Is |v - x| < 8? (1) v and x are integers (2) |v| = 4 and |x| = 6

Step 1: Analyse Question Stem

We need to find out if |v – x| < 8.

The key to solving such questions on absolute inequalities is to understand the definitions of Absolute value.

|x – a| represents the distance of the number x from the number a, when measured on the number line.
Therefore, |x| represents the distance of the number x from ZERO.

As such, the question “Is |v – x| < 8?” can be rephrased as “Is the distance of v from x, less than 8?”

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: v and x are integers

Clearly, this is insufficient since knowing the nature of the numbers is not sufficient to measure the distance between them.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: |v| = 4 and |x| = 6
By definition, |v| = 4 means that the distance of the number v from ZERO is equal to 4.
Therefore, v = 4 or v = -4.
Similarly, |x| = 6 means x = 6 or x = -6.

If we consider v = 4 and x = -6, the distance of v from x is 10 units; is |v – x| < 8? NO.
If we consider v = 4 and x = 6, the distance of v from x is 2 units; is |v – x| < 8? YES.

Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining
From statement 1: v and x are integers
From statement 2: v = 4 or v = -4 AND x = 6 or x = -6.

Now, statement 1 does not add anything to the information given in statement 2. From the analysis of statement 2, we already know that the values of v and x are integers.

Therefore, even after combining the statements, we have a YES and a NO.
The combination of statements is insufficient. Answer option C can be eliminated.

The correct answer option is E.