What Are Those Hundreds For?
Number Theory
Level
2
Which of the following must always be a divisor of the sum of the three 3-digit integers shown above?
3
6
9
11
12
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1 solution
We can rewrite 2 x y + 3 y x + 6 x x as follows:
2 0 0 + 1 0 x + y + 3 0 0 + 1 0 y + x + 6 0 0 + 1 0 x + x , which simplifies to:
1 1 0 0 + 2 2 x + 1 1 y
1 1 ( 1 0 0 + 2 x + y )
So, the number is divisible by 1 1 .