imc

Question

In the five-sided star shown, the letters A, B, C, D, and E are replaced by the numbers 3, 5, 6, 7, and 9, although not necessarily in this order. The sums of the numbers at the ends of the line segments AB, BC, CD, DE, and EA form an arithmetic sequence, although not necessarily in that order. What is the middle term of the arithmetic sequence?

Accepted Answer

(meta-solving; answer choices imply solution exists) Each corner (A,B,C,D,E) goes to two sides/numbers. (A goes to AE and AB, D goes to DC and DE). The sum of every term is equal to 2(3+5+6+7+9)=60 Since the middle term in an arithmetic sequence is the average of all the terms in the sequence, the middle number is 605=12