Explanation:

Let's analyze the statements:

- Statement 1: "To buy 78 gm of coins one must buy at least 7 coins."

- Try using biggest denominations:

- 50 + 25 + 2 + 1 = 78 (but we don't have 1 gm)

- Try 50 + 25 = 75; remainder is 3 gm (cannot use 3 gm coins).

- Try 10s: 50 + 10 + 10 + 5 + 2 + 1 = 78 (no 1 gm coins).

- Using available coins only: 50 + 25 = 75, then use 3*1 gm — not possible, as we lack 1 gm.

- Only possible with 2 gm coins: (7 x 2 = 14, not possible), try combinations. The minimum is:

- 50 + 10 + 10 + 5 + 2 + 1 but again, no 1 gm.

- So, must use smaller coins. Try: 25 + 25 + 10 + 10 + 5 + 2 + 1 (again, no 1 gm).

- If using only available coins: Let's try with 2s and 5s:

- How many 2s? 39 x 2 = 78, so with only 2 gm coins, 39 coins.

- With 25, 50: 50 + 25 = 75, then 2 + 1 = 3, but no 1 gm coin.

- So, must use more coins; however, let's try: 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70, then 5 + 2 + 1 = 8, again, no 1 gm.

- Conclusion: Using only available denominations (2, 5, 10, 25, 50), you cannot sum exactly 78 gm in less than 7 coins. In fact, it's not possible to get 78 gm at all unless we use many 2 gm and 5 gm coins.

- On checking: Let's see 50 + 25 = 75, now use three 1 gm needed to make 78 (not available). But with 10s and 5s, similar issues. Using only 2 gm coins = 39 coins — more than 7.

- So, statement 1 is correct.

- Statement 2: "To weigh 78 gm using these coins one can use less than 7 coins."

- As seen above, not possible—requires more coins.

- Statement 2 is incorrect.

- Options:

- Option 1: 1 only

- Option 2: 2 only

- Option 3: Both 1 and 2

- Option 4: Neither 1 nor 2

Correct Answer:

- Option 1: 1 only