It is currently 20 Nov 2017, 20:13

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

If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42269

Kudos [?]: 132852 [0], given: 12378

If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 13 Mar 2016, 09:53
Expert's post
14
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

50% (01:04) correct 50% (01:33) wrong based on 167 sessions

HideShow timer Statistics

If y = x^2 + d x + 9 does not cut the x-axis, then which of the following could be a possible value of d?

I. 0
II. -3
III. 9

A. III only
B. II only
C. I and II only
D. II and III only
E. I and III only
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132852 [0], given: 12378

Retired Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 874 [0], given: 602

GMAT ToolKit User Premium Member
Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 15 Mar 2016, 01:33
Here C is the answer as A and B statements will provide the discriminant to be negative thereby making the x axis cutting impossible.
Hence only 1 and 2
thus C
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 874 [0], given: 602

Expert Post
3 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 349 [3], given: 10

Location: India
GMAT 1: 760 Q50 V44
If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 15 Mar 2016, 05:27
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
If y = x^2 + d x + 9 does not cut the x-axis, then which of the following could be a possible value of d?

I. 0
II. -3
III. 9

A. III only
B. II only
C. I and II only
D. II and III only
E. I and III only


NOTE:

In the equation \(ax^2 = bx + c = 0\)
Discriminant = \(b^2 - 4ac\)


Solving an inequality with a less than sign: The value of the variable will be greater than the smaller value and smaller than the greater value i.e. it will between the extremes.

Solving an inequality with a greater than sign: The value of the variable will be smaller than the smaller value and greater than the greater value i.e. it can take all the values except the values in the range.



y = x^2 + d x + 9 does not cut the X-axis, this means that there are no real roots.
If there are no real roots, then Discriminant < 0

Discriminant of the given equation = \(d^2 - 4*1*9 = d^2 - 36\)
We know that this is < 0
Therefore

\(d^2 - 36\) < 0 or \(d^2 < 36\)
Hence -6 < d < 6
Therefore d can take the values: 0 and -3

Option C
_________________

Reach out to us at bondwithus@gmatify.com

Image


Last edited by TeamGMATIFY on 18 Mar 2016, 03:40, edited 1 time in total.

Kudos [?]: 349 [3], given: 10

Manager
Manager
avatar
B
Joined: 01 Jul 2010
Posts: 62

Kudos [?]: 10 [0], given: 6

Location: India
GMAT 1: 660 Q43 V38
GPA: 3.4
GMAT ToolKit User
If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 15 Mar 2016, 05:52
-3(minus 3) is not between 0 or 9 and it is also not less that -6.
The answer should be A

Kudos [?]: 10 [0], given: 6

Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 91

Kudos [?]: 3 [0], given: 9

If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 15 Mar 2016, 06:05
TeamGMATIFY wrote:
Bunuel wrote:
If y = x^2 + d x + 9 does not cut the x-axis, then which of the following could be a possible value of d?

I. 0
II. -3
III. 9

A. III only
B. II only
C. I and II only
D. II and III only
E. I and III only


NOTE:

In the equation \(ax^2 = bx + c = 0\)
Discriminant = \(b^2 - 4ac\)


Solving an inequality with a less than sign: The value of the variable will be greater than the smaller value and smaller than the greater value i.e. it will between the extremes.

Solving an inequality with a greater than sign: The value of the variable will be smaller than the smaller value and greater than the greater value i.e. it can take all the values except the values in the range.



y = x^2 + d x + 9 does not cut the X-axis, this means that there are no real roots.
If there are no real roots, then Discriminant > 0

Discriminant of the given equation = \(d^2 - 4*1*9 = d^2 - 36\)
We know that this is > 0
Therefore

\(d^2 - 36\)> 0 or \(d^2 > 36\)
Hence d > 6 or d < -6
Therefore d can take the values: 0 and 9

Option E

Shouldn't the D be <0 if it does not have real roots?

therefore, the answer should be c
as the range becomes -6<x<6

Kudos [?]: 3 [0], given: 9

SC Moderator
User avatar
P
Joined: 13 Apr 2015
Posts: 1505

Kudos [?]: 1179 [0], given: 890

Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)
GMAT ToolKit User Premium Member CAT Tests
Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 15 Mar 2016, 08:09
rahulkashyap wrote:
TeamGMATIFY wrote:
Bunuel wrote:
If y = x^2 + d x + 9 does not cut the x-axis, then which of the following could be a possible value of d?

I. 0
II. -3
III. 9

A. III only
B. II only
C. I and II only
D. II and III only
E. I and III only


NOTE:

In the equation \(ax^2 = bx + c = 0\)
Discriminant = \(b^2 - 4ac\)


Solving an inequality with a less than sign: The value of the variable will be greater than the smaller value and smaller than the greater value i.e. it will between the extremes.

Solving an inequality with a greater than sign: The value of the variable will be smaller than the smaller value and greater than the greater value i.e. it can take all the values except the values in the range.



y = x^2 + d x + 9 does not cut the X-axis, this means that there are no real roots.
If there are no real roots, then Discriminant > 0

Discriminant of the given equation = \(d^2 - 4*1*9 = d^2 - 36\)
We know that this is > 0
Therefore

\(d^2 - 36\)> 0 or \(d^2 > 36\)
Hence d > 6 or d < -6
Therefore d can take the values: 0 and 9

Option E

Shouldn't the D be <0 if it does not have real roots?

therefore, the answer should be c
as the range becomes -6<x<6


Yes I too agree with you. D should be < 0 if the roots are not real.
Answer has to be C.

Kudos [?]: 1179 [0], given: 890

Retired Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 874 [0], given: 602

GMAT ToolKit User Premium Member
Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 15 Mar 2016, 11:07
I. 0
II. -3
III. 9

A. III only
B. II only
C. I and II only
D. II and III only
E. I and III only[/quote]

NOTE:

In the equation \(ax^2 = bx + c = 0\)
Discriminant = \(b^2 - 4ac\)


Solving an inequality with a less than sign: The value of the variable will be greater than the smaller value and smaller than the greater value i.e. it will between the extremes.

Solving an inequality with a greater than sign: The value of the variable will be smaller than the smaller value and greater than the greater value i.e. it can take all the values except the values in the range.



y = x^2 + d x + 9 does not cut the X-axis, this means that there are no real roots.
If there are no real roots, then Discriminant > 0

Discriminant of the given equation = \(d^2 - 4*1*9 = d^2 - 36\)
We know that this is > 0
Therefore

\(d^2 - 36\)> 0 or \(d^2 > 36\)
Hence d > 6 or d < -6
Therefore d can take the values: 0 and 9

Option E[/quote]
Shouldn't the D be <0 if it does not have real roots?

therefore, the answer should be c
as the range becomes -6<x<6[/quote]

Yes I too agree with you. D should be < 0 if the roots are not real.
Answer has to be C.[/quote]


AGREED ...!!
Just waiting for the official solution on this one..!!
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 874 [0], given: 602

Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 349 [0], given: 10

Location: India
GMAT 1: 760 Q50 V44
If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 18 Mar 2016, 03:42
Sorry for the incorrect solution and thanks a lot for pointing it out. I stand corrected guys, might be phased out while solving the question. One incorrect inequality and then solved the whole question considering that equation.
Yes, if the roots are not real, D < 0

Edited the solution
_________________

Reach out to us at bondwithus@gmatify.com

Image

Kudos [?]: 349 [0], given: 10

1 KUDOS received
Manager
Manager
avatar
B
Joined: 06 Aug 2017
Posts: 72

Kudos [?]: 13 [1], given: 27

GMAT 1: 610 Q48 V24
If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow [#permalink]

Show Tags

New post 23 Sep 2017, 07:01
1
This post received
KUDOS
Bunuel wrote:
If y = x^2 + d x + 9 does not cut the x-axis, then which of the following could be a possible value of d?

I. 0
II. -3
III. 9

A. III only
B. II only
C. I and II only
D. II and III only
E. I and III only


The answer is C as follows.

\(x^2 + dx + 9\) is an equation of upward parabola, hence for this equation to not cut x-axis means it should not have any real root.

A quadratic equation do not have any real root when the discriminant (\(b^2 -4ac\)) of the equation is -ve.

So in this case \(b^2 -4ac\)<0 ==> \(d^2 -4*9<0\) ==> \(d^2-36<0\) ==>\(d^2<36\) ==> -6<d<6

Looking at the option only 0 and -3 satisfies this condition.

Hence answer is C (I and II only).
_________________

-------------------------------------------------------------------------------
Kudos are the only way to tell whether my post is useful.

Kudos [?]: 13 [1], given: 27

If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow   [#permalink] 23 Sep 2017, 07:01
Display posts from previous: Sort by

If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow

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


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®.