ash4gmat 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
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
Brent Hanneson - Creator of GMATPrepNow.com
