If |m + 4| = 2, What is the Value of m?

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

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

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are not sufficient.

“If |m + 4| = 2, what is the value of m?” – - is the topic of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Prep Plus 2021”. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements.GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

We know that if |expression|=p
The two solutions are:
=> expression = p
=> expression = -p

Now, using the equation given in the problem statement
=> m=-4+2=-2
=> -4-2=-6

Considering Statement 1 => m<0 =?>
m can be -6 or -2
Hence, it is not sufficient

Considering Statement 2
m^2+8m+12
=> m^2+2m+6m+12=0
=> m(m+2)+6(m+2)
=> m=-2 or -6

This is also not sufficient
Combining Statement 1 and Statement 2
=> m can be -2 or -6

This is also not sufficient.
Hence, E is the correct answer.

Approach Solution 2:

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.
Combination will also give the same result.
Hence, E is the correct answer.

Approach Solution 3:

From the given equation, we get:
|m+4|=2
=> m+4= +2
or m+4= -2
We get: m= -2 or m= -6
On using statement 1 we are getting two values of m= -2 and -6
Hence statement 1 is not sufficient

Now, let us consider statement 2
This is 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
In this also, we get 2 values.
Now, we will combine both and check:
On combining equation 1 and equation 2
we are again getting m= -2 and -6
Since we are not getting a single value, E is the correct answer.

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