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 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? Correct Answer 58

Given:

A treasure chest has less than 100 gold coins.

The conditions:

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

Calculation:

Take the condition (iv)

The possible number of coin in the chest = 10, 16, 22, 28, 34, 40, 46, 52, 58, 62, 68, 74, 80, 86, 92, 98

From the above possible number which satisfied condition (iii) = 28, 58, 68, 98

From the number which satisfied condition (iii), the possible number which satisfied condition (ii) = 58, 98

From the possible number which satisfied condition (ii), the possible number which satisfied condition (i) = 58

∴ The number of coin in the chest is 58.