If 'ABC', a 3 digit number is reversed then the sum of digits of the difference between the original and the reversed number will always be divisible by:

No worries! We‘ve got your back. Try BYJU‘S free classes today!

All of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
All of these

ABC can be written as 100A + 10B + C

Similarly CBA can be written as 100C + 10B + A

ABC - CBA = (100A + 10B + C) - (100C + 10B + A)

= 100A + 10B + C - 100C - 10B - A

= 99 (A - C)

$= 9 \times 11 (A - C) = 3 \times 3 \times 11 (A - C)$

This number is divisible by 3,9,11 and 99.
If a number is divisible by 9 and 3, the sum of the digits of that number must be divisible by 9 and 3 respectively.

Suggest Corrections

Similar questions

If the digits of a 3 digit number abc is reversed, then the difference of original and reversed number is not divisible by 9.

Consider a 3-digit number and reverse its digits. Find the difference between original and reversed number. By what numbers this difference is divisible? Select all that apply.

Q. The difference between a 3 digit number and the number formed by reversing its digits is not always divisible by

Q. Take a two digit number 'ab'. Then reverse the digits. If the difference between ab and the new number is always divisible by .

Q. Take a two-digit number ab. Then reverse the digits. If the difference between ab and the new number is cd, then cd is always divisible by.

Join BYJU'S Learning Program