It is currently 18 Oct 2017, 23:15

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the coordinate plane, rectangular region R has vertices a

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 313

Kudos [?]: 592 [6], given: 193

In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

15 Nov 2010, 11:50
6
KUDOS
34
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

60% (01:43) correct 40% (01:48) wrong based on 821 sessions

### HideShow timer Statistics

In the coordinate plane, rectangular region R has vertices at (0,0), (0,3), (4,3), and (4,0). If a point in region R is randomly selected, what is the probability that the point's y-coordinate will be greater than its x-coordinate?

A. 7/12
B. 5/12
C. 3/8
D. 1/3
E. 1/4
[Reveal] Spoiler: OA

_________________

I'm the Dumbest of All !!

Kudos [?]: 592 [6], given: 193

Math Expert
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128795 [17], given: 12183

### Show Tags

15 Nov 2010, 12:06
17
KUDOS
Expert's post
12
This post was
BOOKMARKED
shrive555 wrote:
In the coordinate plane, rectangular region R has vertices at (0,0), (0,3), (4,3), and (4,0). If a point in region R is randomly selected, what is the probability that the point's y-coordinate will be greater than its x-coordinate?

7/12
5/12
3/8
1/3
1/4
See the diagram below.
Attachment:

graph.PNG [ 15.18 KiB | Viewed 11976 times ]
Now, rectangle R has an area of 3*4=12. All point that has y-coordinate greater than x-coordinate lie above the line $$y=x$$, so in yellow triangle, which has an area of 1/2*3*3=4.5. So, the probability equals to favorable outcomes/total=yellow triangle/rectangle R=4.5/12=3/8.

_________________

Kudos [?]: 128795 [17], given: 12183

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 313

Kudos [?]: 592 [0], given: 193

### Show Tags

15 Nov 2010, 12:21
i took that y intercept 3 to be greater than x all coordinates and divided by 12 and got 1/4. which is completely wrong. and according to your solution in that yellow region every point is greater than x not just only y intercept. Great.
_________________

I'm the Dumbest of All !!

Kudos [?]: 592 [0], given: 193

Math Expert
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128795 [2], given: 12183

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

27 Jun 2013, 23:46
2
KUDOS
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

_________________

Kudos [?]: 128795 [2], given: 12183

MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4707

Kudos [?]: 3708 [0], given: 2420

Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

28 Jun 2013, 04:43
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

I think Bunuel's above explanation is most illuminating and detailed; I do not find any alternate way for the explanation. +1 for that great solution.
_________________

Kudos [?]: 3708 [0], given: 2420

Senior Manager
Status: Student
Joined: 26 Aug 2013
Posts: 253

Kudos [?]: 68 [0], given: 401

Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

08 Jan 2014, 16:44
Hi,

this is how I did it:

The probability if X=3 that Y>X is 0
The probability if X=2 that Y>X is 1/4
The probability if X=1 that Y>X is 2/4
The probability if X=0 that Y>X is 3/4

Then: $$1/4*1/4 + 1/4*2/4 + 1/4*3/4 = 6/16 = 3/8$$

Hope it helps
_________________

Think outside the box

Kudos [?]: 68 [0], given: 401

Intern
Joined: 17 Oct 2013
Posts: 41

Kudos [?]: 15 [2], given: 21

Schools: HEC Dec"18
GMAT Date: 02-04-2014
Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

08 Jan 2014, 23:48
2
KUDOS
shrive555 wrote:
In the coordinate plane, rectangular region R has vertices at (0,0), (0,3), (4,3), and (4,0). If a point in region R is randomly selected, what is the probability that the point's y-coordinate will be greater than its x-coordinate?

A. 7/12
B. 5/12
C. 3/8
D. 1/3
E. 1/4

there is no better solution than this

compute the area above y=x line and below y=x line and then proceed to finding probability

Kudos [?]: 15 [2], given: 21

Senior Manager
Joined: 20 Dec 2013
Posts: 267

Kudos [?]: 106 [0], given: 29

Location: India
Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

29 Mar 2014, 06:47
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

I calculated that the no. of points in the region including the boundaries of the rectangle=$$16$$.
Out of that $$6$$ points [for $$6$$ ordered pairs-$$(0,1),(0,2),(0,3),(1,2),(1,3)$$ and $$(2,3)$$],will have $$x$$ coordinate less than $$y$$ coordinate.
So probability=$$6/16=3/8$$
Isn't this approach right?

Kudos [?]: 106 [0], given: 29

Math Expert
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128795 [1], given: 12183

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

29 Mar 2014, 10:12
1
KUDOS
Expert's post
AKG1593 wrote:
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

I calculated that the no. of points in the region including the boundaries of the rectangle=$$16$$.
Out of that $$6$$ points [for $$6$$ ordered pairs-$$(0,1),(0,2),(0,3),(1,2),(1,3)$$ and $$(2,3)$$],will have $$x$$ coordinate less than $$y$$ coordinate.
So probability=$$6/16=3/8$$
Isn't this approach right?

No, this approach is not right. A point has no dimension, hence there are infinitely many points in any area/segment. The problem with your solution is that you assume that the coordinates must be integers, which is nowhere given.

Hope it's clear.
_________________

Kudos [?]: 128795 [1], given: 12183

Moderator
Joined: 20 Dec 2013
Posts: 185

Kudos [?]: 74 [0], given: 71

Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)
Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

08 Jul 2014, 20:02
Hi Bunuel...I came across this question and kept getting caught up by the y=x line.

If we calculate the isoc triangle's area, wouldn't this include all points on the y=x line (on which y is not > x)?
_________________

Kudos [?]: 74 [0], given: 71

Math Expert
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128795 [2], given: 12183

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

09 Jul 2014, 03:19
2
KUDOS
Expert's post
m3equals333 wrote:
Hi Bunuel...I came across this question and kept getting caught up by the y=x line.

If we calculate the isoc triangle's area, wouldn't this include all points on the y=x line (on which y is not > x)?

A line has no area, hence there won't be any difference.
_________________

Kudos [?]: 128795 [2], given: 12183

Moderator
Joined: 20 Dec 2013
Posts: 185

Kudos [?]: 74 [0], given: 71

Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)
Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

09 Jul 2014, 14:50
ah ha, that clears it up, thanks a bunch
_________________

Kudos [?]: 74 [0], given: 71

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16679

Kudos [?]: 273 [0], given: 0

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

30 Jul 2015, 11:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Intern
Joined: 05 Jun 2016
Posts: 23

Kudos [?]: 1 [0], given: 125

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

06 Nov 2016, 04:43
Bunuel wrote:
AKG1593 wrote:
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

I calculated that the no. of points in the region including the boundaries of the rectangle=$$16$$.
Out of that $$6$$ points [for $$6$$ ordered pairs-$$(0,1),(0,2),(0,3),(1,2),(1,3)$$ and $$(2,3)$$],will have $$x$$ coordinate less than $$y$$ coordinate.
So probability=$$6/16=3/8$$
Isn't this approach right?

No, this approach is not right. A point has no dimension, hence there are infinitely many points in any area/segment. The problem with your solution is that you assume that the coordinates must be integers, which is nowhere given.

Hope it's clear.

Hi Brunei,

How the rectangle has 16 points (if we calculate the borders ). Isn't it should be 20 . e.g (0,0),(1,0),(2,0),(3,0),(4,0).
5 points in 1 row and 4 rows all together 5*4 = 20 . Am I missing something ?

Kudos [?]: 1 [0], given: 125

Math Expert
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128795 [0], given: 12183

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

06 Nov 2016, 04:59
Ganganshu wrote:
Hi Brunei,

How the rectangle has 16 points (if we calculate the borders ). Isn't it should be 20 . e.g (0,0),(1,0),(2,0),(3,0),(4,0).
5 points in 1 row and 4 rows all together 5*4 = 20 . Am I missing something ?

I don't understand why are you concerned about the number of points? The solution talks about the area...
_________________

Kudos [?]: 128795 [0], given: 12183

Intern
Joined: 05 Jun 2016
Posts: 23

Kudos [?]: 1 [0], given: 125

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

06 Nov 2016, 05:14
Bunuel wrote:
Ganganshu wrote:
Hi Brunei,

How the rectangle has 16 points (if we calculate the borders ). Isn't it should be 20 . e.g (0,0),(1,0),(2,0),(3,0),(4,0).
5 points in 1 row and 4 rows all together 5*4 = 20 . Am I missing something ?

I don't understand why are you concerned about the number of points? The solution talks about the area...

Brunei ,

I didnot get your point(in earlier quote) why calculating points is wrong (I know we get an incorrect answer ). Isn't Probability = No of successes(condition)/ Total no of outcomes and if we go by points arenot we just following it .

Kudos [?]: 1 [0], given: 125

Math Expert
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128795 [0], given: 12183

Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

06 Nov 2016, 06:09
Ganganshu wrote:
Bunuel wrote:
Ganganshu wrote:
Hi Brunei,

How the rectangle has 16 points (if we calculate the borders ). Isn't it should be 20 . e.g (0,0),(1,0),(2,0),(3,0),(4,0).
5 points in 1 row and 4 rows all together 5*4 = 20 . Am I missing something ?

I don't understand why are you concerned about the number of points? The solution talks about the area...

Brunei ,

I didnot get your point(in earlier quote) why calculating points is wrong (I know we get an incorrect answer ). Isn't Probability = No of successes(condition)/ Total no of outcomes and if we go by points arenot we just following it .

(Probability) = (Favorable outcomes)/(Total) = (The area of yellow triangle)/(The area of the rectangle). Notice that we have an area there no the number of poiint whose coordinates are integers only.

Check other Probability and Geometry questions in our Special Questions Directory.

Hope it helps.
_________________

Kudos [?]: 128795 [0], given: 12183

Manager
Joined: 12 Oct 2012
Posts: 124

Kudos [?]: 75 [0], given: 198

WE: General Management (Other)
Re: In the coordinate plane, rectangular region R has vertices a [#permalink]

### Show Tags

18 Nov 2016, 05:26
Narenn wrote:
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

I think Bunuel's above explanation is most illuminating and detailed; I do not find any alternate way for the explanation. +1 for that great solution.

I did graph the region correctly. However, when I looked at the region I thought the selected region is slightly less than half.

However, the answer choices are quite close. So you have to calculate the area, no choice.

Kudos [?]: 75 [0], given: 198

Re: In the coordinate plane, rectangular region R has vertices a   [#permalink] 18 Nov 2016, 05:26
Display posts from previous: Sort by