In the number analogy "59 : 62 :: 66 : ____", which number follows the same rule as the first pair?

Introduction / Context:
This numerical analogy checks whether you can identify a constant difference between two numbers and then apply that difference to a new number. In the pair "59 : 62", the second number is slightly larger than the first. You must determine exactly how much has been added and then use the same increment with 66 to select the correct answer from the options.

Given Data / Assumptions:

• First pair: 59 is related to 62.
• Second pair: 66 is related to an unknown number.
• Options: 67, 71, 69, 70 and 73.
• We expect a simple addition pattern, not a complex function.

Concept / Approach:
Calculate the difference between 62 and 59. Subtract 59 from 62: 62 - 59 = 3. This indicates a rule where the second number equals the first number plus 3. To follow the same pattern, we must add 3 to 66. Doing this gives 66 + 3 = 69. Therefore, 69 is the number that correctly fits the analogy and should be chosen from the alternatives.

Step-by-Step Solution:

Compute 62 - 59 to find the increment in the first pair. The result is 3. State the discovered rule: second number = first number + 3. Apply this rule to 66. Calculate 66 + 3 and obtain 69. Scan the options for 69. Select 69 as it exactly matches the applied rule.

Verification / Alternative check:
Test other options briefly to confirm. If we choose 67, we would be adding only 1 to 66, which does not match the first pair. Choosing 70 involves adding 4, and 71 involves adding 5. Choosing 73 would mean adding 7. None of these increments match the constant addition of 3 observed between 59 and 62. Hence, 69 is the only number that preserves the same relationship.

Why Other Options Are Wrong:
Options 67, 70, 71 and 73 each require different additions that are inconsistent with the initial pair. Analogy questions require one single rule that can be applied to both pairs without change. Using any increment other than 3 would break this requirement, so those options cannot be correct.

Common Pitfalls:
Sometimes candidates try to see more complicated patterns, such as alternating addition and subtraction or prime number gaps, when a simple constant difference is sufficient. Another pitfall is miscalculating the difference in the first pair. Carefully subtracting the smaller number from the larger always clarifies the true pattern.

Final Answer:
By adding 3 to each first number, 59 maps to 62 and 66 maps to 69, completing the analogy "59 : 62 :: 66 : 69".