The sum of the digits of a four-digit number 'abed' is subtracted from the number. Then the result of this will be always divisible by
Solution:
A 4-digit number written as abed, where:
The number can be written as:
1000a + 100b + 10e + d
The sum of its digits is:
a + b + e + d
Now subtract the sum of digits from the number:
(1000a + 100b + 10e + d) - (a + b + e + d)
Simplify:
= (1000a - a) + (100b - b) + (10e - e) + (d - d)
= 999a + 99b + 9e
Take common factor:
= 9 × (111a + 11b + e)
So, the result is always divisible by 9
Correct Answer: (A) 9
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