dikku07 wrote: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.



A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.



My answer choice doesn't match OA so, need an better explanation. will post OA later for sure

DarkKnight wrote:Mohit, please check statement 1. It says the tenth digit is a factor of unit digit not multiple. Hence number 21 and 61 does not qualify. The only numbers that would qualify are 24, 26, 33, 36,39 which are all composite. Hence sufficient.

Statement 2: Tenth digit =2 can be 23 or 21. Can't say. not sufficient.
Therefore answer A.

DarkKnight wrote:Hi Vaibhav,

I think the problem states that two digit integer n is greater than 20. That renders 17 - invalid example of prime.
You are right, it was late night and I think I was sleepy


29 - Here tens digit (which is 2) is not a factor of units digit of n (Which is 9). That renders 29 invalid as well.

I have given 29 as example for statement 2 which doesn't have any condition of divisibility. so 29 is fine.

Unless my train of though is wrong, just by using statement A you will discover that there is no prime number greater than 20 that will satisfy condition A. Hence it has to be composite. Hence answer is A.

Do you agree?