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

Question

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

(1)  mn > 0

(2)  \frac{m}{n}  
eq{-1}

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

lostboy · Answer

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

raghavshekhar · Answer

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.

yenbh · Answer

Answer D. Please see enclosed for details

Posted from my mobile device

pk123 · Answer

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

avikroy · Answer

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

GMATBusters · Answer

St 2 doesn't say that m and n are zero.

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

Posted from my mobile device

CrackverbalGMAT · Answer

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.

Answer : D

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

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My Rewards