GMAT Focus EditionQuantitative ReasoningEasy
A certain positive integer 'n' leaves a remainder of 3 when divided by 5. What is the remainder when 'n + 7' is divided by 5?
- A3
- B1
- C2
- D0
Show answer & explanationAnswer & explanation
Correct answer: D. 0
If 'n' leaves a remainder of 3 when divided by 5, we can write n = 5k + 3 for some integer k. Then n + 7 = (5k + 3) + 7 = 5k + 10 = 5(k + 2). Since k + 2 is an integer, n + 7 is a multiple of 5. Therefore, the remainder when n + 7 is divided by 5 is 0.
Why the other options are wrong
- A. This is the remainder of 'n' itself, not 'n+7'.
- B. This would be the remainder if n+7 was (5k+3)+3.
- C. This would be the remainder if n+7 was (5k+3)+4.
Properties of Remainders (Addition)
When adding a number to an integer, the remainder of the sum when divided by N is equal to the remainder of (original remainder + added number) when divided by N.
- If n = qN + r, then n + x = qN + r + x.
- The new remainder is the remainder of (r + x) when divided by N.
- Useful for quickly determining remainders of modified numbers.
Memory trick: Just add the remainders, then re-divide if needed.