Question

Ajay took a four-digit number in base 5 notation. He subtracted the sum of the digits of the numbers from the number. From the result, he struck off one of the digits. The remaining three digits were 1, 0, and 2. Then, the digit struck off by Ajay was:

• A. 2
• B. 1
• C. 4
• D. Cannot be determined

Answer 1

The correct option is B 1

Let us assume the four digit number as wxyz. Then in base system 5 it can be written as 125w + 25x + 5y + z.
Now given that,
125w + 25x + 5y + z - (w + x + y + z) = 124w + 24x + 4y which is a multiple of 4
Hence the sum of digits must be a multiple of 4.
Hence 1 + 0 + 2 + x is equal to either 4
(Sum cannot be 8 or 12 because in that case x will be greater than 4, which is not possible in base 5)
Hence, x = 1