Wow hard number properties

Jinglander wrote:p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

(1) p + q = 110
(2) p – q = 36

Answer C

Prime numbers with the same digits, but in reversed order are: p, q =13, 31; 17, 71; 37, 73; 79, 97

(1) From the above choices 37 + 73 = 110 is the only choice. 73 is the larger of the two.
So, (1) is SUFFICIENT.

(2) From the above choices 73 - 37 = 36 is the only choice. 73 is the larger of the two.
So, (2) is SUFFICIENT.

The correct answer is [spoiler](D)[/spoiler].

Hi All,

The prompt includes a LOT of information about the 2 variables, what severely limits the possibilities. Since both numbers have to be PRIME and have the same digits (in reverse order), we know that the digits CANNOT be EVEN, nor can either be 5. With a little bit of work, you can figure out all of the possibilities before you even look at the two Facts.

Rahul correctly listed out the limited options: 13 and 31, 17 and 71, 37 and 73, 79 and 97. The question asks for the larger of the two numbers.

Fact 1: P + Q = 110

With this new information and the limited options that are available, the two numbers MUST be 37 and 73, so the answer is 73.
Fact 1 is SUFFICIENT

Fact 2: P - Q = 36

With this new information and the limited options that are available, the two numbers MUST be 37 and 73, so the answer is 73.
Fact 2 is SUFFICIENT

Final Answer: D

Zaphod's approach to use both equations at once allows you to actually solve the question using System Math, but you DON'T NEED both equations to get the answer. When dealing with DS questions, you have to assess each Fact individually. IF NEITHER is sufficient on its own, THEN you COMBINED the two Facts and assess from there.

GMAT assassins aren't born, they're made,
Rich