Question 17

Explanation

The conditions that must be satisfied by the number $n$:

• If $n$ is divided by $8$, the remainder is $5$.
• If $n$ is divided by $5$, the remainder is $2$.

Let's check each option.

Check value 29

• Divided by $8$: $29 = 8 \times 3 + 5$ (remainder $5$ ✓)
• Divided by $5$: $29 = 5 \times 5 + 4$ (remainder $4$ ✗)

The value $29$ does not satisfy the second condition.

Check value 37

• Divided by $8$: $37 = 8 \times 4 + 5$ (remainder $5$ ✓)
• Divided by $5$: $37 = 5 \times 7 + 2$ (remainder $2$ ✓)

The value $37$ satisfies both conditions.

Check value 44

• Divided by $8$: $44 = 8 \times 5 + 4$ (remainder $4$ ✗)
• Divided by $5$: $44 = 5 \times 8 + 4$ (remainder $4$ ✗)

The value $44$ does not satisfy the conditions.

Check value 77

• Divided by $8$: $77 = 8 \times 9 + 5$ (remainder $5$ ✓)
• Divided by $5$: $77 = 5 \times 15 + 2$ (remainder $2$ ✓)

The value $77$ satisfies both conditions.

Conclusion

The values that satisfy the conditions in the question are (2) and (4).