In the pattern 27 (15) 33 and 41 (13) 53, each bracketed number is related to the outer pair. Using the same rule, what is the value of A in 26 (A) 35?

Introduction / Context:
This is a numerical pattern problem where the number in brackets is formed from the two outer numbers. We are given two examples and must identify the underlying rule, then use it to determine the missing bracketed value in the third example. The pattern involves digit sums rather than direct arithmetic on the full numbers.

Given Data / Assumptions:

• 27 (15) 33 is valid.
• 41 (13) 53 is valid.
• 26 (A) 35 must follow the same rule.
• The middle number is presumably formed using the digits of the outer numbers.

Concept / Approach:
Instead of adding or subtracting the outer numbers directly, observe the sum of the digits in each one. In many reasoning questions, the bracketed number equals the sum of digit sums of the outer pair. We test this for the given cases and, if it works, apply it to the third pattern to find A.

Step-by-Step Solution:
Consider 27 (15) 33. Digit sum of 27 is 2 + 7 = 9. Digit sum of 33 is 3 + 3 = 6. Add these digit sums: 9 + 6 = 15, which matches the bracketed number. Now consider 41 (13) 53. Digit sum of 41 is 4 + 1 = 5. Digit sum of 53 is 5 + 3 = 8. Add them: 5 + 8 = 13, which matches the bracketed number. So the rule is: middle number = digit sum of left number + digit sum of right number. Apply this rule to 26 (A) 35. Digit sum of 26 is 2 + 6 = 8. Digit sum of 35 is 3 + 5 = 8. Add them: 8 + 8 = 16. Thus A = 16.

Verification / Alternative check:
Check the rule against all given pairs: for both 27 and 33, and 41 and 53, the sum of digit sums exactly reproduces the middle numbers 15 and 13. Therefore, using the same method for 26 and 35 is logically consistent.

Why Other Options Are Wrong:
Values 13, 14 or 11 do not equal 8 + 8, so they do not follow the rule. Choosing any of them would break the consistent relationship between the outer numbers and the bracketed number seen in the first two examples.

Common Pitfalls:
Learners sometimes try to use direct addition or subtraction of the outer numbers and ignore the information hidden in the digits themselves. Always consider digit sums as a first step in pattern-based questions involving two-digit numbers.

Final Answer:
The correct value of A in 26 (A) 35 is 16.