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# If m and n are non-zero integers, is mn > nn?

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Intern
Joined: 07 Aug 2016
Posts: 22
Location: India
WE: Consulting (Energy and Utilities)
If m and n are non-zero integers, is mn > nn?  [#permalink]

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05 Jun 2017, 08:12
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Difficulty:

95% (hard)

Question Stats:

44% (01:44) correct 56% (01:46) wrong based on 106 sessions

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If m and n are non-zero integers, is mn > nn?
Statement 1: |m| = n
Statement 2: m < n
Retired Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
Re: If m and n are non-zero integers, is mn > nn?  [#permalink]

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05 Jun 2017, 09:04
1
RudraM wrote:
If m and n are non-zero integers, is mn > nn?
Statement 1: |m| = n
Statement 2: m < n

Statement 1: it implies that n>0 (as mod cannot be negative) and "m" can be m>0 or m<0
if m>0, then m=n, so mn = nn
if m<0, then m=-n, so mn<nn (as "mn" will be negative & "nn" will be positive)
In either case "mn" will not be greater than "nn". So a definite NO. Hence sufficient

Statement 2: we don't know whether "m" & "n" are positive or negative.
if n>0, then multiplying both sides of the inequality m<n by "n" will give us mn<nn, but
if n<0, then multiplying both sides of the inequality m<n by "n" will yield mn>nn. Hence insufficient

Option A
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Re: If m and n are non-zero integers, is mn > nn?  [#permalink]

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05 Jun 2017, 09:49
Statement 1. |m| = n. Now m and n are non-zero, so |m| Must be positive. This means n is definitely positive, and m could be either positive or negative (but absolute values of m and n are equal)

Now if m is also positive, then m=n, and thus m*n = n*n.
And if m is negative, then m*n < n*n
So we can conclude that m*n will be either equal to or less than n*n. It could never be greater than n*n.

So this gives NO as an answer to the question asked. Thus Sufficient.

Statement 2. m < n

Take a case where m=-2, n = 1. Here m*n < n*n
Take another case where m=-2, n=-1. Here m*n > n*n.

So we cannot conclude. Insufficient.

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Re: If m and n are non-zero integers, is mn > nn?  [#permalink]

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06 Jun 2017, 01:22
RudraM wrote:
If m and n are non-zero integers, is mn > nn?
Statement 1: |m| = n
Statement 2: m < n

Is mn > nn?
Is n*(m-n) > 0?

Statement 1: |m| = n
i.e. n is definitely positive
i.e. if m is positive then n*(m-n) = 0 i.e. answer to the question is NO
and if m is Negative then n*(m-n) < 0 i.e. answer to the question is NO

SUFFICIENT

Statement 2: m < n

@m=2 and n=3, n*(m-n) < 0 i.e. answer to the question is NO
@m=-5 and n=-2, n*(m-n) > 0 i.e. answer to the question is YES

NOT SUFFICIENT

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Re: If m and n are non-zero integers, is mn > nn?  [#permalink]

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04 Sep 2018, 04:31
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Re: If m and n are non-zero integers, is mn > nn?   [#permalink] 04 Sep 2018, 04:31
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