Let \(N\) be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then the sum of the digits in \(N\) is:

Correct answer: 4

Solution

If the same remainder is left, the divisor must divide the differences: \(4665-1305=3360\), \(6905-4665=2240\), and \(6905-1305=5600\). Their HCF is 80, and the sum of its digits is \(8+0=8\).

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