A and B are two number when divided by 7 leaves a remainder 3 and 5. What will…
2025
A and B are two number when divided by 7 leaves a remainder 3 and 5. What will be the remainder when A-B is divided by 7 ?
- A.
1
- B.
2
- C.
5
- D.
4
Attempted by 72 students.
Show answer & explanation
Correct answer: C
Key idea: use modular arithmetic to subtract remainders.
Write A and B in terms of multiples of 7: A = 7k + 3 and B = 7m + 5 for some integers k, m.
Subtract: A − B = (7k + 3) − (7m + 5) = 7(k − m) − 2, so A − B ≡ −2 (mod 7).
Convert the negative remainder to a standard (nonnegative) remainder by adding 7: −2 + 7 = 5. Thus the remainder is 5.
Answer: 5