Target question: What is the value of x?ash4gmat wrote: What is the value of x ?
(1) x² + x + 10 = 16
(2) x = 4y� + 2y² +2
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
As you can see, the value of x depends on the value of y.
Consider these two cases:
Case a: y = 0, in which case x = 4(0�) + 2(0²) + 2. Evaluate to see that x = 2
Case b: y = 1, in which case x = 4(1�) + 2(1²) + 2. Evaluate to see that x = 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 x = 2
Statement 2: Since y� and 2y² are greater than or equal to zero FOR ANY value of y, we can see that 4y� + 2y² + 2 MUST BE POSITIVE. In other words, x must be POSITIVE.
If x must be POSITIVE, then x MUST equal 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
