Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 May 2015, 05:31

### 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 xy-plane, region R consists of all the points (x, y)

Author Message
TAGS:
Director
Joined: 08 Jun 2010
Posts: 608
Followers: 0

Kudos [?]: 43 [0], given: 100

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  26 Feb 2013, 23:44
I want to follow this posting.

this question test out ability to react to numbers, to plug in number. This process is done by Bruno already. og explanation is the same. this process of plugging takes me 2 minutes.

drawing or solving the equation is too time consuming and is not the correct the method.
_________________

LOOKING FOR TINA RINK BULMER, THE GIRL LIVING IN BRADFORD ENGLAND, VISITING HALONG BAY, VIETNAM ON 27 JAN 2014. ANYONE KNOW HER, PLS EMAIL TO: thanghnvn@gmail.com.

Math Expert
Joined: 02 Sep 2009
Posts: 27469
Followers: 4311

Kudos [?]: 42214 [0], given: 5957

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  05 Jul 2013, 01:44
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

_________________
Intern
Joined: 05 May 2013
Posts: 27
GMAT 1: 730 Q50 V39
GRE 1: 1480 Q800 V680
Followers: 0

Kudos [?]: 21 [2] , given: 5

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  07 Jul 2013, 21:50
2
KUDOS
(1) Not sufficient. since we do not know the value of 2r+3s.

(2) If r and s are 0 and 0, it satisfies the inequality. however, if r=3 and s =2, it doesn't. So, insufficient.

We need to know the values of 2r+3s. We are given the value of 3r+2s.
2r+3s=3r+2s-r+s = 6 +(s-r). If s< r inequality is satisfied. Taking (1) +(2) together still doesn't give us the information of whether s <r.

Intern
Joined: 08 Oct 2011
Posts: 42
Followers: 0

Kudos [?]: 10 [0], given: 38

Re: In the xy-plane... [#permalink]  27 Sep 2013, 10:26
Bunuel wrote:
shreya717 wrote:

This is how I solved the question and im arriving at the wrong answer. Please could someone correct me.

Given:- equation of the line is 2x+3y<6
Thus, y<2/3x+2
the y and x intercepts of the given line are y<2 and x <3 respectively.

Statement 2 gives us that r (x) < 2 and s (y) <3. Therefore i concluded statment 2 is suff to answer the question. Am i going wrong in the calculation?

Thanks.

First of all $$2x+3y\leq{6}$$ can be rewritten as $$y\leq{2-\frac{2}{3}*x}$$, not as $$y\leq{2+\frac{2}{3}*x}$$. Next, it's not equation of a line, it gives the region which is below line $$y={2-\frac{2}{3}*x}$$, so all your farther conclusions are wrong.

Thanks for the explanation. I used the same incorrect approach to get to B and I missed that the equation defines a region and not a line.

If the equation was a line, then would "B" be the correct answer?
BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1166
Followers: 99

Kudos [?]: 741 [0], given: 124

Re: In the xy-plane... [#permalink]  30 Sep 2013, 22:37
Expert's post
Bunuel wrote:
metallicafan wrote:
In the xy-plane, region R consists of all the points (x, y) such that $$2x + 3y =< 6$$ . Is the point (r,s) in region R?

(1) $$3r + 2s = 6$$
(2) $$r=< 3$$ and $$s=< 2$$

Though the solution provided by shrouded1 above is perfectly OK, it's doubtful that can be done in 2-3 minutes.

So I'd say the best way for this question would be to try boundary values.

Q: is $$2r+3s\leq{6}$$?

(1) $$3r + 2s = 6$$ --> very easy to see that this statement is not sufficient:
If $$r=2$$ and $$s=0$$ then $$2r+3s=4<{6}$$, so the answer is YES;
If $$r=0$$ and $$s=3$$ then $$2r+3s=9>6$$, so the answer is NO.
Not sufficient.

(2) $$r\leq{3}$$ and $$s\leq{2}$$ --> also very easy to see that this statement is not sufficient:
If $$r=0$$ and $$s=0$$ then $$2r+3s=0<{6}$$, so the answer is YES;
If $$r=3$$ and $$s=2$$ then $$2r+3s=12>6$$, so the answer is NO.
Not sufficient.

(1)+(2) We already have an example for YES answer in (1) which valid for combined statements:
If $$r=2<3$$ and $$s=0<2$$ then $$2r+3s=4<{6}$$, so the answer is YES;
To get NO answer try max possible value of $$s$$, which is $$s=2$$, then from (1) $$r=\frac{2}{3}<3$$ --> $$2r+3s=\frac{4}{3}+6>6$$, so the answer is NO.
Not sufficient.

Hope it's clear.

Hi Bunuel,
Just a quick clarification-
Combining two statements, to get NO as answer, we can also try the first values from Stat.1 - If r=0 and s=3 then 2r+3s=9>6, so the answer is NO..

Please correct me if I'm wrong.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 27469
Followers: 4311

Kudos [?]: 42214 [0], given: 5957

Re: In the xy-plane... [#permalink]  30 Sep 2013, 23:13
Expert's post
bagdbmba wrote:
Bunuel wrote:
metallicafan wrote:
In the xy-plane, region R consists of all the points (x, y) such that $$2x + 3y =< 6$$ . Is the point (r,s) in region R?

(1) $$3r + 2s = 6$$
(2) $$r=< 3$$ and $$s=< 2$$

Though the solution provided by shrouded1 above is perfectly OK, it's doubtful that can be done in 2-3 minutes.

So I'd say the best way for this question would be to try boundary values.

Q: is $$2r+3s\leq{6}$$?

(1) $$3r + 2s = 6$$ --> very easy to see that this statement is not sufficient:
If $$r=2$$ and $$s=0$$ then $$2r+3s=4<{6}$$, so the answer is YES;
If $$r=0$$ and $$s=3$$ then $$2r+3s=9>6$$, so the answer is NO.
Not sufficient.

(2) $$r\leq{3}$$ and $$s\leq{2}$$ --> also very easy to see that this statement is not sufficient:
If $$r=0$$ and $$s=0$$ then $$2r+3s=0<{6}$$, so the answer is YES;
If $$r=3$$ and $$s=2$$ then $$2r+3s=12>6$$, so the answer is NO.
Not sufficient.

(1)+(2) We already have an example for YES answer in (1) which valid for combined statements:
If $$r=2<3$$ and $$s=0<2$$ then $$2r+3s=4<{6}$$, so the answer is YES;
To get NO answer try max possible value of $$s$$, which is $$s=2$$, then from (1) $$r=\frac{2}{3}<3$$ --> $$2r+3s=\frac{4}{3}+6>6$$, so the answer is NO.
Not sufficient.

Hope it's clear.

Hi Bunuel,
Just a quick clarification-
Combining two statements, to get NO as answer, we can also try the first values from Stat.1 - If r=0 and s=3 then 2r+3s=9>6, so the answer is NO..

Please correct me if I'm wrong.

When combining the values must satisfy both statements: r=0 and s=3 does not satisfy the second one.
_________________
BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1166
Followers: 99

Kudos [?]: 741 [0], given: 124

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  30 Sep 2013, 23:19
Expert's post
Oops! My bad...I missed that($$s\leq{2}$$).

Thanks for correcting it.
_________________
Intern
Joined: 20 Nov 2013
Posts: 30
Schools: LBS '17
Followers: 0

Kudos [?]: 9 [0], given: 185

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  06 Jul 2014, 15:45
I can't see why B is insufficient. Since r<= 3 means that x<=3 and s<=2 means y<=2 this covers the region under the line. which is f(x) <0 .
Math Expert
Joined: 02 Sep 2009
Posts: 27469
Followers: 4311

Kudos [?]: 42214 [0], given: 5957

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  06 Jul 2014, 15:54
Expert's post
amz14 wrote:
I can't see why B is insufficient. Since r<= 3 means that x<=3 and s<=2 means y<=2 this covers the region under the line. which is f(x) <0 .

Have you checked Graphic Approach HERE and Number Plugging approach HERE and HERE?
_________________
Intern
Joined: 10 Apr 2014
Posts: 7
Location: United States
Concentration: General Management, Technology
GMAT 1: 700 Q48 V37
GPA: 3.95
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 37

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  08 Jul 2014, 12:58
gmat1220 wrote:
Bunuel,
Thanks for the solution ! Please correct me.

If (r,s) is inside the region R on the XY plane, as per equation 2r + 3s <=6 is true.
That also means that r is bounded (when s=0) i.e. r<=3
s is also bounded (when r=0) is s<=2

Hence r<=3 and s<=2 should be sufficient. Am I missing something? Please clarify.

I made the same mistake as you and marked B.
But the region enclosed by the second statement is a rectangular region where r < = 3 and s<= 2. Only some part of this rectangle lies below the original line 2x + 3y <= 6.
So this option is not sufficient to say that all points (r,s) lie below the original line.
Others have shown this via algebra.
Manager
Joined: 07 Apr 2014
Posts: 148
Followers: 1

Kudos [?]: 10 [0], given: 81

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink]  16 Sep 2014, 09:17
shrouded1 wrote:
metallicafan wrote:
In the xy-plane, region R consists of all the points (x, y) such that $$2x + 3y =< 6$$ . Is the point (r,s) in region R?

(1) $$3r + 2s = 6$$
(2) $$r=< 3$$ and $$s=< 2$$

Ok, the easiest way to solve this is to visualize the graph with the lines plotted on it.
2x+3y<=6, is the region below the line with X-intercept 3 and Y-intercept 2. We know it is that region, because (0,0) lies below the line and it satisfies the inequality. And all points on one side of the line satisfy the same sign of inequality. (BLUE LINE)

(1) : The line 3r+2s=6 (PURPLE LINE) represents the second line shown in the figure. It can be above or below the other line. So insufficient.
(2) : r<=3 & s<=2. Again easy to see from the graph even with that constraint, the point (r,s) may lie above or below the line in question

(1+2) : the two conditions together, only take a section of the 3r+2s=6 line as a solution, but again even with r<=3, s<=2, its not sufficient to keep solutions below the 2x + 3y =< 6 line

In questions like these, once you are comfortable with graphs, you can solve in less than 30 seconds fairly easily.
Let me know if the method isn't clear

graph method is very clear.. thanks a lot
Director
Joined: 08 Jun 2010
Posts: 608
Followers: 0

Kudos [?]: 43 [0], given: 100

In the xy-plane, region R consists of all the points (x,y) such [#permalink]  20 May 2015, 03:04
this is hard question, which require us to pick numbers to come to the oa
_________________

LOOKING FOR TINA RINK BULMER, THE GIRL LIVING IN BRADFORD ENGLAND, VISITING HALONG BAY, VIETNAM ON 27 JAN 2014. ANYONE KNOW HER, PLS EMAIL TO: thanghnvn@gmail.com.

In the xy-plane, region R consists of all the points (x,y) such   [#permalink] 20 May 2015, 03:04

Go to page   Previous    1   2   [ 32 posts ]

Similar topics Replies Last post
Similar
Topics:
In the xy-plane, region R consists of all the points (x, y) 5 05 Nov 2007, 10:30
In the xy-plane, region R consists of all the points (x, y) 4 23 Sep 2007, 07:48
In the xy-plane, region R consists of all the points (x, y) 1 08 Sep 2007, 04:41
In the xy-plane, region R consists of all the points (x.y) 7 26 Jun 2007, 18:51
In the xy-plane, region R consists of all the points (x, y) 7 20 Dec 2006, 06:05
Display posts from previous: Sort by