Question

An integer greater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite? (1) the tens digit of n is a factor of the units digit of n. (2) the tens digit of n is 2.

Answer 1

Step-by-step explanation:

given: n>20 

two digit integer can be written as follows: 

n=10b+a >20

n=10b+a >20

 here, b = 2≤b≤9, 

a = 0≤a≤9.

(1) The tens digit of n is a factor of the units digit of n. This statement implies that a=kb, (0≤k≤4)

 n=10b+a

n=10b+kb

n= b(10+k)

as b≥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.