Number Theory Level pending

What is the sum of all the distinct 2-digit multiples of 11?

The answer is 495.

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1 solution

The 2-digit multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, and 99. The sum is equal to 11+22+33+44+55+6+77+88+99, which can be written as 11(1+2+3+4+5+6+7+8+9). 1+2+...+8+9 is equal to 45, and when 45 is multiplied by 11, the product is 495.

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