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03 Oct 2019, 11:40
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
66% (01:51) correct
34%
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wrong
based on 406
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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
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.
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.
03 Oct 2019, 11:53
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EMPOWERgmatRichC
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
03 Oct 2019, 14:46
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[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.
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.
