Target question: Is the positive integer n odd?
Statement 1: n = 2k + 1, where k is a positive integer
This is the classic definition of an odd integer.
That is, ALL odd integers can be written in the form 2k + 1, where k is a positive integer
This should make sense because, if k is an integer, then 2k will be an EVEN integer, which means 2k+1 must be an ODD integer.
In other words, n must be an odd integer
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: 2n + 1 is an odd integer
As mentioned above, 2n + 1 will be an odd integer for ALL values of n.
Consider these two cases:
Case a: If n = 2, then 2n + 1 = 2(2) + 1 = 5, which is odd. In this case, the answer to the target question is NO, n is not odd
Case b: If n = 3, then 2n + 1 = 2(3) + 1 = 7, which is odd. In this case, the answer to the target question is YES, n is odd
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
