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

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

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

(1) $$mn > 0$$

(2) $$\frac{m}{n}$$$$\neq{-1}$$

GMATbuster's Weekly GMAT Quant Quiz #5 Ques No 10

Answer in this case is D......However I have a doubt.......Statement 1 clearly indicates m-n=2.

However Statement 2 is satisfied if m and n are both zero.

The 2 statements should not contradict each other right??

Roy
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Re: If |m - 1| = |n + 1|, what is the value of m — n ? [#permalink]
St 2 doesn't say that m and n are zero.

Infact, if m and n are zero,
m/n doesn't exist.

avikroy wrote:
gmatbusters wrote:
If $$|m-1| = |n+1|$$, what is the value of $$m — n$$?

(1) $$mn > 0$$

(2) $$\frac{m}{n}$$$$\neq{-1}$$

GMATbuster's Weekly GMAT Quant Quiz #5 Ques No 10

Answer in this case is D......However I have a doubt.......Statement 1 clearly indicates m-n=2.

However Statement 2 is satisfied if m and n are both zero.

The 2 statements should not contradict each other right??

Roy

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

When you have a question with an absolute value on both sides of an inequality or equality, the best approach is to square both sides and remove the absolute value. The reason we can do this is because |x| = \sqrt{x^2}. Also while solving questions containing inequalities and absolute values it makes more sense to breakdown the question stem and rephrasing the data sufficiency question.

Given |m - 1| = |n + 1|
Squaring both sides and removing the absolute value we get,

(m - 1)^2 = (n + 1)^2 -----> (m - 1)^2 - (n + 1)^2 = 0

The above equation is in the form of a^2 - b^2

(m - 1)^2 - (n + 1)^2 ----> (m + n)(m - n - 2) = 0

So EITHER m + n = 0 OR m - n = 2

Remember this information is given to us in the question stem, so the only two possibilities we can consider are m + n = 0 or m - n = 2.

The question asks us for the value for m - n, given m not = n or m - n = 2, so if we are able to prove that m + n is not equal to 0 then we have m - n = 2.

Statement 1 : mn > 0

Here m and n both have the same signs, so m + n will not be equal to 0, so m - n = 2. Sufficient.

Statement 2 : m not = -n

This directly gives us what we want, so m - n = 2. Sufficient.