OG 13, DS Diagnostic Exam, Question 36

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nicole.witkowski: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Feb 26, 2015 5:24 am

by nicole.witkowski » Wed Mar 18, 2015 6:00 pm

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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.

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Source: Beat The GMAT — Data Sufficiency | Wed Mar 18, 2015 6:00 pm

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

OG 13, DS Diagnostic Exam, Question 36

by DavidG@VeritasPrep » 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.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » 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

Final Answer: B

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

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » 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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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nicole.witkowski: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Feb 26, 2015 5:24 am

by nicole.witkowski » 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 <i class="em em-joy"></i>.

Thanks again!

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by Jeff@TargetTestPrep » Thu Jun 21, 2018 3:29 pm

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 don'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.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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