Bunuel wrote:
If |4 – x| = 8, what is the value of x?
(1) x² is an even number.
(2) |x| is the square of a prime number.
When solving equations 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 solutions into original equation to check for extraneous roots
Target question: What is the value of x? Given: |4 – x| = 8 So, 4 - x = 8 or 4 - x = -8
If 4 - x = 8, then x = -4
If 4 - x = -8, then x = 12
So, x = -4 or x = 12
Statement 1: x² is an even number We already know that x = -4 or x = 12, so there are two cases to consider:
case a: If x = -4, then x² = (-4)² = 16, which is an even number. So,
x could equal -4 case b: If x = 12, then x² = (12)² = 144, which is an even number. So,
x could equal 12 Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |x| is the square of a prime number We already know that x = -4 or x = 12, so there are two cases to consider:
case a: If x = -4, then |-4| = 4, and 4 IS the square of a prime number (2). So,
x could equal -4 case b: If x = 12, then |12| = 12, BUT 12 is NOT the square of a prime number. So,
x cannot equal 12 So, x MUST equal -4
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
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