Multiple choice

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

  1. 4

  2. 6

  3. 5

  4. 8
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A Correct answer
Explanation

N must divide the differences: 4665-1305 = 3360, 6905-4665 = 2240, 6905-1305 = 5600. GCD(3360, 2240, 5600) = 1120. Sum of digits of 1120 = 1+1+2+0 = 4.

AI explanation

Using the greatest common divisor method for same remainders, find the HCF of the differences of the numbers. Calculate the differences (4665 - 1305) = 3360 and (6905 - 4665) = 2240. The HCF of 3360 and 2240 is 1120, so the greatest number is 1120. The sum of the digits of 1120 is 1 + 1 + 2 + 0 = 4.

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