jswesth wrote:K is a set of numbers such that:
(i) If x is in K, then -x is in K, and
(ii) if each x and y is in K, then xy is in K.
Is 12 in K?
(1.) 2 is in K.
(2.) 3 in is K.
Target question: Is 12 in K?
Statement 1: 2 is in K
By rule i, -2 is also in set K
By rule ii, if 2 and -2 are in set K, then -4 is in set K
By rule i, 4 is also in set K
By rule ii, if 2 and -4 are in set K, then -8 is in set K
By rule ii, if 2 and 4 are in set K, then 8 is in set K
etc..
So, all we can say is that the following numbers MUST be in K: ...-16, -8, -4, -2, 2, 4, 8, 16...
Since we don't know what other numbers might be in K,
12 might be in K or
12 might NOT be in K.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3 is in K
By rule i, -3 is also in set K
By rule ii, if 3 and -3 are in set K, then -9 is in set K
By rule i, 9 is also in set K
By rule ii, if 3 and -9 are in set K, then -27 is in set K
By rule ii, if 3 and 9 are in set K, then 27 is in set K
etc..
So, all we can say is that the following numbers MUST be in K: ...-27, -9, -3, 3, 9, 27,...
Since we don't know what other numbers might be in K,
12 might be in K or
12 might NOT be in K.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that 4 must be in set K
Statement 2 tells us that 3 must be in set K
By rule ii, if 4 and 3 are in set K, then
12 is in set K
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
