gmatmachoman wrote:An interger greater than 1 that is not prime is called composite. If the two digit integer 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.

It's A

cancel out 2] it give multiple options like 21,22,23,24...some are composite others aren't

from 1] numbers wil be in range [21--66] for other two digits tens digit won't be factor of units digit
now for any number where tens is factor of units, consider odd/even tens digit e.g. 22,24,26... and 33, 36,39... all numbers will be composite, hence 1 alone is sufficient so A

gmatmachoman wrote:An interger greater than 1 that is not prime is called composite. If the two digit integer 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.

From the St 1, I could understand that For the 2 digit numbers n whose ten's digit is a factor of its unit's digit then "n" shall be a composite number.

et us try out few cases : 21, 22, 24, 26, 28,30,33,36,39,42....

In all the above examples ten's digit is a factor of its unit's digit.And they turn out to be Composite number.

Coming to st 2.
2. The tens digit of n is 2

Let us try out some cases :

What if the number is 29?? It starts with 2 but it is a "prime number". So st 2 is not sufficient to state "n" is composite number.

IMO A

The unit digit can be 2 x 1 , 2 x 2 , 2 x 3 , 2 x 4 or 3 x 1 , 3 x 3 . Since the number is > 20, the possible solutions are 22,24,26,36,28,48,33,39.
Each of these number is divisible by the tens digit. 24 / 2 , 36 / 3 , 39 / 3 or 48 / 4. Therefore condition A is sufficient to prove that is is a composite number.

Condition B is not sufficient - The number is > 20 but < 30 , when the tens digit is 2 of which 23 , 29 are prime numbers.

Hence A.

gmatmachoman wrote:An interger greater than 1 that is not prime is called composite. If the two digit integer 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.

another approach from testmagic
Let x be tens digit and y be units digit.
n = 10x + y

(1) The tens digit of n is a factor of the units digit of n.
y = kx where k is a positive integer
n = 10x + kx
= (10 +k)*x
So the number n is composite. SUFFICIENT
(2) The tens digit of n is 2.
if n = 21 it is composite.
if n = 23 it is prime. INSUFFICIENT
Hence A.

komal wrote:

gmatmachoman wrote:An interger greater than 1 that is not prime is called composite. If the two digit integer 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.

another approach from testmagic
Let x be tens digit and y be units digit.
n = 10x + y

(1) The tens digit of n is a factor of the units digit of n.
y = kx where k is a positive integer
n = 10x + kx
= (10 +k)*x
So the number n is composite. SUFFICIENT
(2) The tens digit of n is 2.
if n = 21 it is composite.
if n = 23 it is prime. INSUFFICIENT
Hence A.

that is a good approach komal but a bit lengthy ...I think