Question

Each of the points $A, B, C, D, E,$ and $F$ in the figure below represents a different digit from 1 to 6. Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is 47. What is the digit represented by $B$ ?

Answer 1

• (E) 5

Explanation:

Refer to picture

Calculating sums, we get a result of:

• 2A + 3B + 2C + 2D + 2E + 2E =
• B + 2(sum of all digits) = 47

Sum of all digits is:

• 1 + 2 + 3 +4 + 5 + 6 = 1/2*6*(1 + 6) = 21

Considering this in the equation above, we get:

• B + 2*21 = 47
• B = 47 - 42
• B = 5

Correct answer is (E) 5