Among the numbers of which remainder is 2 when it is divided by 4, and is 3 when it is divided by 5, what is the largest number of two-digit numbers?
Such a number turns into the number which subtracted 2 from the multiple of 20 of the least common multiple of 4 and 5.
The largest number of two-digit is 20 × 5 - 2 = 98.
Answer
98
Solution
A number which will remain 2 when it is divided by 4 and remain 3 when it is divided by 5 is to be a number which can be divided by both of 4 and 5 when 2 is added to the number.
Such a number turns into the number which subtracted 2 from the multiple of 20 of the least common multiple of 4 and 5.
The largest number of two-digit is 20 × 5 - 2 = 98.
