The integers 34041 and 32506 when divided by a three-digit integer ‘n’ leave the same remainder. What is ‘n’?
Explanation:
Let 34041 and 32506 when divided by n leave remainder r.
34041 = nk1 + r …(i)
32506 = nk2 + r …(ii)
Subtract equation (ii) from equation (i)
n (k1 – k2) = 1535
∵ n has to be a factor of 1535.
From the given options, only 307 is a factor of 1535.
Hence, option (d).
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