If S is the sum of all two-digit numbers that give a remainder of 5 when they are divided by 11, what is the remainder when S is divided by 11?
Explanation:
Any number that when divided by 11 gives a remainder of 5 will be of the form 11k + 5.
Since we only need two-digit numbers, k will range from 1 to 8, as 11 × 1 + 5 = 16 and 11 × 9 + 5 = 93.
These numbers form an AP with first term = 16 and last term as 93.
Thus, sum of these numbers
S = 8/2 × (16 + 104) = 480
Dividing S by 11, the remainder comes out to be 7.
Hence, 7.
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