GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 28 Mar 2020, 00:24

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

In the xy-plane shown, the shaded region consists of all points that l

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

Hide Tags

Find Similar Topics 
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10217
Location: Pune, India
Re: In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post 17 Dec 2018, 00:11
1
3
louhit wrote:
Hi Guys,

I have spent too many minutes on this questions which is also on OG quant review 2019 DS01613, I am still not able to get through the questions ask and the explanation given here. I think i have a thick brain it seems, Can Bunuel or VeritasKarishma help me in understanding the question stem and theory/concept behind it. Thanks


First go through these three posts:
https://www.veritasprep.com/blog/2010/1 ... he-graphs/
http://www.veritasprep.com/blog/2010/12 ... s-part-ii/
https://www.veritasprep.com/blog/2011/0 ... -part-iii/

They explain the concept of how the xy co-ordinate plane is divided into two parts by a line. The parabola does the same. It divides the plane into two regions:
y > x^2 - 4x
y < x^2 - 4x

Stmnt 2 gives us that (a, b) lies in the region y > x^2 - 4x which is the region inside the parabola (if you want to verify, check (2, 1). It satisfies y > x^2 - 4x.
Since the question stem tells us that b < 0, so we are looking at a point below the x axis. The region inside the parabola below x axis is the shaded region. So the point must lie on it.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
User avatar
S
Joined: 29 Dec 2018
Posts: 82
Location: India
WE: Marketing (Real Estate)
Re: In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post 20 Jul 2019, 23:25
1
If you are getting confused with the normal way of solving but you are great at visualizing and drawing coordinate geometry, here's the video solution for you

https://gmatquantum.com/official-guides ... nt-review/
_________________
Keep your eyes on the prize: 750
DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 1414
Location: India
Premium Member
In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post Updated on: 18 Nov 2019, 00:18
Statement 1- tells us nothing much. Point can lie inside or outside the parabola in range 0<x<4.
Insufficient

Statement 2- Locus of point (a,b) is \(y>x^2-4x\) , where y<0. In other words locus of the (a, b) lies below the y-axis and inside the parabola \(y=x^2-4x\).

Sufficient.



dgboy765 wrote:
Image
In the xy-plane shown, the shaded region consists of all points that lie above the graph of y=x^2 - 4x and below the the x-axis. Does the point (a,b) (not shown) lie in the shaded region if b<0?

(1) 0 < a < 4
(2) a^2 - 4a < b


Source: Official GMAT Quantitative Review 2016
P. 162 DS #124

Can someone explain the process to solving this problem in the simplest way possible? (but please don't be overly brief. I'm not as intuitive as you.)

Attachment:
2016-01-24_1416.png

Originally posted by nick1816 on 15 Sep 2019, 15:10.
Last edited by nick1816 on 18 Nov 2019, 00:18, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 31 Mar 2019
Posts: 62
Re: In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post 16 Nov 2019, 20:35
VeritasKarishma - could you please help in this question. Difficult to understand

Posted from my mobile device
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10217
Location: Pune, India
Re: In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post 18 Nov 2019, 00:13
LeenaSai wrote:
VeritasKarishma - could you please help in this question. Difficult to understand

Posted from my mobile device



I have talked about it here: https://gmatclub.com/forum/in-the-xy-pl ... l#p2191933
Let me know if you still have doubts.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936
In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post Updated on: 15 Mar 2020, 14:28
Hi there!

In the image attached, we realize point (a,b) is in the given shaded region if, and only if,

\(\left\{ \begin{gathered}
\,0 < a < 4\,\,\,\left( {\text{I}} \right) \hfill \\
\,{a^2} - 4a < b < 0\,\,\,\left( {{\text{II}}} \right) \hfill \\
\end{gathered} \right. \)

\(\left( {\text{I}} \right)\,\,0 < a < 4\,\,\, \) Although \( \,b < 0\, \) is given, we still can have a "yes" and a "no" possibilities:

\( \left. \begin{gathered}
\left( {a,b} \right) = \left( {1, - 2} \right)\,\,\,\,;\,\,\,{a^2} - 4a\mathop < \limits^? b\,\,\,:{\text{yes}}\,\, \hfill \\
\left( {a,b} \right) = \left( {1, - 3} \right)\,\,\,\,;\,\,\,{a^2} - 4a\mathop < \limits^? b\,\,\,:{\text{no}}\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,{\text{INS}}{\text{.}} \)


\( \left( {{\text{II}}} \right)\,\,{a^2} - 4a < b < 0\,\,\, \)

\(\left. {{a^2} - 4a < b < 0\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered}
\,\left( {{\text{II}}} \right)\,\,\,{\text{immediately}} \hfill \\
\,a\left( {a - 4} \right) = {a^2} - 4a < 0\,\,\,\, \Rightarrow \,\,\,\,0 < a < 4\,\,\, \Rightarrow \,\,\,\,\left( {\text{I}} \right)\,\,\,\,\, \hfill \\
\end{gathered} \right.} \right\}\,\,\,\,{\text{SUF}}{\text{.}}\)

Regards,
Fabio.
Attachments

04Mar20_1.gif
04Mar20_1.gif [ 16.15 KiB | Viewed 195 times ]


_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Originally posted by fskilnik on 04 Mar 2020, 06:51.
Last edited by fskilnik on 15 Mar 2020, 14:28, edited 1 time in total.
Manager
Manager
User avatar
B
Joined: 21 Feb 2017
Posts: 203
In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post 13 Mar 2020, 23:03
VeritasKarishma wrote:
louhit wrote:
Hi Guys,

I have spent too many minutes on this questions which is also on OG quant review 2019 DS01613, I am still not able to get through the questions ask and the explanation given here. I think i have a thick brain it seems, Can Bunuel or VeritasKarishma help me in understanding the question stem and theory/concept behind it. Thanks


First go through these three posts:
https://www.veritasprep.com/blog/2010/1 ... he-graphs/
http://www.veritasprep.com/blog/2010/12 ... s-part-ii/
https://www.veritasprep.com/blog/2011/0 ... -part-iii/

They explain the concept of how the xy co-ordinate plane is divided into two parts by a line. The parabola does the same. It divides the plane into two regions:
y > x^2 - 4x
y < x^2 - 4x

Stmnt 2 gives us that (a, b) lies in the region y > x^2 - 4x which is the region inside the parabola (if you want to verify, check (2, 1). It satisfies y > x^2 - 4x.
Since the question stem tells us that b < 0, so we are looking at a point below the x axis. The region inside the parabola below x axis is the shaded region. So the point must lie on it.


Hi VeritasKarishma!! I understand that point "a" lies inside the parabola. But how do we ensure that "b" does too? it just says b<0. it could lie anywhere below the x-axis. how do we assume that it lies inside the parabola only below the x-axis?

Also, we derive this from st 2 "0<a<4", but even statement one says this!! So how come statement 1 isn't sufficiency then (I know i must be missing something very silly)
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10217
Location: Pune, India
Re: In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post 15 Mar 2020, 00:03
1
Kritisood wrote:
VeritasKarishma wrote:
louhit wrote:
Hi Guys,

I have spent too many minutes on this questions which is also on OG quant review 2019 DS01613, I am still not able to get through the questions ask and the explanation given here. I think i have a thick brain it seems, Can Bunuel or VeritasKarishma help me in understanding the question stem and theory/concept behind it. Thanks


First go through these three posts:
https://www.veritasprep.com/blog/2010/1 ... he-graphs/
http://www.veritasprep.com/blog/2010/12 ... s-part-ii/
https://www.veritasprep.com/blog/2011/0 ... -part-iii/

They explain the concept of how the xy co-ordinate plane is divided into two parts by a line. The parabola does the same. It divides the plane into two regions:
y > x^2 - 4x
y < x^2 - 4x

Stmnt 2 gives us that (a, b) lies in the region y > x^2 - 4x which is the region inside the parabola (if you want to verify, check (2, 1). It satisfies y > x^2 - 4x.
Since the question stem tells us that b < 0, so we are looking at a point below the x axis. The region inside the parabola below x axis is the shaded region. So the point must lie on it.


Hi VeritasKarishma!! I understand that point "a" lies inside the parabola. But how do we ensure that "b" does too? it just says b<0. it could lie anywhere below the x-axis. how do we assume that it lies inside the parabola only below the x-axis?

Also, we derive this from st 2 "0<a<4", but even statement one says this!! So how come statement 1 isn't sufficiency then (I know i must be missing something very silly)


Note that (a, b) specifies a single point (a point whose x co-ordinate is 'a' and y co-ordinate is 'b'). So (2, 6) specifies a single point. Only a or only b can't specify a point.
Now the entire plane is divided into two parts - one lying inside the parabola and the other outside.
The one lying inside the parabola is x^2 - 4x < y and the one outside is x^2 - 4x > y. The actual parabola is x^2 - 4x = y.

The shaded region is inside the parabola so all points (a, b) inside it satisfy a^2 - 4a < b (the inequality given by statement 2)

When b is negative (the y coordinate of the point is negative), this will be the shaded region.

So (a, b) are points such as (2, -1).
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
SVP
SVP
User avatar
V
Joined: 03 Jun 2019
Posts: 2287
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
Re: In the xy-plane shown, the shaded region consists of all points that l  [#permalink]

Show Tags

New post 15 Mar 2020, 00:37
dgboy765 wrote:
Image
In the xy-plane shown, the shaded region consists of all points that lie above the graph of y=x^2 - 4x and below the the x-axis. Does the point (a,b) (not shown) lie in the shaded region if b<0?

(1) 0 < a < 4
(2) a^2 - 4a < b


Source: Official GMAT Quantitative Review 2016
P. 162 DS #124

Can someone explain the process to solving this problem in the simplest way possible? (but please don't be overly brief. I'm not as intuitive as you.)

Attachment:
2016-01-24_1416.png


Given: In the xy-plane shown, the shaded region consists of all points that lie above the graph of y=x^2 - 4x and below the the x-axis.

Asked: Does the point (a,b) (not shown) lie in the shaded region if b<0?

(1) 0 < a < 4
Value of b is unknown
NOT SUFFICIENT

(2) a^2 - 4a < b
0 > b > a^2 - 4a
Since b is inside the bound of 0 and a^2 - 4a
SUFFICIENT

IMO B
GMAT Club Bot
Re: In the xy-plane shown, the shaded region consists of all points that l   [#permalink] 15 Mar 2020, 00:37

Go to page   Previous    1   2   [ 29 posts ] 

Display posts from previous: Sort by

In the xy-plane shown, the shaded region consists of all points that l

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





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