Five letters A, E, G, N, R are arranged left to right under certain conditions. Which letter occupies the third position? I. G is second to the right of A; E is immediately to the right of G; exactly two letters lie between R and G. II. N is exactly between A and G; neither A nor G is at an extreme end.

Introduction / Context:
We must find the letter in the 3rd position of a 5-slot linear arrangement.

Reasoning from Statement I:

• Let positions be 1–5. “G second right of A” ⇒ G = A + 2. “E immediately right of G” ⇒ E = G + 1 = A + 3. “Exactly two between R and G” ⇒ |R − G| = 3.

Try A = 2 ⇒ G = 4, E = 5, R = 1 (only valid). Remaining letter N occupies position 3. This is the unique realization; hence I alone suffices and the 3rd letter is N.

Reasoning from Statement II:
N exactly between A and G and neither A nor G is at an end still allows multiple valid configurations; the 3rd position is not fixed uniquely by II alone.

Why Other Options Are Wrong:
II alone is not enough; “either” is false; “neither” is false because I alone is sufficient.

Final Answer:
Statement I alone is sufficient; Statement II alone is not.