Let's analyze the problem step-by-step:
1. We start with a column containing the numbers 61, 24, and 47.
2. Summing the digits of each number:
- For 61: [tex]\(6 + 1 = 7\)[/tex]
- For 24: [tex]\(2 + 4 = 6\)[/tex]
- For 47: [tex]\(4 + 7 = 11\)[/tex]
3. Summing these intermediate results:
[tex]\(7 + 6 + 11 = 24\)[/tex]
4. Now, we sum the digits of 24:
[tex]\[2 + 4 = 6\][/tex]
This gives us the final result of 6 for the first column.
Now, let's interpret the conclusions based on the process described:
- If the end result from the second column is also 6, it means that when a similar summation process (digit summing followed by summing the digits of the total) is applied to the numbers in the second column, the digital root obtained is 6.
- Digital root is a property that a number reduces to a single digit that is congruent modulo 9.
Given this specific problem, here are the possible conclusions:
A. If the end result from the second column is also 6, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
- This statement is false. Having the same digital root (6) does not indicate inequality.
B. If the end result from the second column is not 6, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.
- This statement is false. Not having the same digital root (6) means that the sums are not congruent modulo 9.
C. If the end result from the second column is also 6, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.
- This statement is plausible. When both columns yield the same digital root, it implies that the sums of the columns are congruent when modulo 9.
D. If the end result from the second column is not 6, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
- This statement is also plausible. If the sums in both columns do not result in the same digital root, their sums are not congruent modulo 9 and thus not equal.
Hence, based on the given process and properties of the digital root, we can conclude:
C. If the end result from the second column is also 6, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.
