rohitgoel15 wrote:
What is x?
(1) |x| < 2
(2) |x| = 3x – 2
Target question: What is the value of x? Statement 1: |x| < 2 There are several values of x that satisfy statement 1. Here are two:
Case a:
x = 1 (notice that < 2)
Case b:
x = 0 (notice that |0| < 2)
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |x| = 3x - 2 When solving equation involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says:
If |x| = k, then x = k and/or x = -k2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots
So, first we get:
x = 3x - 2
Solve, to get x =
1To check whether this is an extraneous, plug x =
1 into the original equation to get: |
1| = 3(
1) - 2
Simplify to get: |1| = 1
PERFECT, this solution checks out.
Next, we get:
x = -(3x - 2)
Solve, to get x =
1/2To check whether this is an extraneous, plug x =
1/2 into the original equation to get: |
1/2| = 3(
1/2) - 2
Simplify to get: |1/2| = -1/2
This solution DOES NOT check out.
So, it MUST be the case that
x = 1Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent