• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## OG 13, DS Diagnostic Exam, Question 36 ##### This topic has 4 expert replies and 1 member reply ## OG 13, DS Diagnostic Exam, Question 36 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Hi everyone, In OG 13's Diagnostic Test, under the Data Sufficiency portion, question 36 reads: "If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?" 1) The length of line segment XY is 3 2) The length of line segment OY is 1.5 OG Answer - B I answered D solely because the question stem stated that X lay inside the circle, not inside or on the circle. For statement one, I assumed that because point X lay inside the circle, its co-ordinates could only be some combination of -1, 0 and 1 (ex: (-1,0), (0,1), (1,1), (1,-1) etc...). I didn't bother including 2 or -2 as co-ordinate possibilities because I believed that the question provided me with all the details/restrictions I needed and that I could not ASSUME point X lay ON the circle as well. So if a future question doesn't specify otherwise, is it safe to assume that if a point lies "inside" some shape, it actually means that it lies "inside or on" the shape? If so, can someone please explain why? Since we're obviously not allowed to defend our answer choices on this exam, I need to be sure I understand any implicit assumptions a question stem contains. Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply There's no need to consider a scenario when 'X' is on the circumference. If we know that the radius of the circle is 2, the diameter is 4. Because XY = 3, which is slightly smaller than the diameter, you could have a scenario in which Y lies within the circle. See here: Or you could have a scenario in which Y is outside the circle. See here: Because we can get both a 'YES' and a 'NO' to the question, we've proven that the statement is not sufficient. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

GMAT Instructor
Joined
04 Dec 2012
Posted:
1996 messages
Followed by:
237 members
1443
nicole.witkowski wrote:
I answered D solely because the question stem stated that X lay inside the circle, not inside or on the circle. For statement one, I assumed that because point X lay inside the circle, its co-ordinates could only be some combination of -1, 0 and 1 (ex: (-1,0), (0,1), (1,1), (1,-1) etc...). I didn't bother including 2 or -2 as co-ordinate possibilities because I believed that the question provided me with all the details/restrictions I needed and that I could not ASSUME point X lay ON the circle as well.
You're making a HUGE (and very common) assumption here: you're only considering integers.

Nowhere in the problem does it say that X and Y must have integer coordinates. In fact, on geometry problems (especially coordinate plane problems) we should always consider non-integer possibilities (esp. sqrt(2), sqrt(3), etc), unless the problem explicitly specifies integers.

As David and Rich have demonstrated, if you drew a picture and considered non-integers, you could easily have gotten this one right!

_________________

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

### GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10023 messages
Followed by:
494 members
2867
GMAT Score:
800
Hi All,

We're told that X and Y are points in a plane and X lies inside the circle C with center O and radius 2. We're asked if Y lies inside circle C. This is a YES/NO question and we can solve it with a bit of logic, a picture (if needed) and not much math at all.

To start, you mind find it helpful to draw a quick picture of a circle around the Origin on a graph. We're told that the circle has a radius of 2.

1) The length of line segment XY is 3.

We're told that X is somewhere in this circle, but we don't know exactly where. In that same way, we don't know exactly where the Y is. Since the radius is 2, the diameter of the circle is 4. Thus, a line-segment with a length of 3 COULD be inside the circle - so the answer to the question would be YES. However, if we drew a line from X to the nearest side of the circle (and through the circle), then the Y COULD be outside the circle - so the answer to the question would be NO.
Fact 1 is INSUFFICIENT

2) The length of line segment OY is 1.5

Since the radius of the circle is 2, any line segment that starts at the Origin and is only 1.5 in length MUST be inside the circle (since 1.5 is less than the radius of 2). Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

Junior | Next Rank: 30 Posts
Joined
26 Feb 2015
Posted:
10 messages
I've received a couple of replies to this question, and I do hope it helps others who are preparing for the GMAT.

But I've already written and "passed" the GMAT. Actually, I recently graduated from an MBA program, so I am no longer in need of assistance on this problem .

Thanks again!

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Apr 2015
Posted:
1461 messages
Followed by:
17 members
39
nicole.witkowski wrote:
Hi everyone,

In OG 13's Diagnostic Test, under the Data Sufficiency portion, question 36 reads:

"If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?"

1) The length of line segment XY is 3
2) The length of line segment OY is 1.5
Statement One Alone:

The length of line segment XY is 3.

We donâ€™t have enough information to determine whether Y lies inside circle C. For example, if X is a point near the circumference of the circle, Y could be either inside or outside of the circle and be 3 units away from X. Statement one alone is not sufficient.

Statement Two Alone:

The length of line segment OY is 1.5.

Since the radius of the circle is 2 and O is the center, we see that OY is less than 2, so Y must be inside circle C. Statement two alone is sufficient.

_________________
Jeffrey Miller Head of GMAT Instruction

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

### Top First Responders*

1 Jay@ManhattanReview 67 first replies
2 Brent@GMATPrepNow 53 first replies
3 fskilnik@GMATH 49 first replies
4 GMATGuruNY 32 first replies
5 Rich.C@EMPOWERgma... 29 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

107 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 Max@Math Revolution

Math Revolution

90 posts
4 Jay@ManhattanReview

Manhattan Review

78 posts
5 GMATGuruNY

The Princeton Review Teacher

77 posts
See More Top Beat The GMAT Experts