Question

How many four-digit numbers in base 4, when converted to base 5, will have unit digit zero ?

• A. 45
• B. 39
• C. 34
• D. 29

Answer 1

Answer: (B)

39

Answer 2

Let’s find the number of four-digit numbers in base 4.
The smallest and the largest four-digit numbers in base 4 are 1000 and 3333, respectively.
In base 10, the above numbers will be 43 = 64 and 44 - 1 = 255, respectively.
Now, as per the question stem, we need to find the multiples of 5 from 64 to 255.
65, 70, …………………, 255
i.e $\frac{255-65}{5}+1=39$
So, the correct option is (B) : 39.