One day in December 2015, three 2-digit prime numbers A, B and C, were
given to three members of a High School math team: Ashley, Beth, and Caitlin (respectively).
They had this conversation:
Ashley: \If you two add your numbers, we get precisely today's date!"
Beth: \If you two add your numbers, we get my birthday this month, which was before today."
Caitlin: \If you two add your numbers, we get my birthday this month, which is after today."
What number did Caitlin get?
Choose the correct choice
A) 11
B) 13
C) 17
D) 19
E) 23
The numbers A, B, C belong a priori in the set f11; 13; 17; 19g|Note that the   addition of any of these two 2-digit prime numbers cannot be greater than or equal to 30,   which places a strong restriction on the greatest of the three numbers: this must be at most   19. These are the only valid additions of any two numbers on that set:    11 + 11= 
<gadget id="calculator"> 11 + 11</gadget>
<output>22</output>
22, 11 + 13= 24, 11 + 17 = 29, 11 + 19 = 30, 13 + 13 = 26, 13 + 17 = 30   Note in particular the strict inequalities placed on the addition of any of these two numbers:   22 _&lt;A + C &lt; B + C &lt; A + B _&lt;30   Since C &lt; B, there are only two possibilities for B+C at this point: B = 13,C = 11,B+C =   24, or B = 17,C = 11,B + C = 29.   correct answer 11
<result>A</result>
One day in December 2015, three 2-digit prime numbers A, B and C, were
given to three members of a High School math team: Ashley, Beth, and Caitlin (respectively).
They had this conversation:
Ashley: \If you two add your numbers, we get precisely today's date!"
Beth: \If you two add your numbers, we get my birthday this month, which was before today."
Caitlin: \If you two add your numbers, we get my birthday this month, which is after today."
What number did Caitlin get?