If a positive integer n is divided by 5, the remainder is 3. Which of the…
2023
If a positive integer n is divided by 5, the remainder is 3. Which of the numbers below yields a remainder of 0 when it is divided by 5?
- A.
n
- B.
n + 2
- C.
n + 5
- D.
None of these
Attempted by 21 students.
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Correct answer: B
Given: n divided by 5 leaves remainder 3, so write n = 5k + 3 for some integer k.
Compute n + 2: n + 2 = (5k + 3) + 2 = 5k + 5 = 5(k + 1).
Because n + 2 equals 5 times the integer (k + 1), n + 2 is divisible by 5 and therefore yields remainder 0 when divided by 5.
Why the other expressions are not divisible by 5:
n: equals 5k + 3, so remainder 3.
n + 5: equals 5k + 8 = 5(k + 1) + 3, so remainder remains 3.
None of these: incorrect because n + 2 is divisible by 5.
Conclusion: n + 2 yields remainder 0 when divided by 5.