Bunuel wrote:
If K is a positive 3-digit integer, is K prime?
(1) The last digit of K is not even
(2) K is the smallest number possible where the hundreds digit is the sum of the tens and units digit. Tens and units digits are equal.
Given : K is a positive 3-digit integer
Question : is K prime
Statement 1Except for 2, all the prime numbers are odd. However, the mere fact that the last digit is odd is not sufficient to conclude whether the number is prime.
For example, 115 has its last digit odd, but the number is not prime. However, 101 is prime.
Hence, the statement is not sufficient, and we can eliminate A and D.
Statement 2If a similar statement were to appear in the test, I wouldn't even solve statement 2. After reading the statement, we know that we are talking about a particular number - "K is the smallest number possible". Hence the possibility of multiple values is ruled out and the value of K will always be unique. Hence we can infer that the statement is sufficient.
However for the sake of completion, let's analyze the statement. It's given that "
K is the smallest number possible where the hundreds digit is the sum of the tens and units digit. Tens and units digits are equal."
So K = 211. 211 can either be prime or composite (it's prime btw). As this is a DS question, we don't really need to get bogged down by the actual answer. The answer will be unique, and the statement is sufficient.
Hence
Option B