudos:
839,821
 [1]
Given Kudos: 111,359
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,211
Kudos: 839,821
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,727
Own Kudos:
37,261
 [7]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,727
Kudos: 37,261
 [7]
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
christoph


In the figure above, points P and Q lie on the circle with center O. What is the value of s?


A. \(\frac{1}{2}\)

B. \(1\)

C. \(\sqrt{2}\)

D. \(\sqrt{3}\)

E. \(\frac{\sqrt{2}}{2}\)


Attachment:
image.JPG




Cheers,
Brent
User avatar
altairahmad
Joined: 27 Mar 2017
Last visit: 29 Jul 2021
Posts: 258
Own Kudos:
Given Kudos: 406
Location: Saudi Arabia
GMAT 1: 700 Q47 V39
GPA: 3.36
Products:
GMAT 1: 700 Q47 V39
Posts: 258
Kudos: 88
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1 goofy quetion please chetan2u Bunuel Gladiator59 VeritasKarishma

Since we can calculate that PQ (distance) is 2 root 2 and we know that X coordinate of PO is - root 3 then why isnt x coordinate of QO simply the difference between the two values ?
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 06 Sep 2026
Posts: 16,646
Own Kudos:
81,218
 [1]
Given Kudos: 491
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,646
Kudos: 81,218
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
altairahmad
1 goofy quetion please chetan2u Bunuel Gladiator59 VeritasKarishma

Since we can calculate that PQ (distance) is 2 root 2 and we know that X coordinate of PO is - root 3 then why isnt x coordinate of QO simply the difference between the two values ?

I am not sure why you think that PQ is 2*sqrt(2). Also, PQ is not a line parallel to x axis.
User avatar
jabhatta2
Joined: 15 Dec 2016
Last visit: 21 Apr 2023
Posts: 1,250
Own Kudos:
Given Kudos: 188
Posts: 1,250
Kudos: 353
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
altairahmad
1 goofy quetion please chetan2u Bunuel Gladiator59 VeritasKarishma

Since we can calculate that PQ (distance) is 2 root 2 and we know that X coordinate of PO is - root 3 then why isnt x coordinate of QO simply the difference between the two values ?

I am not sure why you think that PQ is 2*sqrt(2). Also, PQ is not a line parallel to x axis.

Hi VeritasKarishma : PQ is 2*\(\sqrt{2}\) because triangle OPQ is an isosceles triangle given 2 sides are equal with a 90 degree in between.

Hence triangle OPQ is a 45-45-90 . Hence the base is 2*\(\sqrt{2}\)

If PQ would have been a straight line parallel to the x axis (I don't think PQ is parallel to the X axis, but if so, could we have done this to find the value of s ?)

PQ = 2*\(\sqrt{2}\) and distance of PZ is \(\sqrt{3}\), then ZQ should be 2*\(\sqrt{2}\) - \(\sqrt{3}\)

(Z is not shown but z is the point where line PQ intersects with the Y axis)

Thoughts ?
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 06 Sep 2026
Posts: 16,646
Own Kudos:
Given Kudos: 491
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,646
Kudos: 81,218
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
altairahmad
1 goofy quetion please chetan2u Bunuel Gladiator59 VeritasKarishma

Since we can calculate that PQ (distance) is 2 root 2 and we know that X coordinate of PO is - root 3 then why isnt x coordinate of QO simply the difference between the two values ?

I am not sure why you think that PQ is 2*sqrt(2). Also, PQ is not a line parallel to x axis.

Hi VeritasKarishma : PQ is 2*\(\sqrt{2}\) because triangle OPQ is an isosceles triangle given 2 sides are equal with a 90 degree in between.

Hence triangle OPQ is a 45-45-90 . Hence the base is 2*\(\sqrt{2}\)

If PQ would have been a straight line parallel to the x axis (I don't think PQ is parallel to the X axis, but if so, could we have done this to find the value of s ?)

PQ = 2*\(\sqrt{2}\) and distance of PZ is \(\sqrt{3}\), then ZQ should be 2*\(\sqrt{2}\) - \(\sqrt{3}\)

(Z is not shown but z is the point where line PQ intersects with the Y axis)

Thoughts ?

Yes, in that case you could have done this. But do not go by the figure given. It could be drawn to misdirect you. Just because PQ looks parallel to X axis, it doesn't mean it is. Redraw it depending on the data you have and using extreme cases.
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 06 Sep 2026
Posts: 4,849
Own Kudos:
9,365
 [1]
Given Kudos: 230
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,849
Kudos: 9,365
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Solution:

O is the center.

OP and OQ are perpendicular to each other with OP=OQ (radius)

Thus in the other quadrant (Quadrant I), the coordinates for P would be same as Q but in the reversed order with signs according to the quadrant
=>(1, sqrt3)

=> s =1 (option b)

Devmitra Sen
GMAT SME
User avatar
DanTheGMATMan
Joined: 02 Oct 2015
Last visit: 07 Sep 2026
Posts: 385
Own Kudos:
Given Kudos: 10
Expert
Expert reply
Posts: 385
Kudos: 278
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­Should be no sweat really. All about using the slope:

User avatar
Riri15
Joined: 07 Feb 2021
Last visit: 12 Jun 2026
Posts: 33
Own Kudos:
Given Kudos: 52
Location: India
Concentration: General Management, Finance
GPA: 9
Products:
Posts: 33
Kudos: 10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How do we know O is the origin?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 07 Sep 2026
Posts: 113,211
Own Kudos:
Given Kudos: 111,359
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,211
Kudos: 839,821
Kudos
Add Kudos
Bookmarks
Bookmark this Post
RIYA1505
How do we know O is the origin?
­Please read the whole thread:

https://gmatclub.com/forum/in-the-figur ... l#p2039161
User avatar
kaustubhkohli12
Joined: 25 Jul 2023
Last visit: 05 Sep 2026
Posts: 78
Own Kudos:
Given Kudos: 4
Products:
Posts: 78
Kudos: 11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
i was able to calculate the radius of 2 and thought of them as mirror image. Could you please make me understand why reverse order. I thought it woud Sq 3 .
Bunuel


In the figure above, points P and Q lie on the circle with center O. What is the value of s?

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\);
Point P in II quadrant \((-\sqrt{3}, 1)\);
Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP);
Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 07 Sep 2026
Posts: 113,211
Own Kudos:
Given Kudos: 111,359
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,211
Kudos: 839,821
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kaustubhkohli12
i was able to calculate the radius of 2 and thought of them as mirror image. Could you please make me understand why reverse order. I thought it woud Sq 3 .


Such questions are no longer tested on the GMAT. So you can ignore it.
   1   2 
Moderator:
Math Expert
113211 posts