If a three digit number is divided by 43, the remainder of quotient A is B (both a and B are integers)

If a three digit number is divided by 43, the remainder of quotient A is B (both a and B are integers)


Three digit M = 43A + B
First, the largest B = 42
Three digit M = 43A + 42 = 43 (a + 1) - 1
The three digit number is a multiple of 43 - 1
23*43=989
That is, a + 1 = 23
a=22
The maximum value of a + B = 22 + 42 = 64



If a three digit number is divided by 23, the quotient is a and the remainder is B, what is the maximum value of a plus B?
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The largest three digit number is 999, divided by 43 999 △ 23 = 43.10, the largest quotient is 43, the remainder is 10, the sum of quotient and remainder is not the largest
The remainder can be 22, the quotient can be 43-1 = 42, and the sum of quotient and remainder is 42 + 22 = 64,
A: the maximum value of a + B is 64



If a three digit number is divided by 37, the quotient is a and the remainder is B. what is the maximum value of a plus B?


The maximum remainder is 36
999÷37=27
Then 998 △ 37 = 26 and 36
So a + B max = 26 + 36 = 62