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

 It is currently 14 Nov 2018, 03:49

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# 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: 269
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, 00:22
17
00:00

Difficulty:

75% (hard)

Question Stats:

56% (02:03) correct 44% (02:08) wrong based on 350 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
Math Expert
Joined: 02 Sep 2009
Posts: 50580
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

01 Apr 2013, 00:51
7
4
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).

_________________
##### General Discussion
Senior Manager
Joined: 10 Apr 2012
Posts: 269
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, 02:02
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
Intern
Joined: 15 Jan 2013
Posts: 26
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, 06:40
2
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
Senior Manager
Joined: 23 Mar 2011
Posts: 411
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, 05:57
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

Math Expert
Joined: 02 Sep 2009
Posts: 50580
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

25 Apr 2013, 07:34
1
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 $$\sqrt[3]{-64} =-4$$.
_________________
Retired Moderator
Joined: 10 May 2010
Posts: 811
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

25 Apr 2013, 07:53
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 ?

Manager
Joined: 27 May 2014
Posts: 81
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

10 Jul 2014, 13:07
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?
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1827
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, 01:07
$$m^3 - n^2 = -300$$

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

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

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

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 11 Jul 2014
Posts: 6
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

11 Jul 2014, 04:09
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
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
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, 19:56
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

Board of Directors
Joined: 17 Jul 2014
Posts: 2645
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, 18:23
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.
Current Student
Joined: 12 Aug 2015
Posts: 2633
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

15 Apr 2016, 01:39
VP
Joined: 09 Mar 2016
Posts: 1062
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

18 Jul 2018, 09:39
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).

Bunuel hello there how are you ? can you please explain how after this $$m^3-n^2=-300$$ you get this $$m=\sqrt[3]{n^2-300}$$. Exponent 3 is outside of darical sign and exponent 2 is inside radical sign
Math Expert
Joined: 02 Sep 2009
Posts: 50580
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

18 Jul 2018, 09:42
1
dave13 wrote:
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).

Bunuel hello there how are you ? can you please explain how after this $$m^3-n^2=-300$$ you get this $$m=\sqrt[3]{n^2-300}$$. Exponent 3 is outside of darical sign and exponent 2 is inside radical sign

$$m^3-n^2=-300$$;

$$m^3=n^2-300$$;

$$m=\sqrt[3]{n^2-300}$$.
_________________
VP
Joined: 09 Mar 2016
Posts: 1062
If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

18 Jul 2018, 10:03
Bunuel from here $$m^3=n^2-300$$ how do you get ths $$m=\sqrt[3]{n^2-300}$$ what are you doing such that exponent 3 goes to the right please help
Math Expert
Joined: 02 Sep 2009
Posts: 50580
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

18 Jul 2018, 10:05
1
dave13 wrote:
Bunuel from here $$m^3=n^2-300$$ how do you get ths $$m=\sqrt[3]{n^2-300}$$ what are you doing such that exponent 3 goes to the right please help

Take the cube root. The same way we get $$x=\sqrt[3]{y}$$ from $$x^3 = y$$.
_________________
Senior Manager
Joined: 04 Aug 2010
Posts: 305
Schools: Dartmouth College
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

18 Jul 2018, 11:12
1
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

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

To minimize the value of $$m^3$$, we must minimize the right side of the equation in blue.
Since the square of a value cannot be negative, the least possible option for the right side is 0:
$$m^3 + 300 = 0$$
$$m^3 = -300$$

Since $$-5^3 = -125$$ and $$-10^3 = -1000$$, m must be between -10 and -5.

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

Intern
Joined: 31 May 2018
Posts: 17
Location: United States
Concentration: Finance, Marketing
Re: If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

18 Jul 2018, 23:46
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

$$n^2$$ =$$m^3$$+300
since L.H.S (+), R.H.S should be positive
so option (a), (b) is wrong
from (c) (d) and (e) lowest possible value of m
we can get from option c
Intern
Joined: 15 Jul 2018
Posts: 8
GMAT 1: 700 Q47 V39
If m^3-n^2=-300, then the lowest possible value of m is  [#permalink]

### Show Tags

24 Jul 2018, 01:33
When we look at the answer choices, we can see that A and B is too high to get -300 even if we take n=0. Thus eliminate A and B. Since we need the lowest value of m assume that n=0 (it will help minimize m as the higher absolute value of a negative number the lower that number, thus the case, in which m^3= -300 gives the possible lowest value for m ). We get m = -6, smth, which is in the range of -10 and -5. Hence C.

Hope it helps!
If m^3-n^2=-300, then the lowest possible value of m is &nbs [#permalink] 24 Jul 2018, 01:33
Display posts from previous: Sort by