Multiple choice

Find the sum of all $2$-digit numbers which when divided by $5$ leave remainder $1$.

  1. $963$
  2. $863$
  3. $983$
  4. $943$
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A Correct answer
Explanation

The 2-digit numbers leaving a remainder of 1 when divided by 5 are 11, 16, 21, ..., 96. This is an arithmetic progression with a = 11, d = 5, and last term l = 96. The number of terms n = ((96 - 11) / 5) + 1 = 18. The sum = (n / 2) * (a + l) = (18 / 2) * (11 + 96) = 9 * 107 = 963.

AI explanation

The smallest 2-digit number leaving a remainder of 1 when divided by 5 is 11, and the largest is 96. These numbers form an arithmetic progression with a first term of 11, a last term of 96, and a common difference of 5. The number of terms is ((96 minus 11) divided by 5) plus 1, which equals 18. The sum formula gives 18 times (11 plus 96) divided by 2, resulting in 963.

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