It is currently 21 Oct 2017, 00:07

### 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 m^3-n^2=-300, then the lowest possible value of m is

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Apr 2012
Posts: 277

Kudos [?]: 1154 [0], given: 325

Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

01 Apr 2013, 01:22
9
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:35) correct 46% (01:33) wrong based on 285 sessions

### HideShow timer Statistics

If m^3-n^2=-300, then the lowest possible value of m is between

(A) -20 and -15
(B) -15 and -10
(C) -10 and -5
(D) -5 and 0
(E) 0 and 5
[Reveal] Spoiler: OA

Kudos [?]: 1154 [0], given: 325

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129060 [6], given: 12189

Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

01 Apr 2013, 01:51
6
KUDOS
Expert's post
3
This post was
BOOKMARKED
guerrero25 wrote:
If m^3-n^2=-300, then the lowest possible value of m is between

(A) -20 and -15
(B) -15 and -10
(C) -10 and -5
(D) -5 and 0
(E) 0 and 5

$$m^3-n^2=-300$$ --> $$m=\sqrt[3]{n^2-300}$$. To minimize m we should minimize n^2. The lowest value of n^2 is 0, thus the lowest value of m is $$m_{min}=\sqrt[3]{-300}$$.

m is less than -5 (since (-5)^3=-125) and more than -10 (since (-10)^3=-1000).

_________________

Kudos [?]: 129060 [6], given: 12189

Intern
Joined: 15 Jan 2013
Posts: 38

Kudos [?]: 29 [2], given: 6

Concentration: Finance, Operations
GPA: 4
Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

01 Apr 2013, 07:40
2
KUDOS
guerrero25 wrote:
If m^3-n^2=-300, then the lowest possible value of m is between

(A) -20 and -15
(B) -15 and -10
(C) -10 and -5
(D) -5 and 0
(E) 0 and 5

$$m^3-n^2=-300$$
So, $$m^3 = n^2 - 300$$
For $$m^3$$ to be minimum, $$(n^2 - 300)$$ must be minimum
For $$(n^2 - 300)$$ to be minimum, $$n^2$$ must be minimum, so $$n^2$$ = 0
So $$m^3$$ = -300
So m = -6. .....
So m lies between -10 and -5

Kudos [?]: 29 [2], given: 6

Senior Manager
Joined: 10 Apr 2012
Posts: 277

Kudos [?]: 1154 [0], given: 325

Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

01 Apr 2013, 03:02
Bunuel wrote:
guerrero25 wrote:
If m^3-n^2=-300, then the lowest possible value of m is between

(A) -20 and -15
(B) -15 and -10
(C) -10 and -5
(D) -5 and 0
(E) 0 and 5

$$m^3-n^2=-300$$ --> $$m=\sqrt[3]{n^2-300}$$. To minimize m we should minimize n^2. The lowest value of n^2 is 0, thus the lowest value of m is $$m_{min}=\sqrt[3]{-300}$$.

m is less than -5 (since (-5)^3=-125) and more than -10 (since (-10)^3=-1000).

Such an Easy approach , Bunuel . I succumbed to the time pressure . I wish I could think like you

Kudos [?]: 1154 [0], given: 325

Senior Manager
Joined: 23 Mar 2011
Posts: 461

Kudos [?]: 279 [0], given: 59

Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

25 Apr 2013, 06:57
Bunuel, pls help. how are we considering m as minimum with cube root of -300, is that not an unreal number (negative root)?
I was considering the cube root for the lowest positive value of m
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++

-----------------------------

My GMAT journey begins: http://gmatclub.com/forum/my-gmat-journey-begins-122251.html

Kudos [?]: 279 [0], given: 59

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129060 [0], given: 12189

Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

25 Apr 2013, 08:34
sdas wrote:
Bunuel, pls help. how are we considering m as minimum with cube root of -300, is that not an unreal number (negative root)?
I was considering the cube root for the lowest positive value of m

Even roots from negative number is undefined on the GMAT: $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.
_________________

Kudos [?]: 129060 [0], given: 12189

Moderator
Joined: 10 May 2010
Posts: 819

Kudos [?]: 431 [0], given: 192

Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

25 Apr 2013, 08:53
sdas wrote:
Bunuel, pls help. how are we considering m as minimum with cube root of -300, is that not an unreal number (negative root)?
I was considering the cube root for the lowest positive value of m

To add to what Bunnuel said. Try to think in reverse. You can always multiply a negative number 3 times to get an odd number, but you cannot multiply a negative number 2 times to get a negative number
_________________

The question is not can you rise up to iconic! The real question is will you ?

Kudos [?]: 431 [0], given: 192

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16609

Kudos [?]: 273 [0], given: 0

Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

10 Jul 2014, 09:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Manager
Joined: 27 May 2014
Posts: 87

Kudos [?]: 20 [0], given: 21

Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

10 Jul 2014, 14:07
The way I intepreted this problem, is m can be any negative number. M does not have to be an integer. I immediately chose the greatest negative range as the answer because I figured I could offset it with some (n^2) to equal -300. For example if I chose m to be -20 than (m^(3)) would be -8000. and I would find a number that for (n2) that is equal to 7970.

Bunuel whats wrong with this logic?

Kudos [?]: 20 [0], given: 21

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2626 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

11 Jul 2014, 02:07
$$m^3 - n^2 = -300$$

$$n^2 = 300 + m^3$$

$$5^3 = 125; & 10^3 > 300$$

So least value of m should be between -5 & -10

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2626 [0], given: 193

Intern
Joined: 11 Jul 2014
Posts: 6

Kudos [?]: 1 [0], given: 0

Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

11 Jul 2014, 05:09
bankerboy30 wrote:
The way I intepreted this problem, is m can be any negative number. M does not have to be an integer. I immediately chose the greatest negative range as the answer because I figured I could offset it with some (n^2) to equal -300. For example if I chose m to be -20 than (m^(3)) would be -8000. and I would find a number that for (n2) that is equal to 7970.

Bunuel whats wrong with this logic?

Hi Bankerboy30,

In your case, you would need to find n such that square of n would equal -7700 (300-8000). Now, we know that square of a real number cannot be negative and we don't deal with imaginary numbers in GMAT.

So, you need to go by a limitation that square of n can be minimum ZERO, not less than that. If you use that, you will get the answer as Bunuel got.

Does it help?

AEL

Kudos [?]: 1 [0], given: 0

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 622

Kudos [?]: 768 [0], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

05 Aug 2015, 20:56
Thank you
guerrero25 wrote:
If m^3-n^2=-300, then the lowest possible value of m is between

(A) -20 and -15
(B) -15 and -10
(C) -10 and -5
(D) -5 and 0
(E) 0 and 5

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Kudos [?]: 768 [0], given: 59

CEO
Joined: 17 Jul 2014
Posts: 2604

Kudos [?]: 395 [0], given: 184

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

08 Apr 2016, 19:23
guerrero25 wrote:
If m^3-n^2=-300, then the lowest possible value of m is between

(A) -20 and -15
(B) -15 and -10
(C) -10 and -5
(D) -5 and 0
(E) 0 and 5

m will be minimum when n=0, otherwise by deducting a positive number, the negative will get even bigger.
m^3 = 300
ok...
-5x-5x-5=-125..so clearly can be lower than -5. D and E are out.
-10x-10x-10=-1000 clearly not lower than -10. A and B out.
C remains.

Kudos [?]: 395 [0], given: 184

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 841 [0], given: 595

Re: If m^3-n^2=-300, then the lowest possible value of m is [#permalink]

### Show Tags

15 Apr 2016, 02:39
Here the value of M must lie between -6 and -7
_________________

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

Kudos [?]: 841 [0], given: 595

Re: If m^3-n^2=-300, then the lowest possible value of m is   [#permalink] 15 Apr 2016, 02:39
Display posts from previous: Sort by