Last visit was: 27 Apr 2026, 10:10 It is currently 27 Apr 2026, 10:10
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
805+ (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,928
Own Kudos:
811,579
 [13]
Given Kudos: 105,914
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,928
Kudos: 811,579
 [13]
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 05:12
2
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

25% (01:58) correct 75% (01:34) wrong based on 186 sessions

History

Date
Time
Result
Not Attempted Yet
C is a circle with center D and radius 2. E is a circle with center F and radius R. Are there any points that are on both E and C?

(1) The distance from D to F is 1 + R.
(2) R = 3.

Source: Barron's GMAT
ShowHide Answer
Official Answer
C
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,890
 [3]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,890
 [3]
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 06:29
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
C is a circle with center D and radius 2. E is a circle with center F and radius R. Are there any points that are on both E and C?

(1) The distance from D to F is 1 + R.
(2) R = 3.

Source: Barron's GMAT
Show more

Statement 2 is clearly not sufficient.

Per statement 1, distance DF = 1+R , now if R=3, then you do get some common points but if R=0.3, then the smaller circle will lie completely inside the bigger circle , giving you 0 common points. Thus this statement is not sufficient.

Combining, you get R=3, DF=4 and the only case is for the 2 circles to intersect at 2 points, giving you a "yes" for common points between the circle.

Thus C is the correct answer.
avatar
jmikery
avatar
Joined: 09 Nov 2014
Last visit: 13 May 2020
Posts: 50
Own Kudos:
42
Concentration: Finance
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Products:
My Reviews
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Posts: 50
Kudos: 42
C is a circle with center D and radius 2. E is a circle with center F Updated on: 25 Oct 2015, 08:02
Originally posted by jmikery on 25 Oct 2015, 07:19.
Last edited by jmikery on 25 Oct 2015, 08:02, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
So we're given the dimensions of circle C and then we're told circle F has the radius R.

1 tells us that the distance between the two circles is 1+R. If the two circles were separated by more than their radii combined, it means that they don't intersect. However, 1+R is less than the radius of circle C and the radius of Circle F combined (2+R). Therefore, circle C and circle F intersect at 2 points (if 1+R=radius of circle C and circle F, it would be tangent).

SUFFICIENT

2 tells us the value of R but gives us no indication about the location of circle F in relation to circle C.

INSUFFICIENT

Therefore the answer is A

Edit: don't mind me, my answer is wrong
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,890
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,890
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 07:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jmikery
So we're given the dimensions of circle C and then we're told circle F has the radius R.

1 tells us that the distance between the two circles is 1+R. If the two circles were separated by more than their radii combined, it means that they don't intersect. However, 1+R is less than the radius of circle C and the radius of Circle F combined (2+R). Therefore, circle C and circle F intersect at 2 points (if 1+R=radius of circle C and circle F, it would be tangent).

SUFFICIENT

2 tells us the value of R but gives us no indication about the location of circle F in relation to circle C.

INSUFFICIENT

Therefore the answer is A
Show more

IMO, you can not say statement 1 is sufficient without knowing the exact value of R. Case in point R=3 or R=0.3

You will get 2 different answers for the above 2 values of R.
avatar
jmikery
avatar
Joined: 09 Nov 2014
Last visit: 13 May 2020
Posts: 50
Own Kudos:
42
Concentration: Finance
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Products:
My Reviews
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Posts: 50
Kudos: 42
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 07:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Engr2012
jmikery
So we're given the dimensions of circle C and then we're told circle F has the radius R.

1 tells us that the distance between the two circles is 1+R. If the two circles were separated by more than their radii combined, it means that they don't intersect. However, 1+R is less than the radius of circle C and the radius of Circle F combined (2+R). Therefore, circle C and circle F intersect at 2 points (if 1+R=radius of circle C and circle F, it would be tangent).

SUFFICIENT

2 tells us the value of R but gives us no indication about the location of circle F in relation to circle C.

INSUFFICIENT

Therefore the answer is A

IMO, you can not say statement 1 is sufficient without knowing the exact value of R. Case in point R=3 or R=0.3

You will get 2 different answers for the above 2 values of R.
Show more


Here's my POV on it:

No matter what R is, the circles won't touch if the distance between the centers of the two circles is greater than combined radii, R+2, in this case (R being the radius of circle F).

However, statement 1 says that the distance between the centers is R+1, which is shorter than the combined distance of the radii. Therefore, no matter what R is, R+1 is always less than the distance between the two radii and therefore: the circles have to intersect at some point.

Given the two cases: If R=3, the circles are 3+1=4 units apart. The radii are a combined 5 units, therefore the circles intersect.

If R=0.3, the circles are 0.3+1=1.3 units apart. The radii are a combined 2.3 units, therefore the distance is still smaller than the combined length of the radii and thus the circles intersect.

Whatever the value of R, the combined length of the radii will be (R+2)-(R+1)=1 unit larger than the distance between the circles.
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,890
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,890
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 07:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jmikery


Here's my POV on it:

No matter what R is, the circles won't touch if the distance between the centers of the two circles is greater than combined radii, R+2, in this case (R being the radius of circle F).

However, statement 1 says that the distance between the centers is R+1, which is shorter than the combined distance of the radii. Therefore, no matter what R is, R+1 is always less than the distance between the two radii and therefore: the circles have to intersect at some point.

Given the two cases: If R=3, the circles are 3+1=4 units apart. The radii are a combined 5 units, therefore the circles intersect.

If R=0.3, the circles are 0.3+1=1.3 units apart. The radii are a combined 2.3 units, therefore the distance is still smaller than the combined length of the radii and thus the circles intersect.

Whatever the value of R, the combined length of the radii will be (R+2)-(R+1)=1 unit larger than the distance between the circles.
Show more

For R=0.3, the radii will add up to 2.3 but as the centers will only be 1.3 units apart, the smaller circle will completely lie and not tangentially inside the bigger circle. Hence 0 common points.
avatar
jmikery
avatar
Joined: 09 Nov 2014
Last visit: 13 May 2020
Posts: 50
Own Kudos:
42
Concentration: Finance
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Products:
My Reviews
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Posts: 50
Kudos: 42
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 08:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Engr2012
jmikery


Here's my POV on it:

No matter what R is, the circles won't touch if the distance between the centers of the two circles is greater than combined radii, R+2, in this case (R being the radius of circle F).

However, statement 1 says that the distance between the centers is R+1, which is shorter than the combined distance of the radii. Therefore, no matter what R is, R+1 is always less than the distance between the two radii and therefore: the circles have to intersect at some point.

Given the two cases: If R=3, the circles are 3+1=4 units apart. The radii are a combined 5 units, therefore the circles intersect.

If R=0.3, the circles are 0.3+1=1.3 units apart. The radii are a combined 2.3 units, therefore the distance is still smaller than the combined length of the radii and thus the circles intersect.

Whatever the value of R, the combined length of the radii will be (R+2)-(R+1)=1 unit larger than the distance between the circles.

For R=0.3, the radii will add up to 2.3 but as the centers will only be 1.3 units apart, the smaller circle will completely lie and not tangentially inside the bigger circle. Hence 0 common points.
Show more

Ohhh okay, I get it now, I was wrongly attributing the extra +1 to R as part of the radius. Am I correct in saying that we need to know if R>0.5 to confirm if the circles touch? If R is > or = to 0.5, then the center F is at least 1.5 units away from center D and the opposite end of circle E will touch some point of circle C given that it's at least 1.5+0.5=2 units from center D
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,890
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,890
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 08:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jmikery
Engr2012
jmikery


Here's my POV on it:

No matter what R is, the circles won't touch if the distance between the centers of the two circles is greater than combined radii, R+2, in this case (R being the radius of circle F).

However, statement 1 says that the distance between the centers is R+1, which is shorter than the combined distance of the radii. Therefore, no matter what R is, R+1 is always less than the distance between the two radii and therefore: the circles have to intersect at some point.

Given the two cases: If R=3, the circles are 3+1=4 units apart. The radii are a combined 5 units, therefore the circles intersect.

If R=0.3, the circles are 0.3+1=1.3 units apart. The radii are a combined 2.3 units, therefore the distance is still smaller than the combined length of the radii and thus the circles intersect.

Whatever the value of R, the combined length of the radii will be (R+2)-(R+1)=1 unit larger than the distance between the circles.

For R=0.3, the radii will add up to 2.3 but as the centers will only be 1.3 units apart, the smaller circle will completely lie and not tangentially inside the bigger circle. Hence 0 common points.

Ohhh okay, I get it now, I was wrongly attributing the extra +1 to R as part of the radius. Am I correct in saying that we need to know if R>0.5 to confirm if the circles touch? If R is > or = to 0.5, then the center F is at least 1.5 units away from center D and the opposite end of circle E will touch some point of circle C
Show more

Yes, exactly. You need R\(\geq\) 0.5 (and not just R>0.5 as R=0.5 will also give you 1 common points, the point of tangency) is what you need to be absolutely sure. No matter what value of R you assume > 0.5, it will always lead to 2 intersecting circles as the distance between the centers will be 1+R. Additionally, although statement 2 wasnt sufficient on its own, it should provide you the hint that something is going on with this particular value of R=3.

In GMAT DS questions, both statements should lead to the same unique answer. You can not have 2 contradictory unique answers.

Hope this helps.
avatar
jmikery
avatar
Joined: 09 Nov 2014
Last visit: 13 May 2020
Posts: 50
Own Kudos:
42
Concentration: Finance
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Products:
My Reviews
Schools: Anderson '19 (A$) Wharton '19 (D) Kellogg '19 (A) HBS '19 (D) Booth '19 (D) CBS '19 (D) Duke '19 (WL)
GMAT 1: 760 Q51 V41
Posts: 50
Kudos: 42
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 08:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Engr2012
jmikery
Engr2012

For R=0.3, the radii will add up to 2.3 but as the centers will only be 1.3 units apart, the smaller circle will completely lie and not tangentially inside the bigger circle. Hence 0 common points.

Ohhh okay, I get it now, I was wrongly attributing the extra +1 to R as part of the radius. Am I correct in saying that we need to know if R>0.5 to confirm if the circles touch? If R is > or = to 0.5, then the center F is at least 1.5 units away from center D and the opposite end of circle E will touch some point of circle C

Yes, exactly. R>0.5 is what you need to be absolutely sure. No matter what value of R you assume > 0.5, it will always lead to 2 intersecting circles as the distance between the centers will be 1+R. Additionally, although statement 2 wasnt sufficient on its own, it should provide you the hint that something is going on with this particular value of R=3.

In GMAT DS questions, both statements should lead to the same unique answer. You can not have 2 contradictory unique answers.

Hope this helps.
Show more

Awesome, thanks for the explanation!
User avatar
VikashAlex
User avatar
Joined: 22 Sep 2014
Last visit: 05 Jan 2016
Posts: 28
Own Kudos:
289
Given Kudos: 12
Posts: 28
Kudos: 289
C is a circle with center D and radius 2. E is a circle with center F 25 Oct 2015, 08:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
C is a circle with center D and radius 2. E is a circle with center F and radius R. Are there any points that are on both E and C?

(1) The distance from D to F is 1 + R.
(2) R = 3.

Source: Barron's GMAT
Show more

I will go with option C.

statement 1 : if D = 2R < 1 then the answer will be NO. And if D = 2R >=1 then the answer is Yes. There is no definite answer , and hence not sufficient.
Statement 2 : This is clearly not sufficient. These two circle may intersect or may be independent completely.

combination: from statement one we have to check whether 2R< 1 ? And from statement 2 we have R = 3 i.e 2R = 6 and Is 6 < 1. The answer is no. Hence the circle will intersect. Correct option C.
avatar
avikroy
avatar
Joined: 04 Jun 2010
Last visit: 26 Mar 2020
Posts: 94
Own Kudos:
34
Given Kudos: 264
Location: India
GMAT 1: 660 Q49 V31
GPA: 3.22
GMAT 1: 660 Q49 V31
Posts: 94
Kudos: 34
C is a circle with center D and radius 2. E is a circle with center F 02 Aug 2019, 03:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jmikery
Engr2012
jmikery
So we're given the dimensions of circle C and then we're told circle F has the radius R.

1 tells us that the distance between the two circles is 1+R. If the two circles were separated by more than their radii combined, it means that they don't intersect. However, 1+R is less than the radius of circle C and the radius of Circle F combined (2+R). Therefore, circle C and circle F intersect at 2 points (if 1+R=radius of circle C and circle F, it would be tangent).

SUFFICIENT

2 tells us the value of R but gives us no indication about the location of circle F in relation to circle C.

INSUFFICIENT

Therefore the answer is A

IMO, you can not say statement 1 is sufficient without knowing the exact value of R. Case in point R=3 or R=0.3

You will get 2 different answers for the above 2 values of R.


Here's my POV on it:

No matter what R is, the circles won't touch if the distance between the centers of the two circles is greater than combined radii, R+2, in this case (R being the radius of circle F).

However, statement 1 says that the distance between the centers is R+1, which is shorter than the combined distance of the radii. Therefore, no matter what R is, R+1 is always less than the distance between the two radii and therefore: the circles have to intersect at some point.

Given the two cases: If R=3, the circles are 3+1=4 units apart. The radii are a combined 5 units, therefore the circles intersect.

If R=0.3, the circles are 0.3+1=1.3 units apart. The radii are a combined 2.3 units, therefore the distance is still smaller than the combined length of the radii and thus the circles intersect.

Whatever the value of R, the combined length of the radii will be (R+2)-(R+1)=1 unit larger than the distance between the circles.
Show more


I guess this solution works for circles external to each other......................
User avatar
gmatstuff123
User avatar
Joined: 17 May 2023
Last visit: 14 Nov 2024
Posts: 60
Own Kudos:
11
Given Kudos: 85
Location: India
Concentration: Human Resources, Organizational Behavior
Schools: ISB '25 (A)
GMAT 1: 680 Q48 V35
GPA: 3.43
Schools: ISB '25 (A)
GMAT 1: 680 Q48 V35
Posts: 60
Kudos: 11
C is a circle with center D and radius 2. E is a circle with center F 30 Sep 2023, 22:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ENGRTOMBA2018
Bunuel
C is a circle with center D and radius 2. E is a circle with center F and radius R. Are there any points that are on both E and C?

(1) The distance from D to F is 1 + R.
(2) R = 3.

Source: Barron's GMAT

Statement 2 is clearly not sufficient.

Per statement 1, distance DF = 1+R , now if R=3, then you do get some common points but if R=0.3, then the smaller circle will lie completely inside the bigger circle , giving you 0 common points. Thus this statement is not sufficient.

Combining, you get R=3, DF=4 and the only case is for the 2 circles to intersect at 2 points, giving you a "yes" for common points between the circle. I mean they might not touch each other's edges but they will have common points inside the circle right?

Thus C is the correct answer.
Show more


This could be a very silly doubt, but when another circle is completely inside the circle, then automatically don't you get common points on both circles ?
Moderators:
Bunuel
Math Expert
109928 posts
kingbucky
498 posts
Gmat860sanskar
212 posts