The integers 34041 and 32506, when divided by a three-digit integer N, leave the same remainder. What is the value of 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

If 34041 and 32506 are the only two terms in an AP, they will have common difference of 32506 - 34041 = 1535. Thus, all numbers which are factors of this common difference will divide the integers such that they will leave a constant remainder.
Now go from answer options. We are looking for factors of 1535. Among the answer options, only 307 is a factor of 1535. Answer is option (d).

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