Integer 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

289

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367

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453

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307

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Solution

The correct option is D 307
Suppose division 'd' and remainder is 'r'.
$\Rightarrow 34041 = q_{1} d + r$
$a n d 32506 = q_{2} d + r$

$\Rightarrow 15365 = (q_{1} - q_{2}) d$

$\Rightarrow$ d should be factor 1535
So, only 307 is factor of 1535 in given option.

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