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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
Options
183
182
181
179
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Solution
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
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