GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Nov 2018, 03:32

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

In the xy-coordinate plane, is point R equidistant from

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 177
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Dec 2012, 04:25
11
55
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:05) correct 39% (01:24) wrong based on 1965 sessions

HideShow timer Statistics

In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50661
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Dec 2012, 04:32
20
16
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:

Image

Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.

Attachment:
Equidistant points.png
Equidistant points.png [ 9.68 KiB | Viewed 21932 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 13 Aug 2012
Posts: 96
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 11 Aug 2014, 02:21
7
2
We have to find out whether \(R(x,y)\) is equidistant from the two points mentioned

Using the distance formula
\((x+3)^2+(y+3)^2 = (x-1)^2+(y+3)^2\)
\((x+3)^2 = (x-1)^2\)

So basically we have to prove whether \((x+3)^2 = (x-1)^2\)or not?

1)Substituting\(-1\) in the above equation \((x+3)^2 = (x-1)^2\) results in it being equal
Thus sufficient

2)\(y = -3\)wouldn't help us with this eqn:\((x+3)^2 = (x-1)^2\)
Thus insufficient

Ans is A
General Discussion
Senior Manager
Senior Manager
avatar
Joined: 21 Jan 2010
Posts: 272
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 13 May 2013, 19:17
1
2
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Any point that lie on the perpendicular bisector the line segment with extreme points (-3,-3) and (1,-3) will satisfy this condition. The perpendicular bisector of the line segment is x=-1.

1) this means the point lies on x=-1. Sufficient.
2) This may or may not lie in the middle. The point -1,-3 is the mid point of the line segment but their are other points on the line such as (-2,-3) which doesn't satisfy the requirements. Insufficient.

Hence A.
Intern
Intern
avatar
Joined: 04 Jun 2014
Posts: 47
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 06 Aug 2014, 04:30
Why does the green line go through point -1 ? I couldn't find any chapter which explains this system.. can anyone help?
Manager
Manager
User avatar
B
Joined: 15 Mar 2015
Posts: 111
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 16 May 2015, 08:25
I got really scared seeing this question. But visualizing the coordinate plane made for a much simpler approach.

Once I got the two points mapped out it was obvious that point R had to be on X = -1.

I suppose this was possible because the two points had the same Y coordinates, which allowed for several a straight line at equidistance from the two points. Has anyone got any suggestions or Q's that involves points without this possibility? e.g. A=(1,0) B=(6,6)
_________________

I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12883
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 16 May 2015, 10:32
2
Hi MarkusKarl,

Most Geometry questions have a "visual" component to them, so drawing the "work" involved (the shapes, the graph, etc.) will almost always be beneficial - in that way, you can connect conceptual ideas to real-world examples. GMAT questions in general are almost all pattern-based, so if you find yourself 'stuck' conceptually, you have to think about the rules involved and simplify the logic.

In your example, you name two points that don't share an X or Y co-ordinate, but the concept involved in this prompt applies to your example as well. There WILL be a "line" of co-ordinates that are equidistant from the two points that you named (it's just that the "line" will be a diagonal line and will NOT involve any shared X or Y co-ordinates).

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manager
Manager
User avatar
S
Joined: 04 Dec 2016
Posts: 105
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Feb 2017, 23:45
Bunuel wrote:
Kchaudhary wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y=-3.


Merging topics. Please refer to the discussion above.


Hi Bunnel, in statement 1, how can you consider that y-coordinate of R is 0?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50661
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Feb 2017, 23:55
Kchaudhary wrote:
Bunuel wrote:
Kchaudhary wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y=-3.


Merging topics. Please refer to the discussion above.


Hi Bunnel, in statement 1, how can you consider that y-coordinate of R is 0?


The y-coordinate of R is not necessarily 0. The point is that since x-coordinate of R is -1, then R is on the green line, so no matter what is the y-coordinate, R will be equidistant from the given points.

Image
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 216
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 14 May 2017, 04:10
Hi lou34,

Thats because S1 says so.

S1 says - The X-co-ordinate of Point R is -1. This mean it will have to R WILL have to be ANY point on the green line mentioned by Bunuel.

I hope this clears your question.

lou34 wrote:
Why does the green line go through point -1 ? I couldn't find any chapter which explains this system.. can anyone help?

_________________

My Best is yet to come!

Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 216
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 14 May 2017, 04:55
1
HI Kchaudhary,

Just adding to Bunuel's solution.

Even though the term perpendicular bisector is used, we can infer S1 is sufficient without knowing about it. A quick sketch of the Co-ordinate will be able to get us there.

Consider the attached image. In the Image I have taken an Arbitrary point R on the green line. Named the given two points as A and B. Also labelled O for easier understanding.

What is asked is - AR = BR?. If you notice - Point A, B and R form two Right angles at common point O. In these two Right angled triangle, two sides are equal. AO = AB = 2 (Follows from given co-ordinates) and OR is common to both Right triangles. So, it clearly follows that the third side of both right angles MUST be equal. Meaning AR = BR. This makes S1 sufficient.

I hope this helped :)


Kchaudhary wrote:
Bunuel wrote:
Kchaudhary wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y=-3.


Merging topics. Please refer to the discussion above.


Hi Bunnel, in statement 1, how can you consider that y-coordinate of R is 0?

Attachments

File comment: Named given point A and B for clarity. Assumed Point R on green line
Equidistant points.png
Equidistant points.png [ 18.45 KiB | Viewed 10299 times ]


_________________

My Best is yet to come!

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6526
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 14 May 2017, 09:43
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

From the original condition, we can set up as this question as follows.
The distance between \(R(x,y)\) and \((-3,-3)\) is \(\sqrt{(x+3)^2 + (y+3)^2}\) and the distance between \(R(x,y)\) and \((1,-3)\) is \(\sqrt{(x-1)^2 + (y+3)^2}\).
Thus, we have \(\sqrt{(x+3)^2 + (y+3)^2} = \sqrt{(x-1)^2 + (y+3)^2}\).
Then \(x^2 + 6x + 9 + y^2 + 6y + 9 = x^2 -2x + 1 + y^2 + 6y + 9\).
\(6x + 9 = -2x + 1\)
\(8x = -8\)
\(x = -1\)

We have 2 variables \(x\) and \(y\) and 1 equation, \(x = -1\).
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.

For 1), \(x = -1\), which is equivalent to the condition from the original question. No additional condition is provided. Thus this is not sufficient.

For 2), \(y = -3\). Then the point R is (-1,-3). This is sufficient.

Therefore, the answer is B.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
User avatar
G
Joined: 09 Jan 2016
Posts: 115
GPA: 3.4
WE: General Management (Human Resources)
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 10 Jul 2017, 07:04
MathRevolution wrote:
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

From the original condition, we can set up as this question as follows.
The distance between \(R(x,y)\) and \((-3,-3)\) is \(\sqrt{(x+3)^2 + (y+3)^2}\) and the distance between \(R(x,y)\) and \((1,-3)\) is \(\sqrt{(x-1)^2 + (y+3)^2}\).
Thus, we have \(\sqrt{(x+3)^2 + (y+3)^2} = \sqrt{(x-1)^2 + (y+3)^2}\).
Then \(x^2 + 6x + 9 + y^2 + 6y + 9 = x^2 -2x + 1 + y^2 + 6y + 9\).
\(6x + 9 = -2x + 1\)
\(8x = -8\)
Got...methodical way.
\(x = -1\)

We have 2 variables \(x\) and \(y\) and 1 equation, \(x = -1\).
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.

For 1), \(x = -1\), which is equivalent to the condition from the original question. No additional condition is provided. Thus this is not sufficient.

For 2), \(y = -3\). Then the point R is (-1,-3). This is sufficient.

Therefore, the answer is B.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
Got it..methodical way.
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 08 Aug 2017, 08:10
1
Top Contributor
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Target question: Is point R equidistant from points (-3,-3) and (1,-3)?
This question is a great candidate for rephrasing the target question.

First sketch the two given points
Image

Notice that the point (-1, -3) is equidistant from the two given points. MORE IMPORTANTLY, every point on the line x = -1 is equidistant from the two given points.
Image

So, we can rephrase the target question . . .
REPHRASED target question: Is point R on the line x = -1?

Statement 1: The x coordinate of point R is -1
If the x-coordinate is -1, then point R is definitely on the line x = -1
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: Point R lies on the line y= -3
This tells us nothing about whether or not point R is on the line x = -1?
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
B
Joined: 04 Sep 2018
Posts: 6
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 18 Oct 2018, 04:19
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Key in this question is paying careful attention to the wording: the Q focuses on equidistant however the initially urge is to interpret this as midpoint (which is incorrect).

Since both points have the same y-values, any point that is half-way between their x-values will be equidistant. Hence (1) is sufficient since it tells us what the x-value is. (2) is insufficient alone since it tells us nothing about the x-value. Answer is A.
GMAT Club Bot
Re: In the xy-coordinate plane, is point R equidistant from &nbs [#permalink] 18 Oct 2018, 04:19
Display posts from previous: Sort by

In the xy-coordinate plane, is point R equidistant from

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.