algebra- inequalities

pritam.ryders wrote:Is y a negative number?

1) y + 2 is positive
2) y² > 10

Target question: Is y negative?

Statement 1: y + 2 is positive
In other words, y + 2 > 0
Subtract 2 from both sides to get y > -2
From this information, can we determine whether or not y is negative?
No.
Consider these two conflicting cases:
Case a: y = -1, in which case y IS negative
Case b: y = 1, in which case y is NOT negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y² > 10
There are two possible sets of y-values that satisfy this inequality
Case a: y > √10, in which case y is NOT negative
Case b: y < -√10, in which case y IS negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 presents us with two possible cases:
Case a: y > √10
Case b: y < -√10

Statement 1 tells us that y > -2. This eliminates case b, since y cannot simultaneously be greater than -2 AND less than -√10 (≈3.2).
This means that it MUST be the case that y > √10, which means y is definitely NOT negative.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent