It is currently 24 Feb 2018, 07:45

### 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

# If f(x) = x^3 + 9, is f(x) positive?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43896
If f(x) = x^3 + 9, is f(x) positive? [#permalink]

### Show Tags

08 Feb 2017, 00:46
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

55% (00:59) correct 45% (00:34) wrong based on 95 sessions

### HideShow timer Statistics

If f(x) = x^3 + 9, is f(x) positive?

(1) x < −1

(2) x > −3
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
If f(x) = x^3 + 9, is f(x) positive? [#permalink]

### Show Tags

08 Feb 2017, 01:47
1
This post was
BOOKMARKED
Bunuel wrote:
If f(x) = x^3 + 9, is f(x) positive?

(1) x < −1

(2) x > −3

St I
x < -1
if x = -2 we have $$(-2)^3+9$$ = 1 f(x) is positive.
if x = -3 we have $$(-3)^3+9$$ = -18 f(x) is negative ----------Insufficient.

St II
x > -3
if x = -2 we have $$(-2)^3+9$$ = 1 f(x) is positive.
if x = -2.5 we have $$(-2.5)^3+9$$ = -6.25 f(x) is negative. ----------Insufficient.

St. I and II ----------Insufficient.

Hence Option E is correct.
Hit Kudos if you liked it
Manager
Joined: 13 Dec 2013
Posts: 171
Location: United States (NY)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: If f(x) = x^3 + 9, is f(x) positive? [#permalink]

### Show Tags

08 Feb 2017, 10:10
Bunuel wrote:
If f(x) = x^3 + 9, is f(x) positive?

(1) x < −1

(2) x > −3

1) If x is -2 f(x) is +ve. If x is -3 f(x) is -ve. Not suff.
2) If x is -2 f(x) is +ve. If x is -2.9 f(x) is -ve. Not suff.
1)&2) Constraints for 2) still apply. Not suff. E.
Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1277
Location: Malaysia
If f(x) = x^3 + 9, is f(x) positive? [#permalink]

### Show Tags

11 Feb 2017, 20:06
Bunuel wrote:
If $$f(x) = x^3 + 9$$, is $$f(x)$$ positive?

(1) $$x < −1$$

(2) $$x > −3$$

Official solution from Veritas Prep.

If $$x<−1$$, then x could be $$−2$$ in which case $$f(x)$$ is positive or $$x$$ could be $$−3$$ in which case $$f(x)$$ is negative. Therefore, Statement 1 alone is not sufficient.

If $$x>−3$$, the x could be $$−2$$ in which case $$f(x)$$ is positive. However, the problem never stated that $$x$$ is an integer. Then, $$x$$ could be $$-2.99999$$, that is almost $$-3$$. In this case, $$f(x)$$ will be a negative. $$f(x)=(-2.99999)^3+9 = -17.99973$$ Therefore, Statement 2 is not sufficient.

Combining Statement 1 and Statement 2, $$f(x)$$ could still either be positive or negative. Therefore, the answer is $$E$$.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Manager
Joined: 24 Oct 2013
Posts: 153
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: If f(x) = x^3 + 9, is f(x) positive? [#permalink]

### Show Tags

13 Feb 2017, 00:48
I think it should be B.

(-2.9999)^3 is less than 9 and therefor -899999+9 >0

Hence it should be B
Senior Manager
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: If f(x) = x^3 + 9, is f(x) positive? [#permalink]

### Show Tags

13 Feb 2017, 01:28
deepthit wrote:
I think it should be B.

(-2.9999)^3 is less than 9 and therefor -899999+9 >0

Hence it should be B

(-2.9999)^3 = -26.997300 < 0.
Re: If f(x) = x^3 + 9, is f(x) positive?   [#permalink] 13 Feb 2017, 01:28
Display posts from previous: Sort by

# If f(x) = x^3 + 9, is f(x) positive?

 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®.