Question
Quantitative Aptitude Question on Number Systems
How many natural numbers, when converted to base 3, are four-digit numbers, but when converted to base 4, are three-digit numbers ?
A
27
B
37
C
41
D
47
Answer
37
Explanation
Solution
Let ‘x’ be the total number of natural numbers.
Since x has four-digit numbers in base 3, 33 ≤ x < 34 or 27 ≤ x < 81.
Also, x has three-digit numbers in base 4, 42 ≤ x < 43 or 16 ≤ x < 64.
Thus, the common part of the ranges of x will be 27 ≤ x < 64.
So, the desired answer is (64 – 27) = 37 numbers.
So, the correct option is (B) : 37.