Question

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

विकल्प

• 183

• 182

• 181

• 179

Answer 1

183

Explanation:

Let the number are like this:

13511 = a. n + m ....(i)

13903 = b. n + m ....(ii)

and, 14589 = c. n + m ...(iii)

from, (iii - ii), (ii - i), and (iii - i), we get.

14589 – 13903 = 686 = (c – b) .n.

13903 – 13511 = 392 = (b – a) .n.

14589 – 13511 = 1078 = (c – a).n.

Thus, n will be H.C.F of (392, 686, 1078).

∴ n = 98

and, then,

13511 = 137 × 98 + 85

13903 = 141 × 98 + 85

and, 14589 = 148 × 98 + 85

Hence, n = 98 and m = 85

n + m = 98 + 85 = 183