Bunuel wrote:
Is x ≥ 3 ?
(1) x² - 9 = 0
(2) x < 10
Target question: Is x ≥ 3 ? Statement 1: x² - 9 = 0 Add 9 to both sides of the equation to get: x² = 9
When we solve this we see that EITHER x = 3 OR x = -3
Let's examine both possible cases:
Case a: If x = 3, then the answer to the target question is
YES, it is the case that x ≥ 3Case b: If x = -3, then the answer to the target question is
NO, it is not the case that x ≥ 3Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x < 10There are several values of x that satisfy statement 2. Here are two:
Case a: If x = 9, then the answer to the target question is
YES, it is the case that x ≥ 3Case b: If x = 0, then the answer to the target question is
NO, it is not the case that x ≥ 3Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that EITHER x = 3 OR x = -3
Notice that
both of these possible x-values are less than 10.
If x = 3, then the answer to the target question is
YES, it is the case that x ≥ 3If x = -3, then the answer to the target question is
NO, it is not the case that x ≥ 3Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent