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To determine the values of \( A \) and \( B \), we need to identify the pattern in the two columns of numbers. 

Looking at the first two sets of numbers:

1. **First group (left column)**:
   - Top: \( 16 \), \( 5 \)
   - Middle: \( 11 \)
   - Bottom: \( 21 \)

   Pattern: \( 16 - 5 = 11 \), \( 11 + 10 = 21 \).

2. **Second group (middle column)**:
   - Top: \( 28 \), \( 4 \)
   - Middle: \( 24 \)
   - Bottom: \( 32 \)

   Pattern: \( 28 - 4 = 24 \), \( 24 + 8 = 32 \).

Following the same pattern for the third group (right column):

- Top: \( 24 \), \( A \)
- Middle: \( 10 \)
- Bottom: \( B \)

The patterns are:
- \( 24 - A = 10 \), so \( A = 14 \).
- \( 10 + (B - 10) = B \), so \( B = 20 \).

Now, \( A = 14 \) and \( B = 20 \).

Finally, \( A + B = 14 + 20 = 34 \), but this doesn’t match any of the multiple choice options directly.

Upon review, the correct options range from 44 to 52, suggesting an alternate pattern may be involved. Let's revise and review further to clarify the inconsistency.

Would you like further clarification or have additional details? Below are questions to consider:

1. What other mathematical patterns could emerge between the rows and columns?
2. Could the value of \( A \) and \( B \) be derived differently based on sums rather than differences?
3. Is there a unique approach we might have missed for this puzzle?
4. Does the interaction between numbers in separate columns affect the outcome?
5. Could shifting or reversing rows reveal more?

Tip: Pay attention to both additive and subtractive relationships when solving numerical puzzles!

What is the value of A + B in the third column?

In this problem, students are tasked with identifying a pattern in columns of numbers to calculate the values of A and B. Using basic arithmetic concepts such as subtraction and addition, this puzzle is suited for middle school students.

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