Gate 2018 ce set 2 10

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

a+b+c=13 ---- 1

c+d+e=13 ---- 2

e+f+g=13 ---- 3

g+h+k=13 ---- 4

Add all four equations:

(a+b+c+d+e+f+g+h+k)+(c+e+g)=52

$\sum _{i=a} ^k i = 45$

c+e+g= 7 ---- 5

So, Option c and d are eliminated.

Now let's assume e=1, put in eq.2,3 and 5, add eq.2 and 3

c+d+2+f+g=26

c+d+f+g=24 ---- 6

c+1+g=7 from eq5

c+g=6 put in eq. 6

d+f=18, which is not possible

So, option a is eliminated.

Hence, Answer is B.

Answer 2

9     3      1

                8

                4      7      2

                                6

                                5