jain2016 wrote:What is the value of X ?
1) x² + x + 10 = 16
2) x = 4y� + 2y² + 2
Target question: What is the value of x?
Statement 1: x² + x + 10 = 16
Rewrite as: x² + x - 6 = 0
Factor: (x + 3)(x - 2) = 0
So, x = -3 or x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x = 4y� + 2y² + 2
There are several values of x and y that satisfy statement 2. Here are two:
Case a: if y = 0, then x = 4(0�) + 2(0²) + 2 = 2
Case b: if y = 1, then x = 4(1�) + 2(1²) + 2 = 8
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 = -3 or 2
Statement 2 tells us that x = 4y� + 2y² + 2
IMPORTANT: Since y� > 0 and since y² > 0 for all values of y, we can see that 4y� + 2y² + 2 MUST BE greater than or equal to 2.
This means that x CANNOT EQUAL -3, which means x MUST EQUAL 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
