Question:
How many four-digit numbers in base 4, when converted to base 5, will have unit digit zero ?
How many four-digit numbers in base 4, when converted to base 5, will have unit digit zero ?
Updated On: Aug 21, 2024
- 45
- 39
- 34
- 29
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The Correct Option is B
Solution and Explanation
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.
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.
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