GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Dec 2019, 22:19

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

Which quadrant, if any, contains no point (x, y) that satisfies the in

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
Which quadrant, if any, contains no point (x, y) that satisfies the in  [#permalink]

Show Tags

New post 21 Nov 2019, 01:07
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

45% (01:45) correct 55% (02:18) wrong based on 40 sessions

HideShow timer Statistics

Manager
Manager
avatar
S
Joined: 16 Feb 2015
Posts: 160
Location: United States
Concentration: Finance, Operations
Schools: INSEAD, ISB
Re: Which quadrant, if any, contains no point (x, y) that satisfies the in  [#permalink]

Show Tags

New post 21 Nov 2019, 11:14
Bunuel wrote:
Image
Which quadrant, if any, contains no point (x, y) that satisfies the inequality \(y ≥ (x - 3)^2 - 1\)?

(A) I
(B) II
(C) III
(D) IV
(E) All quadrants contain at least one point that satisfies the given inequality.


Attachment:
1.png


Explanation: y ≥ (x - 3)^2 - 1
Solving above equation, we get y ≥ (x-2)(x-4)
So, Putting y=0, We get two values of x=2,4
by putting x=0, we get y ≥ 8

To find out which area is covered by the graph put the Coordinate (0,0) in the original question y ≥ (x - 3)^2 - 1

We get: 0≥8 Which is False.

So (0,0) does not lie in the area covered by the graph, Therefore the equation covers the area above the line.

Thus 4th Quadrant does not contain any point that satisfies the inequality. ( Rest 3 Quadrants will have a few points that would satisfy the inequality).

Answer is D.

Hoping other will reply, so we can have good discussion over this question :) :)

:please Please provide kudos, if you find my explanation good enough :please
Intern
Intern
avatar
B
Joined: 11 Sep 2018
Posts: 11
Re: Which quadrant, if any, contains no point (x, y) that satisfies the in  [#permalink]

Show Tags

New post 24 Nov 2019, 16:40
1
y>= (x-3)^2 -1

I quadrant -> x +ve, y +ve
Ex: (20,5)
20 >= (5-3)^2-1
20>=3
satisfied. Hence we can conclude that it lies in first quadrant.

II Quadrant -> x -ve, y +ve
Ex: (20, -1)
50>=(-1-3)^2-1
50>= 15
Satisfied.

III Quadrant -> x -ve, y -ve
Ex: (-1,-1)
-1>=(-1-3)^2 -1
-1>=15
Not satisfied. As x is within a square term, it will always be positive, y will remain negative. Hence there will be no points in this quadrant.

IV Quadrant -> x +ve, y -ve
(3,-1)
-1>= (3-3)^2-1
-1>=-1
Satisfied.

Ans: C
Intern
Intern
avatar
B
Joined: 11 Sep 2018
Posts: 11
Re: Which quadrant, if any, contains no point (x, y) that satisfies the in  [#permalink]

Show Tags

New post 24 Nov 2019, 16:43
Bunuel VeritasKarishma chetan2u Can you please suggest any alternate solutions other than assuming numbers?
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8305
Which quadrant, if any, contains no point (x, y) that satisfies the in  [#permalink]

Show Tags

New post 24 Nov 2019, 19:01
1
Bunuel wrote:
Image
Which quadrant, if any, contains no point (x, y) that satisfies the inequality \(y ≥ (x - 3)^2 - 1\)?

(A) I
(B) II
(C) III
(D) IV
(E) All quadrants contain at least one point that satisfies the given inequality.


Attachment:
1.png


Neferteena, the other way would be to simplify the inequality

\(y ≥ (x - 3)^2 - 1\)....... \(y ≥ (x - 3-1)(x-3+1)\)........ \(y ≥ (x - 4)(x-2)\)

(x-4)(x-2) will always be POSITIVE when x is negative, but in quadrant III y is NEGATIVE.
So can negative be greater than positive....NO
Thus answer is quadrant III

C
_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9871
Location: Pune, India
Re: Which quadrant, if any, contains no point (x, y) that satisfies the in  [#permalink]

Show Tags

New post 24 Nov 2019, 23:40
1
Bunuel wrote:
Image
Which quadrant, if any, contains no point (x, y) that satisfies the inequality \(y ≥ (x - 3)^2 - 1\)?

(A) I
(B) II
(C) III
(D) IV
(E) All quadrants contain at least one point that satisfies the given inequality.


Attachment:
The attachment 1.png is no longer available


The inequality is

\(y ≥ (x - 3)^2 - 1\)
\(y ≥ x^2 - 6x + 8\)

We have a quadratic in x which is a parabola. Since the co-efficient of x^2 is positive, it is upward opening. Also, its roots are 4 and 2.
\(x^2 - 6x + 8 = (x - 4)(x - 2) = 0\)

Now the inequality is \(y ≥ x^2 - 6x + 8\) so which region does it represent?
Let's try to put in (3, 0) lying inside the parabola.
So this is what its graph will look like:

Attachment:
IMG_7737.jpg
IMG_7737.jpg [ 1.76 MiB | Viewed 153 times ]


0 ≥ - 1 (true)
So our inequality represents the region inside the parabola. So no point of quadrant III will satisfy it.

Answer (C)
_________________
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 >
GMAT Club Bot
Re: Which quadrant, if any, contains no point (x, y) that satisfies the in   [#permalink] 24 Nov 2019, 23:40
Display posts from previous: Sort by

Which quadrant, if any, contains no point (x, y) that satisfies the in

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





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