There are large number of silver coins weighing 2gm, 5gm, 10gm, 25gm, 50gm 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?

1. A. 1 only
2. B. 2 only
3. C. Both 1 and 2
4. D. Neither 1 nor 2

Answer: C

Explanation

Coin denominations: 2gm, 5gm, 10gm, 25gm, 50gm.
Statement 1: ‘To buy 78 gm of coins one must buy at least 7 coins.’ To minimize the number of coins, we use the largest denominations first. To make 78gm:
– One 50gm coin (1 coin). Remaining: 28gm.
– Two 10gm coins (2 coins, 20gm). Remaining: 8gm.
– Four 2gm coins (4 coins, 8gm). Remaining: 0gm.
Total coins = 1 + 2 + 4 = 7 coins. It’s not possible to make 78gm with fewer than 7 coins using only addition. So, Statement 1 is correct.
Statement 2: ‘To weigh 78 gm using these coins one can use less than 7 coins.’ This implies using a balance scale where coins can be placed on both pans. To weigh 78gm, we can place the object on one pan. On the other pan, place coins that sum to slightly more than 78gm, and then add coins to the object’s pan to balance. For example:
– Place 50gm + 25gm + 5gm = 80gm on one pan (3 coins).
– Place the 78gm object on the other pan. The 80gm pan is 2gm heavier.
– Add one 2gm coin to the pan with the 78gm object to balance it (1 coin).
Total coins used = 3 (on one side) + 1 (on the other side) = 4 coins. Since 4 is less than 7, Statement 2 is correct. This question tests careful reading of ‘buy’ vs ‘weigh’ and understanding of balance scales, a challenging aspect of CSAT.