# Q. There are large number of silver coins D weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm R each.

Consider the following statements:

1. To buy 78 gm of coins one must buy at least 7 coins.

2. To weigh 78 gm using these coins one can use less than 7 coins.

Which of the statements given above is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Correct Answer: (c) Both 1 and 2

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## Minimum Number of Coins to Buy 78 gm

To buy 78 gm of coins, with the largest coin being 50 gm and the smallest coin being 2 gm, we need to find the minimum number of coins required.

If we try to use only one of each coin weight, the sum would be: 50 + 10 + 10 + 2 + 2 + 2 + 2 = 78

So, using one coin of each weight, we need to buy 7 coins to get a total of 78 gm.

To weigh 78 gm using these coins, one can use 5 coins of 50 gm, 25 gm, 10 gm, -5 gm, and -2 gm. This is done by placing the 50 gm, 25 gm, and 10 gm coins on one side of the balance and the -5 gm and -2 gm coins (which are actually 5 gm and 2 gm coins, but placed on the opposite side) on the other side.

Therefore, both statements are correct. The answer is (c) Both 1 and 2.