Data Sufficiency

If n is an integer between 10 and 99, is n<80?

(1) The sum of the two digits of n is a prime number
(2) Each of the two digits of n is a prime number

Please explain.

dferm wrote:If n is an integer between 10 and 99, is n<80?

(1) The sum of the two digits of n is a prime number
(2) Each of the two digits of n is a prime number

Please explain.

(1) the sum of the digits is prime.

We can pick n=83, since 8+3=11 which is prime.

Is 83 < 80? No.

We can also pick 32, since 3+2=5 which is prime.

Is 32 < 80? Yes.

No and Yes, therefore insufficient.

(2) Each of the digits is prime.

Well, that means that each digit is either 2, 3, 5 or 7. In other words, the biggest possible value for n is 77. Therefore, every possible value for n will be less than 80: sufficient.

(1) is insufficient, (2) is sufficient: choose (b).