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If [m]|m-1| = |n+1|[/m] , what is the value of [m]m — n[/m]?

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If [m]|m-1| = |n+1|[/m] , what is the value of [m]m — n[/m]?  [#permalink]

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New post 20 Oct 2018, 09:44
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

42% (01:55) correct 58% (01:53) wrong based on 44 sessions

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If \(|m-1| = |n+1|\) , what is the value of \(m — n\)?
1) \(mn > 0\)
2) \(\frac{m}{n}\)\(\neq{-1}\)

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Re: If [m]|m-1| = |n+1|[/m] , what is the value of [m]m — n[/m]?  [#permalink]

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New post 20 Oct 2018, 09:52
Answer d:

statement 1 tells us that m and n are either both positive or both negative
lets take the case where theyre both positive:
therefore the absolute value turns into
m-1 = n+1
so m-n = 2

if they're both negative then its
-m+1 = -n-1
and you still get that m-n = 2
Therefore sufficient

Statement 2 rearranged gives you m =! -n
then again you see they have the same signs and it will also be sufficient
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Re: If [m]|m-1| = |n+1|[/m] , what is the value of [m]m — n[/m]?  [#permalink]

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New post 20 Oct 2018, 10:01
C.

Can't get m-n from first if both are negative. The second is insufficient as it just states that they are same or different sign. Together sufficient.
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Re: If [m]|m-1| = |n+1|[/m] , what is the value of [m]m — n[/m]?  [#permalink]

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New post 20 Oct 2018, 10:05
Answer D. Please see enclosed for details

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Re: If [m]|m-1| = |n+1|[/m] , what is the value of [m]m — n[/m]?  [#permalink]

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New post 20 Oct 2018, 10:11
Given |m-1|=|n+1|

Case 1: which means if m>1 and n>-1
it becomes m-1=n+1
so m-n=2

Case 2: if m<1 and N>-1
1-m=1+n
so, m+n=0

Case 3:if m>1, and n<-1
m-1= -1-n
m+n=0

Case 4:if m<1 and n<-1
1-m=-1-n
so, m-n=2

case 5: m=1 and n=-1
m-1=n+1
which means m-n=2

Option A , mn>0,
which means either m>0, n>0 or m<0 , n<0
if both m, n >0, both case 1 and case 2 are applicable
so not deductible

if both are <0, ie m<0 and n<0
case 3 and case 4 applies
hence A is not sufficinet

Option B: m/n is not equal to -1 which is the limiting case of m=1 and n=-1 or m=-1 and n=1
hence not sufficient

Combing both,
cant decide whether m-n=2 or m+n=0


hence E is the answer
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Re: If [m]|m-1| = |n+1|[/m] , what is the value of [m]m — n[/m]? &nbs [#permalink] 20 Oct 2018, 10:11
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