|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 18 Jun 2011
Posts: 58
Followers: 1
Kudos [?]:
27
[1] , given: 0
|
A rectangle is plotted on the standard coordinate plane [#permalink]
 19 Jun 2011, 23:18
1
This post received
KUDOS
Question Stats:
25% (01:20) correct
75% (00:51) wrong based on 1 sessions
A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (0,6). If the coordinates of all vertices of the rectangle are non-negative integers, what are the coordinates of the other two vertices? (1) The distance between the origin and one of the other vertices is 10 units. (2) The distance between the origin and one of the other vertices is 8 units.
|
|
|
|
|
|
|
Senior Manager
Joined: 30 Aug 2009
Posts: 296
Location: India
Concentration: General Management
Followers: 2
Kudos [?]:
65
[1] , given: 5
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 04:56
1
This post received
KUDOS
guygmat wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (0,6). If the coordinates of all vertices of the rectangle are non-negative integers, what are the coordinates of the other two vertices?
(1) The distance between the origin and one of the other vertices is 10 units.
(2) The distance between the origin and one of the other vertices is 8 units. stmnt 1- if the other coordinate is on y-axis we have coordinate as (0,10) and (6,10). Suff but if the distance of 10 is b/w origin and diagonally opposite vertices then we get different coordinates. hence statement 1 becomes insufficient stmnt2 - Same reasoning as above makes statement 2 as insufficient. taking together we can conclude that distance of 10 is b/w origin and diagonally opposite vertices and distance of 8 lies on y axis. So we can find the values of the other vertices. hence together they are sufficient. Ans C
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
655
[0], given: 376
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 05:18
guygmat wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (0,6). If the coordinates of all vertices of the rectangle are non-negative integers, what are the coordinates of the other two vertices?
(1) The distance between the origin and one of the other vertices is 10 units.
(2) The distance between the origin and one of the other vertices is 8 units. What if one of the statements were: (1) The distance between the origin and one of the other vertices is 6 units.
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 26 Oct 2010
Posts: 19
Followers: 0
Kudos [?]:
8
[0], given: 3
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 07:54
fluke wrote: What if one of the statements were:
(1) The distance between the origin and one of the other vertices is 6 units. Well in that case St 1 gives us no new information, since we know its a rectangle, we already know one side is of 6 units, the other side is either bigger or smaller than 6. So St 1 is insuff. We already know St 2 is insuff. But this time both together are also insuff since we don't know what 8 represents (the diagonal or one of the perpendicular sides). Is my analysis valid?
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
655
[0], given: 376
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 08:03
microair wrote: fluke wrote: What if one of the statements were:
(1) The distance between the origin and one of the other vertices is 6 units. Well in that case St 1 gives us no new information, since we know its a rectangle, we already know one side is of 6 units, the other side is either bigger or smaller than 6. So St 1 is insuff. We already know St 2 is insuff. But this time both together are also insuff since we don't know what 8 represents (the diagonal or one of the perpendicular sides). Is my analysis valid? Actually, st1 is sufficient in this case. A square is a specialized rectangle. And it's only 6 units away from origin, thus it is directly above it.
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Instructor
Joined: 24 Jun 2008
Posts: 973
Location: Toronto
Followers: 167
Kudos [?]:
443
[0], given: 3
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 10:51
fluke wrote: guygmat wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (0,6). If the coordinates of all vertices of the rectangle are non-negative integers, what are the coordinates of the other two vertices?
(1) The distance between the origin and one of the other vertices is 10 units.
(2) The distance between the origin and one of the other vertices is 8 units. What if one of the statements were: (1) The distance between the origin and one of the other vertices is 6 units. You could interpret that statement in two different ways, so I think the question becomes ambiguous. That statement is only sufficient if by 'one of the other vertices' you mean 'one of the vertices not mentioned in the question'. In that case, we must have a square, which is of course a type of rectangle. But, if by 'one of the other vertices' you mean 'one of the other vertices of the rectangle' (which is how I'd interpret it), then it's not sufficient; we already know that (0,0) and (0,6) are six apart.
_________________
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.
Private GMAT Tutor based in Toronto
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
655
[0], given: 376
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 11:06
IanStewart wrote: fluke wrote: guygmat wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (0,6). If the coordinates of all vertices of the rectangle are non-negative integers, what are the coordinates of the other two vertices?
(1) The distance between the origin and one of the other vertices is 10 units.
(2) The distance between the origin and one of the other vertices is 8 units. What if one of the statements were: (1) The distance between the origin and one of the other vertices is 6 units. You could interpret that statement in two different ways, so I think the question becomes ambiguous. That statement is only sufficient if by 'one of the other vertices' you mean 'one of the vertices not mentioned in the question'. In that case, we must have a square, which is of course a type of rectangle. But, if by 'one of the other vertices' you mean 'one of the other vertices of the rectangle' (which is how I'd interpret it), then it's not sufficient; we already know that (0,0) and (0,6) are six apart. Good that pointed out the ambiguity. I was just trying to create a situation where knowing one of the vertices of the rectangle that doesn't lie on the x-axis can still suffice to answer the question. So, I rephrase my statement. (1) The distance between the origin and one of the rectangle's other vertices that don't lie on the x-axis is 6 units.
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Instructor
Joined: 24 Jun 2008
Posts: 973
Location: Toronto
Followers: 167
Kudos [?]:
443
[0], given: 3
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 11:13
fluke wrote: [
I was just trying to create a situation where knowing one of the vertices of the rectangle that doesn't lie on the x-axis can still suffice to answer the question. I think it's a more interesting question that way, and a more GMAT-like one as well - if one of the statements turns out to be sufficient alone. If, in your rephrased statement, you make the distance any number less than 6, then there would be no ambiguity and the statement would be sufficient alone, since then the distance cannot possibly be the length of the diagonal.
_________________
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.
Private GMAT Tutor based in Toronto
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
655
[0], given: 376
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 11:17
IanStewart wrote: fluke wrote: [
I was just trying to create a situation where knowing one of the vertices of the rectangle that doesn't lie on the x-axis can still suffice to answer the question. I think it's a more interesting question that way, and a more GMAT-like one as well - if one of the statements turns out to be sufficient alone. If, in your rephrased statement, you make the distance any number less than 6, then there would be no ambiguity and the statement would be sufficient alone, since then the distance cannot possibly be the length of the diagonal. Got the point!!! thanks Ian.
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 16 Mar 2011
Posts: 180
Followers: 1
Kudos [?]:
10
[0], given: 13
|
Re: Coordinate Geometry Problem [#permalink]
20 Jun 2011, 11:21
Hhmm I think C, statement 1 and 2 could both refer to either the diagonal distance between the vertices or just the sides.. Combined, 10 is bigger so it must be the diagonal leaving 8 for the sides, from there you can figure out the coordinates..
|
|
|
|
|
|
Manager
Joined: 26 Dec 2011
Posts: 119
Followers: 1
Kudos [?]:
6
[0], given: 17
|
Re: A rectangle is plotted on the standard coordinate plane, [#permalink]
23 Jun 2012, 21:58
Am I right in stating that when the question means that the distance between one of the vertices and origin, it may be construed as that distance between the origin and diagonal/ length of the side...??
Because, then C makes sense and diagonally opposite would be 10, 6 and the other would be 8,0.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11532
Followers: 1795
Kudos [?]:
9552
[1] , given: 826
|
Re: A rectangle is plotted on the standard coordinate plane [#permalink]
24 Jun 2012, 05:00
1
This post received
KUDOS
Answer to this question is B, not C. A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (0,6). If the coordinates of all vertices of the rectangle are non-negative integers, what are the coordinates of the other two vertices?Notice that we are told that the coordinates of all vertices of the rectangle are non-negative integers. That basically means that the rectangle is plotted entirely in the first quadrant: one vertex at the origin (0, 0), another on Y-axis (0, 6), third one somewhere in the first quadrant (x, 6) and the fourth vertex on the X-axis (x, 0). (1) The distance between the origin and one of the other vertices is 10 units. 10 units is either the length of the other side or the length of the diagonal. The vertices could be: (0, 0), (0, 6), (10, 6) and (10, 0) OR (0, 0), (0, 6), (8, 6) and (8, 0), in this case the distance of 10 units is the distance between (0, 0) and (6, 8). Not sufficient. (2) The distance between the origin and one of the other vertices is 8 units. Now, 8 units can not be the length of the diagonal since in this case the coordinates of the other two vertices won't be integers: if the diagonal=8, then the length of the other side of the rectangle is \sqrt{8^2-6^2}=2\sqrt{7}, so the coordinates of the other two vertices are: (2\sqrt{7}, \ 6) and (2\sqrt{7}, \ 0). So, 8 units must be the length of the side, therefore the vertices are (0, 0), (0, 6), (8, 6) and (8, 0). Sufficient. Answer: B. Hope it's clear.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Senior Manager
Joined: 06 Aug 2011
Posts: 262
Followers: 2
Kudos [?]:
22
[0], given: 42
|
Re: A rectangle is plotted on the standard coordinate plane [#permalink]
21 Sep 2012, 04:50
Bunuel..but official ans is c??
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11532
Followers: 1795
Kudos [?]:
9552
[1] , given: 826
|
Re: A rectangle is plotted on the standard coordinate plane [#permalink]
21 Sep 2012, 04:54
1
This post received
KUDOS
|
|
|
|
|
|
|
Re: A rectangle is plotted on the standard coordinate plane
[#permalink]
21 Sep 2012, 04:54
|
|
|
|
|
|
|
|
|
|
|
close
