Help divisibility problem and remainders?

edgarthendoschool

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Feb 10, 2016
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problem is

If A/B has a remainder of 4, what is the smallest possible value of a+b.

I got the answer to be 14 because the divisor B must be atleast 5 (the remainder is always smaller than the divisor then I added 4 to get a total of 9 for A. so I got 9/5 = 1 remainder 4.A+B = 9+5 = 14

The answer in the back said that the smallest possible value for A is 4 so they got A+B= 4+5= 9 as the answer. How is 4 the smallest possible value for A?!?!?!
 
problem is

If A/B has a remainder of 4, what is the smallest possible value of a+b.

I got the answer to be 14 because the divisor B must be atleast 5 (the remainder is always smaller than the divisor then I added 4 to get a total of 9 for A. so I got 9/5 = 1 remainder 4.A+B = 9+5 = 14

The answer in the back said that the smallest possible value for A is 4 so they got A+B= 4+5= 9 as the answer. How is 4 the smallest possible value for A?!?!?!
A little more detail: Note that if A divided by B leaves a remainder of 4, that means
A = B n + 4
As Denise pointed out, if we chose n as 0, then A = 4 and we now want to minimize B+4. That means making B as small as possible which is B=5.
 
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