Multiple choice

What is the sum of all the 2-digit numbers that give a remainder of 3 when divided by 7?

  1. 666

  2. 676

  3. 682

  4. 728
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B Correct answer
Explanation

The 2-digit numbers giving a remainder of 3 when divided by 7 are of the form 7n + 3. The smallest such number is 10 (n=1) and the largest is 94 (n=13). This forms an arithmetic progression: 10, 17, ..., 94, with 13 terms. The sum is (n/2) * (first + last) = (13/2) * (10 + 94) = (13/2) * 104 = 13 * 52 = 676.

AI explanation

The smallest 2-digit number leaving a remainder of 3 when divided by 7 is 10, and the largest is 94, forming an arithmetic progression with a common difference of 7. The number of terms is calculated as 94 minus 10 divided by 7, plus 1, which equals 13 terms. Using the arithmetic series sum formula, we multiply the number of terms 13 by the sum of the first and last terms 104, divided by 2. This gives 13 times 52, which equals 676. The sum of all such 2-digit numbers is 676.

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