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CAT 2003 Slot 2 — QA Question 44

Number TheoryEasy
Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

  1. The first letter is any vowel.
  2. The second letter is m, n or p.
  3. If the second letter is m, then the third letter is any vowel which is different from the first letter.
  4. If the second letter is n, then the third letter is e or u.
    1. If the second letter is p, then the third letter is the same as the first letter.

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

Answer & solution

  • A

    666

  • 676

  • C

    683

  • D

    777

Solution

Any number that gives a remainder of 3 when divided by 7 will be of the form 7k + 3.

Since we only need two-digit numbers, k will range from 1 to 13 {where 7(1) + 3 = 10 and 7(13) + 3 = 94}

Sum of all these numbers = ∑k=1137k+3

= 13 × 3 + 7(1 + 2 + ... + 13)

= 39 + 7×13×142

= 39 + 637 = 676

Hence, option (b).

CAT 2003 Slot 2 QA Q44: What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7? — Solution | TheCATExam