composite integer

[dikku07]

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

[kaulnikhil]

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

A

[mohitsharda]

Statement 1: we can have 61,21 both. ( Many more are also possible, but lets take these two)
21- composite
61- prime
=> not sufficient

Statement 2: we can have 23,24 and so on.
23 is prime, 24 is composite
=> not sufficient

Statement 1&2:
Only 2 cases possible
21 and 22
Both composite
=> sufficient
hence C

[dikku07]

I think this one is tricky. we all are getting diff answers. any more explanations or I'll post OA soon

[DarkKnight]

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.

[tanviet]

pick number

a, tens digit is 2, 3, 4, the unit digit is 4-6-8, 6-9 and 8,

a is sufficient

b, tens digit is 2, so the number is 23 or 24 not suffieicn

A is answer

[vaibhav.iit2002]

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.

IMO C

Mohit is right but gave wrong example
1. 17 : prime
18 : composite

2. 29 : prime
28 : composite

1 and 2: no. is composite

[DarkKnight]

Hi Vaibhav,

I think the problem states that two digit integer n is greater than 20. That renders 17 - invalid example of prime.

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.

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?

[vaibhav.iit2002]

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?

Plz read inline comments. You are right, its A

[hypermeganet]

Isn't it A?

2 is the ones digit of 32 but 32 isn't composite. So 2 alone isn't sufficient.

If the number is greater than 20, and the tens is a factor of the ones digit, it can't be prime, ever.

[srivas]

It is A only

[riteshbindal]

It HAS to be A.

[Dobrov]

A. OA?