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When the positive integer x is divided by each of 4, 5, and 6, it has a remainder of 3. What is the sum of the three smallest possible values of x?

 Jul 26, 2020
 #1
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One way is to list all the possibilities for division by 4, for division by 5, and for division by 6, until you get the same number in each list.

 

The integers that, divided by 4, leave a remainder of 3 are:  7, 11, 15, 19, ...   (notice that these numbers increase by 4)

The integers that, divided by 5, leave a remainder of 3 are:  8, 13, 18, 23, ...   (these numbers increase by 5)

The integers that, divided by 6, leave a remainder of 3 are:  9, 15, 21, 27, ...    (these numbers increase by 6)

 

Extend each list until you get the same number in each list (the answer is smaller than 125).

 
 Jul 26, 2020
 #2
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The smallest 3 integers are: 3,  63,  123 (3 is a very valid solution). The next integer would be 183.

 
 Jul 26, 2020

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