Question 61

If r is the remainder when each of 1059, 1417 and 2312 is divided by k, where k is an integer greater than 1, then the value of r+k is

Name: If r is the remainder when each of 1059, 1417 and 2312 is divided by k, where k is an integer greater than 1, then the value of r+k is
Uploaded: 2026-04-27T20:08:29.596957+05:30
Duration: 14 min 31 s
Description: If r is the remainder when each of 1059, 1417 and 2312 is divided by k, where k is an integer greater than 1, then the value of r+k is

Solution

Since, each has the same remainder, we need to find the H.C.F. [(1417-1059),(2312-1417),(2312-1059)]

= H.C.F. (358,895,1253) = 179

Now, when we divide 1059, 1417 and 2312 by 179, we get remainder as 164

$$\therefore$$ $$r+k=164+179=343$$

=> Ans - (C)

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