vittovangind wrote:
"K is a set of integers such that

i) if x is in K, then 2x is in K

ii) if each of x and y is in K, then x + y is in K

Is 15 in K?

(1) 1 is in K.
(2) 3 is in K."

Target question: Is 15 in set K?

Given:
Rule #1: if x is in K, then 2x is in K
Rule #2: if each of x and y is in K, then x + y is in K

Statement 1: 1 is in K.
Rule #1 says that if 1 is in set K, then 2 must be in set K
Rule #1 says that if 2 is in set K, then 4 must be in set K
Rule #1 says that if 4 is in set K, then 8 must be in set K
etc.
So, we know that set K must contain 1, 2, 4, 8, etc
Rule #2 says that if 1 and 2 are in set K, then their sum (3) must be in set K
Rule #2 says that if 4 and 8 are in set K, then their sum (12) must be in set K
If 3 and 12 are in set K, Rule #2 says that their sum must be in set K. In other words, 15 must be in set K
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3 is in K
Rule #1 says that if 3 is in set K, then 6 must be in set K
Rule #2 says that if 3 and 6 are in set K, then their sum (9) must be in set K
If 6 and 9 are in set K, Rule #2 says that their sum must be in set K. In other words, 15 must be in set K
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent