Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that

Q. Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A × B × C), (B × G × E) and (D × E × F) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F or G?

(A) 4                           (B) 5                           (C) 6                           (D) 9

Ans: 5

Sol:

Among the given options, only 5 is a prime number.

Thus, if any of A, B, C, D, E, F or G represents 5,

then (A × B × C) = (B × G × E) = (D × E × F) = multiple of 5.

This would imply at least two letters represent 5, which is not possible due to the unique representation by the letters.

Hence 5 cannot be represented by the letters A, B, C, D, E, F and G.