Question

The integers 34,041 and 32,506 when divided by a three-digit integer $n$ leave the same remainder. What is $n$?

• A. 289
• B. 367
• C. 453
• D. 307

Hint:

“Same remainder” $\Rightarrow$ divisor must divide the difference of the numbers.

Answer 1

The Correct Option is D

If two numbers leave the same remainder when divided by $n$, then their difference is divisible by $n$. Difference: \[ 34041 - 32506 = 1535 \] We need a three-digit divisor of 1535. Factorising: \[ 1535 \div 5 = 307 \] Since $307$ is prime and three-digit, $n = 307$. \[ \boxed{n = 307} \]