If a positive integer n is divided by 5 then the remainder is 3. Which of the…
2024
If a positive integer n is divided by 5 then the remainder is 3. Which of the following numbers gives remainder 0,when it is divided by 5?
- A.
n + 3
- B.
n –2
- C.
n + 2
- D.
n + 1
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Correct answer: C
Answer: n + 2
Reasoning: Let n = 5k + 3 for some integer k (since n leaves remainder 3 when divided by 5).
n + 2 = 5k + 5 = 5(k + 1), which is divisible by 5, so remainder 0.
n + 3 = 5k + 6 = 5(k + 1) + 1, remainder 1 (not 0).
n − 2 = 5k + 1, remainder 1 (not 0).
n + 1 = 5k + 4, remainder 4 (not 0).
Therefore, n + 2 is the only choice that gives remainder 0 when divided by 5.