gmatmba wrote:

X & Y wrote:

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?

(1) The tens digit of n is a factor of the units digit of n.

(2) The tens digit of n is 2

Plz Explain..

(1) 24 (2 is a factor of 4), 39 (3 is a factor of 9), 48 (4 is a factor of 8) ... sufficient

(2) 22 composite, 23 not composite - not sufficient

This isn't a good way to do it because really you should be looking at primes and not composites. If one prime had a factor where the tens digit was a factor of its units then your answer is destroyed. All you did was prove that composites have some tens digits which are factors of units digits--it is impossible above 5 really for the tens to be a factor of the units because 6 doesn't go into 1,2,3,4,5,7,8,9. And we know 66,77,88 and 99 aren't prime as they have factors of 11 .

(1) It's better to list the prime. The prime between 20-60--you should memorize. Are: 23,29,31,37,41,43,49,53,59 and 61. Notice how none of the Tens are factors of the units number. So we know for a prime that the tens digit is not a factor of the units digit. For a composite we can have one example 22, in which we see the tens is a factor of the units. (2 is a factor of 2). So we can see primes don't have tens that are factors of units between 20-100 and composites can.

Therefore it is not a prime and therefore is a composite(2) If the 10's digit is 2, the number could be 22 or 23. NS

Answer is therefore A