Multiple choice

[CAT 2003(R)] What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

  1. 666

  2. 676

  3. 683

  4. 777
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Two-digit numbers with remainder 3 when divided by 7 are of the form 7n + 3. Smallest is 10 (7*1 + 3), largest is 94 (7*13 + 3). This is an arithmetic progression: 10, 17, ..., 94. Number of terms = (94-10)/7 + 1 = 13. Sum = (n/2)(first + last) = (13/2)(10 + 94) = 13/2 * 104 = 13 * 52 = 676.

AI explanation

The two-digit numbers leaving a remainder of 3 when divided by 7 form an arithmetic progression starting at 10 and ending at 94. The sequence is 10, 17, 24, up to 94. The sum of an arithmetic progression is calculated as the number of terms multiplied by the first term plus the last term, divided by 2. There are 13 terms in this sequence, so the sum is 13 multiplied by 10 plus 94, divided by 2, which results in 676.

Keep practicing — related questions