JEE MAIN - Mathematics (2025 - 3rd April Morning Shift - No. 25)
If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to__________
Answer
14
Explanation
When numbers are uniformly distributed, half of them have even digit sums and half have odd digits sums.
Number of 7-digit numbers with even digit sum =
$$\frac{1}{2} \cdot 9 \cdot 10^6=4.5 \cdot 10^6$$
Note that $9 \cdot 5 \cdot 10^5=4.5 \cdot 10^6$
$$m+n=9+5=14$$
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