Multiple choice general knowledge math & puzzles

The number of common terms in the two sequences 17,21,25,....417 and 16,21,26,....466 is

  1. 78

  2. 19

  3. 20

  4. 22
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C Correct answer
Explanation

First sequence: 17,21,25,... (difference 4). Terms = 17 + 4(n-1) for n=1 to 100. Second sequence: 16,21,26,... (difference 5). Terms = 16 + 5(n-1) for n=1 to 91. Common terms satisfy 17 + 4a = 16 + 5b → 4a - 5b = -1. Solving: terms are 21,41,61,...,401 (21 + 20k for k=0 to 19). Total = 20 terms.

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