In the three–digit series 372, 823, 644, 582, 46?, 8?7, which pair of digits should replace the two question marks so that the pattern of the sequence is correctly continued?

Introduction / Context:
This question presents a series of three digit numbers with two missing digits marked by question marks. The task is to detect the hidden rule that governs how the digits are arranged from term to term and then use that logic to fill in the missing digits in the numbers 46? and 8?7. This is a classic number series problem commonly seen in verbal reasoning and aptitude tests.

Given Data / Assumptions:

• The given series is: 372, 823, 644, 582, 46?, 8?7.
• Each term is a three digit number.
• Two digits are missing: the units digit in 46? and the tens digit in 8?7.
• The same underlying rule should apply consistently to every term in the sequence.
• No term is to be treated as an exception unless clearly forced by the pattern.

Concept / Approach:
In many three digit series, the pattern lies in relationships between digits rather than in the whole numbers. One simple and powerful idea is to examine the sum of digits for each term. If the digit sums follow a recognizable pattern, we can use that pattern to determine the unknown digits. This avoids overcomplicating the problem with differences of whole numbers, which often look irregular for such sequences.

Step-by-Step Solution:
Step 1: Compute digit sums of the known terms. 372 → 3 + 7 + 2 = 12. 823 → 8 + 2 + 3 = 13. 644 → 6 + 4 + 4 = 14. 582 → 5 + 8 + 2 = 15. Step 2: Observe that the digit sums are increasing by 1: 12, 13, 14, 15. Step 3: The next digit sum should be 16 for the term 46?. Step 4: For 46?, 4 + 6 + ? = 16, so ? = 16 - 10 = 6. Therefore, the fifth term is 466. Step 5: The sixth term should then have a digit sum of 17, since the pattern continues. Step 6: For 8?7, 8 + ? + 7 = 17, so ? = 17 - 15 = 2. Therefore, the sixth term is 827.

Verification / Alternative check:
We now have the full sequence: 372 (12), 823 (13), 644 (14), 582 (15), 466 (16), 827 (17). The digit sums form a simple arithmetic progression from 12 to 17 with common difference 1. No anomalies appear, and each step fits the pattern precisely, which strongly validates the solution.

Why Other Options Are Wrong:
Options such as 4 and 4, 3 and 2, or 2 and 5 produce numbers whose digit sums do not follow the strict +1 increment sequence. For example, if we chose 4 and 4, the term 464 would have digit sum 14, which breaks the smooth progression from 15 to 16 to 17. Hence, these alternatives are inconsistent with the discovered rule.

Common Pitfalls:
A common mistake is to look at the differences between the whole numbers, which appear irregular here and can be misleading. Another error is to guess the missing digits based on superficial patterns in individual columns (hundreds, tens, units) without checking consistency across all terms. Focusing on the simple digit sum pattern avoids these traps.

Final Answer:
The correct pair of digits that fits the pattern of increasing digit sums is 6 and 2, giving the series terms 466 and 827.