When a integer is divided by 4, remainder is 2 and when it is divided by 5, remainder is 3.
Find the largest integer of tens digit applicable to this result.
Find the largest integer of tens digit applicable to this result.
Answer
98
Solution
What remainder is 2 when a certain number is divided by 4 means that if you add 2 to the certain number, it can be divided by 4.
What remainder is 3 when a certain number is divided by 5 means that if you add 2 to the certain number, it can be divided by 5.
That is, if 2 is added to a certain number, it will become a number which can be divided both by 4 and 5.
Then what is necessary to find a certain number is to ask for the least common multiple of 4 and 5 and subtract 2 from the number.
The minimum number applicable to it is 20 - 2 =18.
Since it is the maximum number of tens digit, the number to find is calculated as 20 × 5 - 2 = 98.
