Data Sufficiency

Brent@GMATPrepNow wrote:

prernamalhotra wrote:
K is a set of numbers such that
i) if x is in K, then (-x) is in K and,
ii) if each of x and y is in K, then xy is in K

Is 12 in K?

1) 2 is in K
2) 3 is in 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 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 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