Multiple choice

If a number N is of the form (5k + 2), where k is a whole number, what remainder does N leave when divided by 10?

  1. 2

  2. 5

  3. 7

  4. No fixed remainder
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D Correct answer
Explanation

N = 5k + 2. If k is even (k = 2m), N = 5(2m) + 2 = 10m + 2, so the remainder is 2. If k is odd (k = 2m + 1), N = 5(2m + 1) + 2 = 10m + 5 + 2 = 10m + 7, so the remainder is 7. Since the remainder depends on whether k is even or odd, there is no fixed remainder.

AI explanation

To find the remainder when a number N of the form (5k + 2) is divided by 10, we can substitute different whole numbers for k. If k is 0, the number is 2, leaving a remainder of 2 when divided by 10. If k is 1, the number is 7, leaving a remainder of 7 when divided by 10. Since the remainder changes depending on the value of k, there is no fixed remainder. The result is no fixed remainder.

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