In what modulus is it true that 9 + 8 = 5?

Analyze the question: We need a modulus n such that 9 + 8 ≡ 5 (mod n). That means 17 and 5 leave the same remainder when divided by n.

Concept: a ≡ b (mod n) means n divides (a − b).

Solution: 9 + 8 = 17 17 − 5 = 12

So n must divide 12. Check each option:

• A. mod 10: 17 ÷ 10 leaves remainder 7, not 5. ✗
• B. mod 11: 17 ÷ 11 leaves remainder 6, not 5. ✗
• C. mod 12: 17 ÷ 12 leaves remainder 5. ✓
• D. mod 13: 17 ÷ 13 leaves remainder 4, not 5. ✗

Tip: For "a + b = c (mod n)" questions, compute a + b − c and find which option divides it exactly. Here 17 − 5 = 12, so the modulus is 12 (think of a clock: 9 o'clock + 8 hours = 5 o'clock).