In mathematics, establishing relationships between numbers can often resemble solving a riddle. This article will guide you through the reasoning process that will help you solve the analogy: 2 is to 55 as 6 is to ?
Breaking Down the Analogy
To tackle this problem, we first need to understand the relationship between the first pair of numbers, 2 and 55. Let’s analyze how these numbers are connected:

Step 1: Identify the operation. To connect the two numbers, we can look for a mathematical operation that takes 2 to 55. If we observe closely:
[ 2^2 \times 14 = 4 \times 14 = 56 ]
This isn't exact but shows that the multiplication plays a role. Let’s find a more accurate approach.

Step 2: Calculate the relationship. You could also see this as an arithmetic operation or scaling factor that can potentially apply to both numbers. One possible connection is that 55 is a multiple of 2.
Finding the Missing Number
Next, we want to find the number that corresponds to 6 based on the discovered relationship.
The Approach:
If we take a similar approach to relate 2 to 55, let’s see if multiplying by a certain factor makes sense.
Operation Example:
If we multiply 2 by 27.5 (which is 55 divided by 2):
[ 2 \times 27.5 = 55 ]
Now applying the same factor for 6:
[ 6 \times 27.5 = 165 ]
Conclusion
Thus, we conclude that 6 is to 165. So, 2 is to 55 as 6 is to 165.
Summary
 The relationship between 2 and 55 was identified through multiplication.
 Applying the same logic, we found 6 corresponds to 165.
This type of analogy not only challenges our mathematical skills but also enhances critical thinking and problemsolving capabilities. If you enjoyed this explanation, you might also find our article on Number Relationships and Patterns interesting for a deeper dive into mathematical concepts.
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In conclusion, mastering these relationships can not only help in solving problems but can also enhance our overall mathematical reasoning. Keep practicing, and you'll find these puzzles become easier and more intuitive!