Each of the letters in the figure below represents a unique integer from 1 to 9. The letters are positioned in the figure such that each of (A + B + C), (C + D + E), (E + F + G), and (G + H + A) is equal to 13. Which integer does B represent?
A. 1 B. 8 C. 6 D. 7
GATE 2018 · General Aptitude · Number Relations · medium
Answer: B = 8
Add all four sum equations: LHS = 2A + B + 2C + D + 2E + F + 2G + H = 52. So (A+B+C+D+E+F+G+H) + (A+C+E+G) = 52.
Find the sum of all eight letters: We need to find which value from 1 to 9 is not used. Since A+C+E+G = 52 - S_8, and the corner nodes' sum must be consistent with the individual equations, try possibilities. If missing = 9, S_8 = 36, then A+C+E+G = 52-36 = 16, and B+D+F+H = 36-16 = 20. Per arm: A+B+C = 13 => B = 13 - A - C. With A+C+E+G=16 and trying values: A=1,C=4,E=6,G=5 gives sum=16; then B=13-1-4=8, D=13-4-6=3, F=13-6-5=2, H=13-5-1=7. Check: all distinct from {1,2,3,4,5,6,7,8} (missing 9). B=D+F+H = 8+3+2+7=20. Confirmed.