ziyuenlau wrote:Is √x a prime number?
(1) |3x − 7| = 2x + 2
(2) x² = 9x
Target question: Is √x a prime number?
Statement 1: |3x − 7| = 2x + 2
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says:
If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
So, we get two equations: 3x − 7 = 2x + 2 or 3x − 7 = -(2x + 2)
If 3x − 7 = 2x + 2, then we get x = 9. When we plug this x-value into the original equation, it WORKS.
If x = 9, then
√x = √9 = 3, and 3 IS a prime number.
If 3x − 7 = -(2x + 2), then we get x = 1. When we plug this x-value into the original equation, it WORKS.
If x = 1, then
√x = √1 = 1, and 1 is NOT a prime number.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x² = 9x
Rearrange to get: x² - 9x = 0
Factor: x(x - 9) = 0
So, EITHER x = 0 OR x = 9
If x = 0, then
√x = √0 = 0, and 0 is NOT a prime number.
If x = 9, then
√x = √9 = 3, and 3 IS a prime number.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x = 9 or x = 1
Statement 2 tells us that x = 9 or x = 0
Since BOTH equations are TRUE, it MUST be the case that x = 9.
Since x = 9, then
√x = √9 = 3, and 3 IS a prime number.
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
C
Cheers,
Brent
