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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed May 27, 2020 6:28 pm

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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

OA D

Source: EMPOWERgmat

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Source: Beat The GMAT — Problem Solving | Wed May 27, 2020 6:28 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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

by Jay@ManhattanReview » Wed May 27, 2020 10:06 pm

BTGmoderatorDC wrote: ↑
Wed May 27, 2020 6:28 pm
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

OA D

Source: EMPOWERgmat

Let's take each statement one by one.

A. M – N:

If say M = 2 and N = 1, then M – N = 2 – 1 = 1 > 0. Not a correct answer.

B. (M – N)^2

Since (M – N)^2 is a square of (M – N), it is always non-negative. Not a correct answer.

C. (M – N)^3:

If say M = 2 and N = 1, then (M – N)^3 = (2 – 1)^3 = 1 > 0. Not a correct answer.

D. M^2 – N^2

With M and N are non-zero integers and M > N and M^2 and N^2 are both positive and M ^2 > N^2; thus, M^2 – N^2 > 0. Correct answer.

E. M^3 – N^3

If say M = 2 and N = 1, then M^3 – N^3 = 2^3 – 1^3 = 8 – 1 = 7 > 0. Not a correct answer.

The correct answer: D

Hope this helps!

-Jay
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

by Brent@GMATPrepNow » Thu May 28, 2020 9:15 am

BTGmoderatorDC wrote: ↑
Wed May 27, 2020 6:28 pm
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

OA D

Source: EMPOWERgmat

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

by Scott@TargetTestPrep » Sun May 31, 2020 4:01 am

BTGmoderatorDC wrote: ↑
Wed May 27, 2020 6:28 pm
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

OA D

Solution:

Recall that M^2 - N^2 = (M - N)(M + N). Since M > N, M - N is positive. However, if both M and N are negative, then M + N is negative and (M - N)(M + N) would be negative i.e., not greater than 0.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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