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
