Vedadots
Q6869/80Q70
Q69·CSAT · Prelims 2023

Weighing 78g with specific silver coins combinations

NumericalOptimization / Number PuzzlesNumber theoryMedium

Question

There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:

1To buy 78 gm of coins one must buy at least 7 coins.
2To weigh 78 gm using these coins one can use less than 7 coins.

Which of the statements given above is/are correct?

Options

a

1 only

b

2 only

c

Both 1 and 2

Answer
d

Neither 1 nor 2

Explanation

Evaluate the coin combination limits independently under both constraints:

Statement 1 focuses on buying exactly 78 gm, meaning the sum of the positive values must equal 78. To minimize the coin count, use the largest possible denominations:

Use one 50 gm coin \rightarrow Remaining = 28 gm.
Use one 25 gm coin \rightarrow Remaining = 3 gm.
Since the remaining denominations are 2, 5, 10, etc., we cannot form 3 gm with a single coin. We must back up or use 2 gm coins: 50 + 10 + 10 + 4(2) = 7 coins. Can we do it in 6? 50 + 25 + 2 + 1- no, 1 isn't available. Try 50 + 10 + 10 + 5 + 3 (no). Thus, the absolute minimal count to assemble 78 gm additively is exactly 7 coins (50+10+10+4+2+2 or similar configurations). Statement 1 is correct.

Statement 2 covers weighing 78 gm. In a standard two-pan balance scale system, you can place coins on both sides of the balance pans (subtraction). Let's optimize using subtraction: Place 50 + 25 + 5 = 80 gm on one pan, and a single 2 gm coin on the opposite pan with the target material. Net balance weight = 80 - 2 = 78 gm. This requires a total of only 4 coins, which is strictly less than 7. Statement 2 is correct.

In scale measurement puzzles, "buying" implies a strict positive summation, while "weighing" allows you to subtract values by placing weights on the opposite balance pan.

Answer: (c).

Question details

Year

2023

Paper

CSAT

Question

Q69

Section

Numerical Ability

Sub-topic

Optimization / Number Puzzles

Type

Number theory

Difficulty

Medium

Source hint

Number theory

See all questions on Optimization / Number Puzzles

Browse every tagged question across all years

Explore →