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CAT 2000 — QA Question 14

DivisibilityEasy

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

Answer & solution

  • A

    289

  • B

    367

  • C

    453

  • 307

Solution

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).

CAT 2000 QA Q14: The integers 34041 and 32506 when divided by a three-digit integer ‘n’ leave the same remainder. W — Solution | TheCATExam