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

It is currently 12 Dec 2019, 07:21

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

If M and N are non-zero integers and M > N, then which of the

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

Hide Tags

Find Similar Topics 
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15704
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
If M and N are non-zero integers and M > N, then which of the  [#permalink]

Show Tags

New post 03 Oct 2019, 11:40
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (01:44) correct 49% (01:36) wrong based on 74 sessions

HideShow timer Statistics

EMPOWERgmat PS Series:
Pack 2, Question 2

If M and N are non-zero integers and M > N, then which of the following is not necessarily greater than 0?

A. M – N
B. (M – N)^2
C. (M – N)^3
D. M^2 – N^2
E. M^3 – N^3



48 Hour Window To Win An $85 EMPOWERgmat Tuition Credit (1 Month Free!)
Share your explanation! The GMAT Club member with the most verified Kudos in total on the 5 question PS Block 2 question pack will win an $85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win.

To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct

The OA and official explanation will be held until the 48 hour window has lapsed.

_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4136
Location: Canada
If M and N are non-zero integers and M > N, then which of the  [#permalink]

Show Tags

New post 03 Oct 2019, 11:53
1
Top Contributor
EMPOWERgmatRichC wrote:
EMPOWERgmat PS Series:
Pack 2, Question 2

If M and N are non-zero integers and M > N, then which of the following is not necessarily greater than 0?

A. M – N
B. (M – N)^2
C. (M – N)^3
D. M^2 – N^2
E. M^3 – N^3


Given: M > N
Subtract N from both sides to get: M - N > 0
In other words, M - N is positive

Check the answer choices...
A. M – N = some positive value. ELIMINATE A

B. (M – N)^2 = (some positive value)^2 = POSITIVE. ELIMINATE B

C. (M – N)^3 = (some positive value)^3 = POSITIVE. ELIMINATE C

D. M^2 – N^2 = (M - N)(M + N) = (some positive value)(M + N)
Hmmm, if we can find a way to make M+N NEGATIVE, we can see that M^2 – N^2 will be NEGATIVE

Let's test M = -1 and N = -2 (this meets the condition that M > N, and it will result in a NEGATIVE sum (M + N)
In this case M^2 – N^2 = (-1)^2 – (-2)^2 = 1 - 4 = -3
Aha!

Answer: D
_________________
Test confidently with gmatprepnow.com
Image
Manager
Manager
avatar
G
Status: Student
Joined: 14 Jul 2019
Posts: 135
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
Re: If M and N are non-zero integers and M > N, then which of the  [#permalink]

Show Tags

New post 03 Oct 2019, 14:46
1
[quote="EMPOWERgmatRichC"]EMPOWERgmat PS Series:
Pack 2, Question 2

If M and N are non-zero integers and M > N, then which of the following is not necessarily greater than 0?

A. M – N
B. (M – N)^2
C. (M – N)^3
D. M^2 – N^2
E. M^3 – N^3



We can take plug-in value approach for this problem. Since M , N are non-zero, let us consider M=3, N=2 and M=-2, N=-3.
A. M - N, (3-2)=1> 0 AND{-2-(-3)}=1> 0
B. (M - N)^2 , in both case 1 > 0.
C.(M - N)^3 , as M - N= 1, this is also greater than 0.
D. M^2 - N^2 , (3^2 -2^2) = (9 - 4) =5, {(-2)^2 -(-3)^2} =(4-9) = -5 , which is not greater than 0.
E. M^3 - N^3, (3^3 -2^3) = (27-8) = 19, {(-2)^3-(-3)^3}=(-8+27)= 19, both are greater than 0.

Hence, the answer is D.
Manager
Manager
avatar
G
Joined: 28 Feb 2014
Posts: 214
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE: Engineering (Education)
Re: If M and N are non-zero integers and M > N, then which of the  [#permalink]

Show Tags

New post 03 Oct 2019, 19:45
1
EMPOWERgmatRichC wrote:
EMPOWERgmat PS Series:
Pack 2, Question 2

If M and N are non-zero integers and M > N, then which of the following is not necessarily greater than 0?

A. M – N
B. (M – N)^2
C. (M – N)^3
D. M^2 – N^2
E. M^3 – N^3



We can use values. Let M=2 N =-3
A. 2+3 Positive. Incorrect
B. 5^2 Positive. Incorrect
C. 5^3 Incorrect
D. 4 - 9 = -5 Correct
E. 2^3 + 3^3 Positive. Incorrect

D is correct
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15704
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If M and N are non-zero integers and M > N, then which of the  [#permalink]

Show Tags

New post 06 Oct 2019, 21:05
OFFICIAL EXPLANATION

Hi All,

We're told that M and N are NON-ZERO INTEGERS and M > N. We're asked which of the following is not necessarily greater than 0? This question can be solved with Number Properties or by TESTing VALUES.

The 'key' to this question is to realize that N could be NEGATIVE (and specifically, "more negative" than M is "positive"; for example M = 2 and N = - 3). Using that example, we can quickly find the one answer that is not necessarily greater than 0.

A. (2) - (-3) = +5
B. (2 - (-3))^2 = +25
C. (2 - (-3)^3 = +125
D. (2)^2 - (-3)^2 = 4 - 9 = -5
E. (2)^3 - (-3)^3 = 8 - (-27) = +35

There's only one answer here that isn't greater than 0...

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Bot
Re: If M and N are non-zero integers and M > N, then which of the   [#permalink] 06 Oct 2019, 21:05
Display posts from previous: Sort by

If M and N are non-zero integers and M > N, then which of the

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





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