What is the value of m ? (1) |m + 2| = 0 (2) |m + 4| + m = 0

Question

What is the value of m ?

(1) |m + 2| = 0
(2) |m + 4| + m = 0

rajatchopra1994 · Answer

Explanation:

To find: the value of m

(1) |m + 2| = 0
m + 2 = 0 ; -m-2 = 0
m=-2 ; m=-2
Sufficient

(2) |m + 4| + m = 0
2m+4 = 0 ; -m-4+m = 0
m = -2 ; N.A
Not Sufficient

IMO-A

Ozzy11100 · Answer

Why do you believe that B isn't also sufficient?

By your own calculations, there is  only one valid value for m in B's equation . So is B not sufficient so say m=-2?

What am I missing?

QuantMadeEasy · Answer

(1) |m + 2| = 0
 Step 1: Understanding statement 1 alone 
m = -2 
Sufficient

(2) |m + 4| + m = 0
 Step 2: Understanding statement 2 alone 
Case 1:m + 4 + m = 0; m = -2
Case 2: -m - 4 + m = 0 Not possible as LHS not equal to RHS
Sufficient

D is correct

Buggs23Bunny · Answer

In statement 2 we get m=-2 for m>=0 so how can we consider this to be sufficient to answer this question?

MonkeyDDes · Answer

1st answer: m=-2 
2nd answer: NS
Can I assume that m is equal to -2?

AndrewN · Answer

Hello, everyone. I am surprised to see so much confusion on this one.  Buggs23Bunny , the notion that  m  must be greater than or equal to 0 in statement (2) is false, an oversight, perhaps, of the information provided  outside  the absolute value:

A simple algebraic manipulation shows that  m   must , in fact, be negative:

|m + 4| + m - m = 0 - m

|m + 4| = -m

There is simply no way for the left-hand side to produce a negative value, since the distance from 0 can only ever be 0 or a positive value. But a negative value for  m  on the right-hand side would yield a positive value, and |m + 4| can certainly produce such a value.

Per your concern,  MonkeyDDes , about  assuming  that "m is equal to -2," there is no need for such an assumption. The math leads us to the same conclusion, with or without a rigorous test. That is, if  m  must be negative, as explained above, we only have to ask ourselves whether a single negative value would produce a valid equation (leading to a SUFFICIENT answer) or whether multiple values exist. One way you can feel better about  m  equaling -2 without doing any more than mental math is to attempt to  disprove  that it is the only valid value. Of course,

|(-2) + 4| = -(-2) or

|2| = 2

But, try as you might, you will be unable to balance the two sides of the equation with any other input for  m . You can test 0, decimals, whatever, but your efforts will prove unsuccessful. (Of course, you would also be welcome to work through the algebra, as others have done in earlier posts.)

I hope this post may clarify a few concerns. Good luck with your studies.

- Andrew

What is the value of m ? (1) |m + 2| = 0 (2) |m + 4| + m = 0

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What is the value of m ? (1) |m + 2| = 0 (2) |m + 4| + m = 0

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