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

a. 289

b. 367

c. 453

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.(1, 5, 307, 1535)

Among the answer options, only 307 is a factor of 1535.

Answer is option (d).

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