The sum of the digits of a 4-digit number is subtracted from the number. The resulting number is always
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → divisible by 9
Writing the number by its place values shows what is left after the digits are taken away. Let the 4-digit number have the digits \(a, b, c, d\).
Number \(=1000a+100b+10c+d\)
Number \(-\) sum of digits \(=999a+99b+9c\)
\(999a+99b+9c=9(111a+11b+c)\), always a multiple of 9
The other divisibilities fail for some numbers: for 1000 the result is \(1000-1=999\), which is odd, so it is not divisible by 6, 4 or 8.