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

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If M and N are non-zero integers and M > N, then which of the  [#permalink]

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03 Oct 2019, 11:40
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Difficulty:

65% (hard)

Question Stats:

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

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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

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If M and N are non-zero integers and M > N, then which of the  [#permalink]

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03 Oct 2019, 11:53
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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

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!

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Re: If M and N are non-zero integers and M > N, then which of the  [#permalink]

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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.

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Re: If M and N are non-zero integers and M > N, then which of the  [#permalink]

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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
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Re: If M and N are non-zero integers and M > N, then which of the  [#permalink]

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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...

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Rich
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Re: If M and N are non-zero integers and M > N, then which of the   [#permalink] 06 Oct 2019, 21:05
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