A treasure chest has less than 100 gold coins. The number of coin is i) One more than a multiple of 3 ii) Two more than a multiple of 4 iii) Three more than a multiple of 5 and iv) Four more than a multiple of 6 How many coins are there in the chest?

A treasure chest has less than 100... - Solved

Question 70

Logical Reasoning Number representations Easy

(A) 58

(B) 88

(C) 98

(D) 38

✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Quick Solution

This puzzle can be solved quickly by testing the options, but a more elegant method is to find a hidden pattern in the conditions.

1. Find the Hidden Pattern in the Conditions

Let the number of coins be N. We are given four conditions. Let's look at the difference between the divisor and the remainder in each case:

3 - 1 = 2
4 - 2 = 2
5 - 3 = 2
6 - 4 = 2

The difference is always 2. This means that if we had 2 more coins (N + 2), the number would be perfectly divisible by 3, 4, 5, and 6.
In other words, the number (N + 2) must be a common multiple of 3, 4, 5, and 6.

2. Calculate the Least Common Multiple (LCM)

To find the smallest possible value for N, we need to find the Least Common Multiple (LCM) of the numbers {3, 4, 5, 6}.

The smallest number that is divisible by all of them is 60.

3. Solve for the Number of Coins (N)

- We found that the smallest possible value for (N + 2) is the LCM, which is 60.
- N + 2 = 60
- N = 60 - 2 = 58.

The problem states the chest has less than 100 coins, and 58 fits this condition. (The next possible number would be based on the next common multiple, 120, which would give N=118, a number greater than 100).

Final Answer: There are 58 coins in the chest.