arellalu wrote:What is Ryan's age now?
1) Ryan is twice as old as he was 8 years ago.
2) Ryan's sister Katie is now 3 times as old as Ryan was exactly 8 years ago

Let R = Ryan's current age.
Target question: What is the value of R?

Statement 1: Ryan is twice as old as he was 8 years ago.
R-8 = Ryan's age 8 years ago.
From statement 1, we can write the equation R = 2(R-8)
Solve for R to get:
R = 2R - 16
R = 16
Since we're able to definitively find the value of R, statement 1 is SUFFICIENT

Statement 2: Ryan's sister Katie is now 3 times as old as Ryan was exactly 8 years ago
Since we know nothing about Katie's age, this statement is not sufficient.
We can demonstrate this by show two conflicting possible cases.
case a: Ryan's current age is 16, and Katie's current age is 24.
case b: Ryan's current age is 9, and Katie's current age is 3.

Since we get two different answers to the target question, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent