Single correct option
A number, when divided by 7, leaves a remainder of 5, and when divided by 11, leaves a remainder of 3. Find the remainder when the number is divided by 77.
- A. 37
- B. 40
- C. 44
- D. 47
Show answer and solution
Answer: (D) 47
Let the number be n = 11k+3 (satisfying the mod-11 condition). Substituting into the mod-7 condition: 11k+3 ≡ 5 (mod 7) → 4k ≡ 2 (mod 7). Since 4×2=8≡1 (mod 7), the inverse of 4 mod 7 is 2, so k ≡ 2×2 = 4 (mod 7). Taking k = 4: n = 11(4)+3 = 47, which satisfies both conditions and is less than 77, so the remainder mod 77 is 47.
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