An integer grater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?Given: \(n>20\) --> two digit integer can be written as follows: \(n=10b+a>20\) --> \(2\leq{b}\leq{9}\), \(0\leq{a}\leq{9}\).
(1) The tens digit of n is a factor of the units digit of n. This statement implies that \(a=kb\), (\(0\leq{k}\leq{4}\)) --> \(n=10b+a=10b+kb=b(10+k)\) --> as \(b\geq{2}\), \(n\) will always be composite and factor of \(b\). Sufficient
(2) The tens digit of n is 2. This statement implies that \(b=2\), but \(n\) can be for instance composite 25 or prime 29. Not sufficient.
Answer: A.
chetan2u wrote:
A..
SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite....
SII.. no can be any of 21,22,23.....29..ie mix of composite and prime
Actually units digit of \(n\) can be any digit but 1, meaning that 0, 2, 3, 5, 7 too. And for 9: 99 also fits: eg . 30, 40, 50, 60, 70, 80, 90, 22, 33, 55, 77, 99.
What about No. 71 .