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Register now and save up to $200 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 • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 • 5 Day FREE Trial Study Smarter, Not Harder 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code ## OG 13, DS Diagnostic Exam, Question 36 This topic has 3 expert replies and 1 member reply nicole.witkowski Junior | Next Rank: 30 Posts Joined 26 Feb 2015 Posted: 10 messages #### OG 13, DS Diagnostic Exam, Question 36 Wed Mar 18, 2015 6:00 pm 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 ceilidh.erickson GMAT Instructor Joined 04 Dec 2012 Posted: 1778 messages Followed by: 228 members Upvotes: 1443 Top Reply Fri Feb 23, 2018 11:11 am 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 Harvard Graduate School of 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 DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 119 members Upvotes: 1153 GMAT Score: 770 Top Reply Wed Mar 18, 2015 7:26 pm 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

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9301 messages
Followed by:
478 members
2867
GMAT Score:
800
Mon Feb 19, 2018 8:39 pm
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

nicole.witkowski Junior | Next Rank: 30 Posts
Joined
26 Feb 2015
Posted:
10 messages
Fri Feb 23, 2018 7:04 pm
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!

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