When 13511 13903 and 14589 are divided by the greatest number lsquo n rsquo the remainder in each ca...........

Quantitative Aptitiude (CLAT) Number System

When 13511, 13903 and 14589 are divided by the greatest number ‘n’, the remainder in each case is ‘m’. The value of (n + m) is

183

182

181

179

Explanation:

If a number 'a' and a number 'b' are divisible by a number 'n' then, a+b and a-b is also divisible by n
=> let the number be n which divides 13511, 13903 and 14589 leaving a reminder m.
=> the required number then becomes H.C.F of 13511-m, 13903-m and 14589-m.
=> it could also be the H.C.F of
(13903-m)-(13511-m) and (14589-m)-(13903-m)
i.e. 392 and 686.
=> H.C.F of 392 and 686 = 98
the required number n is 98.
To find the remainder m , divide any of the given numbers by 98 . Lets take 13511
13511/98 gives 85 as remainder.
Hence , m+n = 98+85 = 183 ,i.e., option a) 183.