If |m + 4| = 2, what is the value of m?

Question

(1) m < 0 
(2) m^2 + 8m + 12 = 0

stonecold · Answer

If |expression|=p
=> expression = p
and expression = -p are two solutions
Hence => m=-4+2=-2
-4-2=-6
Statement 1 => m<0 =?> m can be -6 or -2 => not suff
m^2+8m+12=> m^2+2m+6m+12=0=> m(m+2)+6(m+2) => m=-2 or -6
not suff

Combining them => m can be -2 or -6
Hence E

smita12345 · Answer

IMO E 
 |m+4|=2 
 Gives m=-2 or -6

Statement 1: m <0 
Not sufficient since -2 & -6 both are less than 0

Statement 2:
m^2+8m+12=0
m =-2,-6
not sufficient

Hence E

daboo343 · Answer

Analytically

from the given equation
|m+4|=2
=> m+4= +2 or m+4= -2
m= -2 or m= -6
on using condition 1 we are getting two values of m= -2 and -6
hence statement 1 is not sufficient
now consider statement 2
its a quadratic equation
m^2+8m+12=0
=> m^2 +6m+2m+12=0
=>m(m+6)+2(m+6)=0
=>(m+2)(m+6)=0
=> m=-2 and -6
again we are getting two values
on combining equation 1 and equation 2 
we are again getting m= -2 and -6
 here this equation can also be solved graphically. the graph will look like a parabola opening upward and cutting the x axis at -2 and -6. 
we will get the same result
Hence E

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

It is given that |m + 4| = 2. We have to find the value of m

|x – a| represents the distance of x from a, on the number line.

Therefore, |m + 4| represents the distance of m from -4; since |m + 4| = 2, we can say,

Distance of m from -4 = 2units
Therefore, m = -2 or -6.

We now analyse the statements to find out a unique value for m.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  m < 0.
From the question data, m = -2 or -6.

Since both values are negative, the data given in statement 1 is something that has already been established in the analysis of the question.

The data in statement 1 is insufficient to find out a unique value for m.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:   m^2  + 8m + 12 = 0

Factorising the quadratic,  m^2 + 8m + 12 = 0 can be written as,

(m + 6) (m + 2) = 0.

Therefore, m = -2 or m = -6. This is the same information furnished by the question.

The data in statement 2 is insufficient to find out a unique value for m.
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1:  m < 0

From statement 2:  m = -2 or m = -6
Since both the values of m are less than 0, there is no way of finding out the unique value of m.

The combination of statements is insufficient to find a unique value as the answer.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.

The correct answer option is E.

If |m + 4| = 2, what is the value of m?

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If |m + 4| = 2, what is the value of m?

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