The nearest integer to 6650 which is exactly divisible by 429 is

The correct answer is Option (1) → 6864

The nearest number divisible by 429 is one of the two multiples of 429 on either side of 6650; the remainder tells how far 6650 is from the lower one.

• \(6650=429\times15+215\), so the lower multiple is \(429\times15=6435\), which is 215 below 6650

• The next multiple is \(6435+429=6864\), which is \(6864-6650=214\) above 6650

• 214 is less than 215, so 6864 is nearer

Tip: When the remainder is more than half the divisor (here 215 against 214.5), the next multiple up is the nearer one; when it is less than half, the multiple below is nearer.