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 that order. The sums of the numbers at the ends of the line segments vector (AB, BC, CD, DE and EA) form an arithmetic sequence, although not necessarily in that order. What is the middle term of this arithmetic sequence.

(1)9

(2)10

(3)11

(4)12

Answer 1

Correct option (4)12

Explanation:

Each number appears in two sums, so the sum of the sequence is 2(3+5+6+7+9)=60. The middle term of a five term arithmetic sequence is the mean of its terms, so 12 is the middle term.