In this number analogy, “95 is to 105 as 89 is to ______”. Select the number that stands at the same distance from 100 as 89 does, mirroring the symmetric relationship in the first pair.

Introduction / Context:
This number analogy is based on symmetry around a central reference value, which here is 100. The pair “95 : 105” consists of two numbers equidistant from 100, one below and one above. We must find a number that is similarly placed with respect to 100 for the second pair, where 89 is given on one side.

Given Data / Assumptions:

• First pair: 95 and 105. • Second pair: 89 and ? • Options: 109, 809, 111, 98. • The central reference 100 is implied by how 95 and 105 are arranged around it.

Concept / Approach:
Notice that 95 is 5 less than 100, and 105 is 5 more than 100. Thus, 95 and 105 are symmetric around 100. In the second pair, 89 is 11 less than 100. To preserve the same kind of symmetry, we must select a number that is 11 more than 100. This kind of reasoning is common in number analogies involving a central “pivot” value like 0, 50, or 100.

Step-by-Step Solution:
Step 1: Compute the difference between 95 and 100. 100 − 95 = 5, so 95 is 5 units below 100. Step 2: Check 105 relative to 100. 105 − 100 = 5, so 105 is 5 units above 100. The pair (95, 105) is symmetric about 100. Step 3: Compute the difference between 89 and 100. 100 − 89 = 11, so 89 is 11 units below 100. Step 4: To preserve symmetry, we need a number 11 units above 100. That number is 100 + 11 = 111. Step 5: Check the options; 111 appears as option C.

Verification / Alternative check:
We can represent the pattern with a simple formula. For the first pair, 95 = 100 − 5 and 105 = 100 + 5. For the second pair, we should have 89 = 100 − 11 and the unknown number = 100 + 11 = 111. This gives a neat symmetric structure: (100 − x, 100 + x). No other option—109, 809, or 98—fits this pattern for x = 11.

Why Other Options Are Wrong:
• 109: 109 − 100 = 9, so it is not equally distant from 100 as 89 is; the symmetry breaks. • 809: Far away from 100 and clearly not a symmetric partner for 89. • 98: This lies below 100, so both numbers (89 and 98) would be on the same side of 100, which does not mirror the first pair.

Common Pitfalls:
Some candidates try to look for constant differences like +10 or digit based manipulations, overlooking the central idea of symmetry around 100. Whenever you see pairs like 95 and 105, 45 and 55, or −3 and +3, check for this symmetric pattern. Once recognised, the correct partner for 89 becomes immediately clear as 111.

Final Answer:
The number that correctly completes the analogy is 111.