question_answer

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

A)  4                                  

B)  Rs. 700            

C)         Rs. 710

D)  5

E)  6                    

F)         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 \[=1+1+2+0=4\]