Question

One column of numbers consists of 61, 24, and 47. When the digits of the

numbers are added together, the result is 6 + 1 + 2 + 4 + 4 + 7 = 24, and when
the digits of 24 are then added together, the end result is 2 + 4 = 6. If the
same process is performed on the numbers in a second column, what can De
concluded?
• A. 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.
B. 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.
C. 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.
D. 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.

Answer 1

The question is incomplete because it must content a list of choices to select the right one.

Any way, a conclusion that you can make, and that is a common one for this kind of questions, is about whether the sum of the numbers of the second column may or not be the same sum of the numbers of the first column.

The condition for the two sums be the same is that when the digits of the second column are added together the result be the same obtained for the sum of the digits of the first column. In this case that is 6.

So, the possible answer is:

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.

Explanation:

Answer 2

A. 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.

Explanation:

You want to know the relationship between the sums of two columns of numbers if the sum of digits of the first column is 6, and the same sum of digits computation is performed on the second column.

Sum of digits

The sum of digits of a number is the modulo-9 value of that number. When a column of numbers is added, the modulo-9 value of the sum will be the sum of the modulo-9 values of the individual numbers.

If 6 is the modulo-9 value of the sum of a column of numbers, another column of numbers will not have the same sum if its modulo-9 value is not also 6.

The description of choice A applies:

• 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.

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Additional comment

Here "sum of digits" refers to the process of repeatedly summing the digits of any multi-digit number until the total is in the range 1–9. This is effectively a modulo-9 calculation.

The "modulo-9" value of a number is normally a digit in the range 0–8. For any non-zero number, the sum of digits will be a number in the range 1–9. The sum of digits calculation will give 9 instead of 0 when the modulo-9 value is 0.

Modulo arithmetic is useful for a number of purposes. One of them is checking evaluation of an expression. This process is also referred to as "casting out nines." Casting out nines is a simple time-honored method of checking arithmetic for errors, though it cannot find digit transpositions.