Which of the following numbers must be added to 4567 to give a remainder of 25…

Concept: For any division, Dividend = Divisor × Quotient + Remainder. To make the remainder change after adding some number to the dividend, we look for the next value of the form Divisor × (new Quotient) + (new Remainder) that is reachable by adding a number to the given dividend.

1. Divide 4567 by 360: 4567 = 360 × 12 + 247, so the current remainder is 247.

2. We need the remainder to become 25. Since 25 is less than 247, we look at the next multiple of 360 after 4567 by raising the quotient to 13: 4567 + x = 360 × 13 + 25.

3. 360 × 13 = 4680, so 4567 + x = 4680 + 25 = 4705.

4. Solving, x = 4705 − 4567 = 138.

Cross-check: 4567 + 138 = 4705, and 4705 ÷ 360 = 13 remainder 25 — this matches the required condition.