Question

Find the even number between 25 and 85 that is divisible by 5, and when divided by 8 has a remainder of 2.

Answer 1

The even number between 25 and 85, divisible by 5, and having a remainder of 2 when divided by 8 is 50.

Find multiples of 5 between 25 and 85:

25 ÷ 5 = 5

85 ÷ 5 = 17

Look for even multiples of 5:

5 × 2 = 10 (Even, but not in the range)

5 × 4 = 20 (Even, not in the range)

5 × 6 = 30 (Even, in the range)

5 × 8 = 40 (Even, in the range)

5 × 10 = 50 (Even, in the range)

5 × 12 = 60 (Even, in the range)

5 × 14 = 70 (Even, in the range)

5 × 16 = 80 (Even, in the range)

Check which of these multiples leave a remainder of 2 when divided by 8:

For 30:
`\(30 / 8 = 3\)` remainder 6 (Not 2)

For 40:
`\(40 / 8 = 5\)` remainder 0 (Not 2)

For 50:
`\(50 / 8 = 6\)`remainder 2 (Matches)

For 60:
`\(60 / 8 = 7\)` remainder 4 (Not 2)

For 70:
`\(70 / 8 = 8\)` remainder 6 (Not 2)

For 80:
`\(80 / 8 = 10\)` remainder 0 (Not 2)

Therefore, the even number between 25 and 85 that is divisible by 5 and leaves a remainder of 2 when divided by 8 is
`\(50\)`.