In the number pattern 111 13, 112 24, 113 35, 117 ?, what number should replace the question mark in the final pair?

Introduction / Context:
This question is a classic number sequence and pattern recognition puzzle. You are given pairs of numbers, such as 111 13, 112 24 and 113 35, and asked to determine the missing number that should be paired with 117. Such puzzles commonly appear in reasoning sections of competitive exams and are designed to test your ability to detect hidden relationships between numbers, including digit sums and positional patterns.

Given Data / Assumptions:

• We are given the pairs (111, 13), (112, 24), (113, 35) and (117, ?).
• The question mark stands for an unknown two digit number to be determined.
• The relationship between each three digit number and its corresponding two digit number is consistent and must be discovered.
• The options provided are 46, 57, 68 and 79.

Concept / Approach:
In many such puzzles, the smaller number in each pair is related to the digits of the larger number through operations like digit sum, differences or rearrangement. Here, observing the pairs carefully suggests that the two digit number can be thought of as two separate digits with specific meanings. In particular, the first digit of the two digit number matches the last digit of the three digit number, and the second digit is equal to the sum of the digits of the three digit number. Recognising this simple but non obvious rule is the key to solving the sequence.

Step-by-Step Solution:
Step 1: Look at the first pair 111 and 13. The digits of 111 are 1, 1 and 1. The sum of these digits is 1+1+1 = 3. The last digit of 111 is 1. Putting the last digit and the sum together gives 1 and 3, which form 13. Step 2: Examine the second pair 112 and 24. The digits of 112 are 1, 1 and 2. Their sum is 1+1+2 = 4. The last digit of 112 is 2. Putting the last digit and the sum together gives 2 and 4, which form 24. Step 3: Consider the third pair 113 and 35. The digits of 113 are 1, 1 and 3. Their sum is 1+1+3 = 5. The last digit of 113 is 3. Combining last digit 3 and sum 5 gives 35, matching the given pair. Step 4: Now apply the same rule to 117. The digits are 1, 1 and 7. Their sum is 1+1+7 = 9. The last digit of 117 is 7. Joining last digit 7 and sum 9 gives the number 79. Step 5: Check the options: 79 is present as one of the answer choices, so this value fits the discovered pattern perfectly.

Verification / Alternative check:
As a quick verification, apply the rule back to each of the earlier pairs. For 111, sum of digits is 3 and last digit is 1, giving 13. For 112, sum of digits is 4 and last digit is 2, giving 24. For 113, sum is 5 and last digit is 3, giving 35. Since the same pattern works for all given pairs, it is very likely that this is the intended rule. Applying it consistently to 117 produces 79, so the rule is stable and the answer is reliable.

Why Other Options Are Wrong:
The options 46, 57 and 68 do not follow the discovered logic. For 117, the last digit is 7, so the first digit of the correct two digit number must be 7. That alone rules out 46, 57 and 68, because none of them start with 7. Even if you try to force another rule, those options do not provide a consistent mapping for the earlier pairs, so they cannot represent the intended solution to the sequence.

Common Pitfalls:
Learners sometimes focus only on simple differences between the two digit numbers, for example noting that 13, 24 and 35 all increase by 11, but this does not meaningfully connect to the three digit numbers. Others may try random arithmetic operations like dividing the large number by a constant, which quickly becomes messy. The better strategy in sequence questions is to relate the digits of each number in a pair and to look for patterns involving sums or positions of digits. That leads quickly to the simple rule involving digit sum and last digit, which explains all the examples clearly.

Final Answer:
The number that should replace the question mark in the pair with 117 is 79.