Hi VJesus12,

This prompt gives us a number of facts to work with:
1) The ages of three friends are PRIME numbers.
2) The SUM of the ages is LESS than 51.
3) The ages are in an Arithmetic Progression (AP)
4) At least one of the ages is greater than 10.

We're asked for the difference between the maximum possible MEDIAN and minimum possible MEDIAN of the ages of the three friends. Since the sum of the 3 ages is LESS than 51, it will likely be easiest to 'brute force' the solution by listing out the possible primes and then finding the groups that fit all of the 'restrictions' offered by the prompt.

Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31...

The arithmetic progression means that the numbers have to be 'evenly spaced out' - and that won't happen very often with a group of 3 primes. As an example: 3, 5, 7 fits the arithmetic progression 'restriction' BUT one of the numbers isn't greater than 10, so this is not a possibility. The only groups that fit all of the restrictions are:
3, 7, 11
3, 11, 19
3, 13, 23
5, 11, 17
7, 13, 19

Thus, the largest median is 13 and the smallest median is 7... and the difference is 6.

Final Answer: D

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

VJesus12 wrote:The ages of three friends are prime numbers. The sum of the ages is less than 51. If the ages are in Arithmetic Progression (AP) and if at least one of the ages is greater than 10, what is the difference between the maximum possible median and minimum possible median of the ages of the three friends?

(A) 0
(B) 1
(C) 13
(D) 6
(E) 8

The OA is D.

I am really interested in knowing how to solve this PS question. Experts, may you help me? Thanks in advanced.

The set with the minimum possible median is {3, 7, 11}, and one of the sets with the maximum possible median is {3, 13, 23}. (Note that {7, 13, 19} is another one.) Therefore, the difference is 13 - 7 = 6.

(Note: The fact that the sum of the ages is less than 51 and the ages are in an arithmetic progression means the median age must be less than 51/3 = 17.)

Answer: D