question_answer

If N is 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

A) 4         

B) 5

C) 6                                 

D) 8

Correct Answer: A

Solution :

The greatest number N = HCF of \[(1305-x),\]\[(4665-x)\]and \[(6905-x),\] where x is the remainder,

= HCF of \[(4665-1305),\]\[(6905-4665)\] and\[(6905-1305)\]

HCF of 3360, 2240 and 5600

Again,

\[\therefore \]      \[N=1120\]

Sum of digits \[=1+1+2+0=4\]