Target question: What is the value of x?riz_gmat wrote:What is the value of x?
1) |x² + 1| < 1
2) |x² - 1| < 1
Statement 1: |x² + 1| < 1
Rule: If |something| < k (where k > 0), then -k < something < k
So, we can take |x² + 1| < 1 and rewrite it as -1 < x² + 1 < 1
Subtract 1 from both sides to get -2 < x² < 0
Since x² is always greater than or equal to 0, we can see that x must equal 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: |x² - 1| < 1
Rewrite as -1 < x² - 1 < 1
Add 1 to both sides to get: 0 < x² < 2
There are many values of x that satisfy this inequality.
For example, x = 0 and x = 1 both work.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
