Multiple choice

The sum of all two digit numbers that that give a remainder 2 when divided by 7 is

  1. 652

  2. 654

  3. 658

  4. 690

  5. 696
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B Correct answer
Explanation

The two-digit numbers giving a remainder of 2 when divided by 7 are of the form 7n + 2. The sequence is 16, 23, ..., 93. This is an arithmetic progression with first term 16, last term 93, and common difference 7. The number of terms is (93-16)/7 + 1 = 12. The sum is (12/2) * (16 + 93) = 6 * 109 = 654.

AI explanation

The sequence of two-digit numbers leaving a remainder of 2 when divided by 7 begins at 16 and ends at 93. This forms an arithmetic progression with 12 terms, a first term of 16, and a common difference of 7. Using the sum formula S = n/2 x [2a + (n-1)d], we calculate 12/2 x [2(16) + 11(7)], which simplifies to 6 x 109, equaling 654.

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