In the analogy 23 : 8 :: 62 : ?, find the missing number that follows the same exponent based pattern.

Introduction / Context:
This is another analogy style number question where you must find the hidden mathematical rule connecting the first number in a pair to the second. Such problems often use exponents or digit based operations to create a neat pattern.

Given Data / Assumptions:

• The first pair given is 23 : 8.
• You need to determine the missing term in 62 : ?.
• The options available are 8, 36, 12, and 40.

Concept / Approach:
The digits of the first number may be used as a base and an exponent to produce the second number. For example, in the pair 23 : 8, you can interpret 23 as the digits 2 and 3, and observe that 2^3 equals 8. Extending this idea, for 62 you might interpret the digits as 6 and 2 and consider 6^2. If this yields one of the options, then you have found a consistent and elegant rule.

Step-by-Step Solution:
Step 1: Examine the pair 23 and 8. Take the digits 2 and 3 from 23. Step 2: Compute 2^3, which is 2 * 2 * 2 = 8. This matches the second number in the first pair, so the rule looks like a digit based exponent: left digit raised to the power of right digit. Step 3: Apply the same idea to 62. The digits are 6 and 2. Step 4: Compute 6^2, which is 6 * 6 = 36. Step 5: Check the options. The number 36 appears as one of the choices, so it is the logical continuation of the same pattern.

Verification / Alternative check:
You can test other possible patterns to be sure this exponent based rule is the most consistent. For example, you might try adding the digits or multiplying them, but 2 + 3 equals 5 and 2 * 3 equals 6, neither of which equals 8, so those rules do not work. Similarly, for 62, digit sums or products do not match 36. Only the exponent rule 2^3 = 8 and 6^2 = 36 matches both pairs cleanly and provides a direct link between the given numbers and the answer option.

Why Other Options Are Wrong:

• 8: This value comes from the first pair and does not represent the result of 6^2, so it cannot complete the second pair in the same way.
• 12: No simple exponent rule using digits 6 and 2 yields 12, and it does not fit consistently with the first pair.
• 40: Also not obtained through the 6^2 pattern, and it does not match any natural extension of the 23 : 8 relationship.

Common Pitfalls:
One common mistake is to treat 23 and 62 as entire numbers and search for a direct arithmetic relation, such as adding or subtracting constants. However, this approach often fails in digit based analogy questions. Instead, focusing on the positional role of digits and considering exponentiation leads to a simple and elegant rule that accurately explains the given pair and predicts the missing number.

Final Answer:
36