It is currently 17 Oct 2017, 04:47

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

Events & Promotions in June
Open Detailed Calendar

In the xy-plane, point O is located at the origin, point A has coordin

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

Hide Tags

2 KUDOS received
Intern
Intern
avatar
Joined: 06 May 2012
Posts: 9

Kudos [?]: 10 [2], given: 0

In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 02 Jul 2016, 09:38
2
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

50% (01:52) correct 50% (02:15) wrong based on 157 sessions

HideShow timer Statistics

In the xy-plane, point O is located at the origin, point A has coordinates (p,q), and point B has coordinates (r,0). If p, q, and r are all positive values and AO > AB, is the area of triangular region ABO less than 12 ?

(1) r = 7

(2) p = 4 and q = 3
[Reveal] Spoiler: OA

Kudos [?]: 10 [2], given: 0

Intern
Intern
avatar
Joined: 06 May 2012
Posts: 9

Kudos [?]: 10 [0], given: 0

Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 02 Jul 2016, 09:51
I am getting D.

St 2 is correct for obvious reasons.
St 1 Given r=7
Also, AO>AB

[(P-0)^2+(Q-0)^2]^1/2>[(P-R)^2+Q^2]^1/2
P^2+Q^2>(P-R)^2+Q^2
P^2>(P-R)^2
P^2>P^2+R^2-2PR
2PR>R^2
2P>R
2P>7
P>3.5
Area(AOB)= 1/2b.h
=1/2X7XP
since P>3.5
Area(AOB)>12.25
Thus A is sufficient.


Let me know what mistake I made..

Kudos [?]: 10 [0], given: 0

Intern
Intern
User avatar
B
Joined: 02 Jul 2016
Posts: 22

Kudos [?]: 1 [0], given: 36

Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 02 Jul 2016, 10:16
Saurabh I think you considered the height of the triangle in incorrectly


Sent from my iPhone using GMAT Club Forum mobile app

Kudos [?]: 1 [0], given: 36

Intern
Intern
User avatar
B
Joined: 02 Jul 2016
Posts: 22

Kudos [?]: 1 [0], given: 36

Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 02 Jul 2016, 10:20
By using Heron's Formula
Area of triangle is 1/2(x1(y2-y3)+x2(y3-y1)+x3(y1-y2))
Consider statement 1 which is not enough
Now consider statement 2 which still does not gives us all three coordinates of vertices.
Thus, C is the answer.


Sent from my iPhone using GMAT Club Forum mobile app

Kudos [?]: 1 [0], given: 36

Intern
Intern
avatar
Joined: 02 Jan 2015
Posts: 5

Kudos [?]: [0], given: 3

Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 02 Jul 2016, 11:56
comprehensive soln anyone folks?

Kudos [?]: [0], given: 3

Manager
Manager
User avatar
Joined: 03 Apr 2016
Posts: 103

Kudos [?]: 15 [0], given: 31

Location: India
Concentration: Operations, General Management
GMAT 1: 720 Q50 V37
WE: Analyst (Computer Software)
GMAT ToolKit User
Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 07 Jul 2016, 23:31
1
This post was
BOOKMARKED
Ans should be B.
The most important clue that we have is AO>AB
This restricts how far r can go.
AO from coordinates will be 5 units in length. So maximum value of AB < 5.
And all points are in first quadrant only so maximum value of r can be 8 (excluding 8).
So maximum area of tringle could be
1/2 * 8 * 3 = 12 (excluding 12)
Let me know if its not clear or if I am wrong somewhere. :)

Sent from my SM-N910H using Tapatalk

Kudos [?]: 15 [0], given: 31

Manager
Manager
User avatar
Joined: 03 Apr 2016
Posts: 103

Kudos [?]: 15 [0], given: 31

Location: India
Concentration: Operations, General Management
GMAT 1: 720 Q50 V37
WE: Analyst (Computer Software)
GMAT ToolKit User
Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 07 Jul 2016, 23:56
To add to my solution above,
Algebraically we can show how r should be less than 8.
We know that length of a line between two coordinates is equal to sqrt of ( (x1-x2)^2 + (y1-y2)^2 )
So from AO > AB we get:
AO^2 > AB^2 (since both sides are positive )
So (4-0)^2 + (3-0)^2 > (r-4)^2 + (3-0)^2
Simplifying :
(r-4)^2 < 16
This gives us 0 < r < 8

Let me know if its not clear or if I am wrong somewhere. :)



Sent from my SM-N910H using Tapatalk

Kudos [?]: 15 [0], given: 31

CEO
CEO
User avatar
G
Joined: 17 Jul 2014
Posts: 2604

Kudos [?]: 392 [0], given: 182

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 25 Oct 2016, 07:20
saurabh87 wrote:
In the xy-plane, point O is located at the origin, point A has coordinates (p,q), and point B has coordinates (r,0). If p, q, and r are all positive values and AO > AB, is the area of triangular region ABO less than 12 ?

(1) r = 7

(2) p = 4 and q = 3


oh wow...took 3 minutes just to make sure i don't need 1...
a truly 700 level question

Kudos [?]: 392 [0], given: 182

Intern
Intern
avatar
B
Joined: 21 Jan 2017
Posts: 20

Kudos [?]: 1 [0], given: 7

Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 15 Jul 2017, 07:28
shashanksagar wrote:
Ans should be B.
The most important clue that we have is AO>AB
This restricts how far r can go.
AO from coordinates will be 5 units in length. So maximum value of AB < 5.
And all points are in first quadrant only so maximum value of r can be 8 (excluding 8).
So maximum area of tringle could be
1/2 * 8 * 3 = 12 (excluding 12)
Let me know if its not clear or if I am wrong somewhere. :)

Sent from my SM-N910H using Tapatalk



Hey! Why is it excluding 8 here? maximum value of r can be 8 rite? area can also be 12, which is the maximum. Pls throw some light here!

Thanks,
Uma

Kudos [?]: 1 [0], given: 7

Expert Post
3 KUDOS received
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2677

Kudos [?]: 1722 [3], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 15 Jul 2017, 09:01
3
This post received
KUDOS
Expert's post
saurabh87 wrote:
In the xy-plane, point O is located at the origin, point A has coordinates (p,q), and point B has coordinates (r,0). If p, q, and r are all positive values and AO > AB, is the area of triangular region ABO less than 12 ?

(1) r = 7

(2) p = 4 and q = 3


Detailed solution.

We can clearly see the following things from the question statement:

1. All p,q,r >0
2. As AO > AB

\(p^2 + q^2 > (p-r)^2 + q^2\)

Giving you, \(2*p*r > r^2\)

2 cases possible -->

Case 1: \(2pr-r^2 > 0\) ---> r>0 and 2p>r or

Case 2:\(2pr-r^2 >0\) ---> r<0 and 2p<r . BUT this goes against #1 above as r MUST BE > 0. Hence ignore this case.

Thus the only possible set of values are r>0 and 2p>r

3. Area of Triangle ABO = 0.5*r*q

The question asks, is 0.5*r*q<12 or is r*q<24

Per Statement 1: No information on q. NOT SUFFICIENT.

Per Statement 2: q=3 and p=2 --> 2p>r --> r<8

Thus, the value of r*q MUST BE <24 as q=3 and r<8. By any combination of values of r and q, you will NEVER get a value >= 24.

Hence, this statement is sufficient.

Hope this helps. The question is very straightforward if you break it down into recognizable chunks.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1722 [3], given: 792

Senior Manager
Senior Manager
User avatar
S
Joined: 19 Oct 2012
Posts: 316

Kudos [?]: 39 [0], given: 99

Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GPA: 3.81
WE: Information Technology (Computer Software)
CAT Tests
Re: In the xy-plane, point O is located at the origin, point A has coordin [#permalink]

Show Tags

New post 20 Aug 2017, 22:20
shashanksagar wrote:
Ans should be B.
The most important clue that we have is AO>AB
This restricts how far r can go.
AO from coordinates will be 5 units in length. So maximum value of AB < 5.
And all points are in first quadrant only so maximum value of r can be 8 (excluding 8).
So maximum area of tringle could be
1/2 * 8 * 3 = 12 (excluding 12)
Let me know if its not clear or if I am wrong somewhere. :)

Sent from my SM-N910H using Tapatalk


While I understood the algebraic approach to deduce that r should be <8. The length of the 3rd side should be: greater than 1 and less than 9. Is there any other way to deduce that r<8? :oops:

Bunuel: Please throw some light here.
_________________

Citius, Altius, Fortius

Kudos [?]: 39 [0], given: 99

Re: In the xy-plane, point O is located at the origin, point A has coordin   [#permalink] 20 Aug 2017, 22:20
Display posts from previous: Sort by

In the xy-plane, point O is located at the origin, point A has coordin

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.