Observe the following number analogy: 10001 is related to 10101 according to a specific rule. Using the same numeric rule, 101 will be related to which of the following numbers?

Introduction / Context:
This is a number analogy that tests your ability to spot a simple arithmetic transformation between two numbers and transfer it to a new pair. The pattern between 10001 and 10101 must be identified and then applied to 101 to obtain the correct related number from the options.

Given Data / Assumptions:

• First pair: 10001 : 10101
• Second pair: 101 : ?
• The numbers are in decimal notation and the relation is expected to be straightforward.
• Options are relatively small numbers, suggesting basic addition or subtraction.

Concept / Approach:
A common strategy is to look for the difference between the numbers in the first pair. If that difference is clean and easy to work with, we can propose that as the rule. That rule is then applied to the second base number, and the result must match one of the available choices.

Step-by-Step Solution:

Verification / Alternative check:
Double check that there is no alternative rule that would generate a different option in a cleaner way. For example, multiplication or digit reversal patterns do not fit as neatly as a fixed addition of 100. Since the same plus 100 step works perfectly on the first pair and gives a unique matching option in the second pair, the rule is reliable.

Why Other Options Are Wrong:

• 11 results from subtracting 90, which does not match the plus 100 pattern.
• 100 would require subtracting 1 instead of adding 100, which contradicts the first pair.
• 121 could arise from squaring 11, but there is no evidence of such a rule in the first pair.
• 301 would arise from adding 200 which is again inconsistent with the observed difference of 100.

Common Pitfalls:
Some test takers may be distracted by the repeated digits and assume a base conversion or pattern in the arrangement of ones and zeros. Others may try complex operations like squares or cubes. In many exam analogies, a simple arithmetic difference is sufficient, so it is wise to test that possibility first before attempting more advanced ideas.

Final Answer:
According to the same rule, 101 is related to 201.