In this number analogy, “56 is to 41 as 94 is to ______”. Identify the number that completes the pair by applying the same “half then add” arithmetic rule used in the first pair.

Introduction / Context:
This is a numerical analogy that uses an arithmetic rule involving division and addition. The pair “56 : 41” is connected through a two step operation. Your task is to discover exactly how 56 becomes 41 and then apply that same operation to 94 in order to select the correct answer from the options. Such questions examine your ability to decompose a transformation into simple mathematical steps.

Given Data / Assumptions:

• First pair: 56 corresponds to 41. • Second pair: 94 corresponds to an unknown number. • Options: 49, 53, 60, 89. • We assume a consistent arithmetic pattern (same rule) is applied to both 56 and 94.

Concept / Approach:
We first examine the transformation from 56 to 41. A good approach is to try simple operations such as halving, doubling, or adding and subtracting a constant. Notice that 56 divided by 2 gives 28, and then adding 13 produces 41. So the rule can be written as “take half the number, then add 13”. Once that pattern is recognised in the first pair, we apply it directly to 94 and see which option matches the result.

Step-by-Step Solution:
Step 1: Apply possible operations to 56. Half of 56 is 28. If we then add 13, 28 + 13 = 41, which matches the right side of the first pair. Step 2: Formulate the rule clearly. Rule: For any number n, compute (n / 2) + 13. Step 3: Apply the rule to 94. Half of 94 is 47. Now add 13: 47 + 13 = 60. Step 4: Check the options. The only option that matches this value is 60.

Verification / Alternative check:
To ensure the rule is consistent, verify that no simpler single step rule works as cleanly. For instance, subtracting a fixed number from 56 gives 41 if we subtract 15, but applying the same subtraction to 94 would give 79, which is not one of the options. The two step rule “divide by 2 and then add 13” works perfectly for both 56 and 94 within the given answer choices, making it the most reasonable and consistent pattern for this analogy.

Why Other Options Are Wrong:
• 49: To reach 49 from 94 using this rule, you would need a different constant instead of 13, breaking the pattern established by 56 : 41. • 53: This value does not equal (94 / 2) + 13 and is not consistent with the transformation seen in the first pair. • 89: Much closer to the original 94 and not connected by halving and then adding a constant.

Common Pitfalls:
Students sometimes search for patterns using only addition or subtraction and overlook combined operations like dividing then adding. Another mistake is to test the rule only on the second number without confirming that it also explains the first pair fully. Always ensure the same rule can be applied consistently to both parts of the analogy before deciding on your answer.

Final Answer:
The number that correctly completes the analogy is 60.