Question

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 + K) is equal to 13. Which integer does E represent?

• A. 1
• B. 4
• C. 6
• D. 7

Answer 1

The correct option is B 4

A + B + C = 13 ...(i)
C + D + E = 13 ...(ii)
E + F + G = 13 ...(iii)
G + H + K = 13 ...(iv)

Adding [(i) + (ii) + (iii) + (iv)]

A + B + C + D + E + F + G + H + K +
(C + E + G) = 13 × 4 = 52 ............(v)

Also A, B, C, D, E, F, G, H & K represents natural numbers from (1 to 9)

There sum will be given by $\frac{n(n+1)}{2}=45$

Substituting (iv) C + E + G = 7 ......(vi)

Only possibly for sum 7 will be (1, 2, 4)

Now, C + E cannot be (1 and 2)

As eq. (ii) is C + D + E = 13

Now, D will become equal to 10 (which is not possible because digits 1 to 9 given)

C & E can be either $\begin{array}{c}(1,4)\\ (2,4)\end{array}]$ ..........(vii)

If C = H from eq. (vi) C + E + G = 7

Now, E + G = 3

(Not possible in eq. (iii) E + F + G = 10, F = 10 which is not possible)

So from eq. (vii) only possibility remains is E = H