Understanding the Pattern Recognition Question

The question asks us to carefully examine a given pattern consisting of sets of three numbers enclosed in parentheses. We need to identify the logical rule or relationship that connects these three numbers in each set. Once the pattern is identified, we apply it to the third set which has a missing number represented by a question mark (?). We are specifically told that operations should be performed on the whole numbers themselves, not on their individual digits.

Analyzing the Given Number Sets

We are given the following sets of numbers:

• (6, 1, 18)
• (5, 4, 60)
• (6, 2, ?)

Let's denote the three numbers in each set as the first number (A), the second number (B), and the third number (C). We need to find a relationship between A, B, and C that holds true for the first two sets.

Discovering the Pattern or Logic

Let's look at the first set (6, 1, 18). The numbers are A=6, B=1, and C=18. We can try simple arithmetic operations to see if they connect these numbers.

• Addition: 6 + 1 = 7. This doesn't directly relate to 18.
• Subtraction: 6 - 1 = 5. This doesn't directly relate to 18.
• Multiplication: 6 × 1 = 6. How does 6 relate to 18? $6 \times 3 = 18$.
• Division: 6 ÷ 1 = 6. Again, $6 \times 3 = 18$.

It appears that multiplying the first two numbers (A × B) and then multiplying the result by 3 gives the third number (C). Let's check if this rule holds for the second set.

Verifying the Pattern with the Second Set

For the second set (5, 4, 60), A=5, B=4, and C=60.

Let's apply the potential rule we found: $C = 3 \times (A \times B)$

Calculate the product of the first two numbers: $A \times B = 5 \times 4 = 20$.

Now, multiply this product by 3: $3 \times 20 = 60$.

This result matches the third number (C=60) in the second set. The pattern is confirmed: The third number is three times the product of the first two numbers.

The rule is: $$C = 3 \times (A \times B)$$.

Applying the Pattern to Find the Missing Number

Now we apply the discovered pattern to the third set (6, 2, ?), where A=6, B=2, and C is the missing number (?).

Using the rule $$C = 3 \times (A \times B)$$, substitute the values of A and B:

$$C = 3 \times (6 \times 2)$$.

First, calculate the product inside the parentheses:

$$6 \times 2 = 12$$.

Now, multiply this result by 3:

$$C = 3 \times 12 = 36$$.

The missing number is 36.

Summary of the Pattern and Solution

The pattern in the given sets is that the third number is equal to three times the product of the first two numbers. Applying this pattern to the set (6, 2, ?), we find the missing number.

The missing number is 36.

Conclusion

Based on the pattern identified and verified with the first two sets, the number that replaces the question mark (?) in the set (6, 2, ?) is 36.

Revision Table: Pattern Analysis

Additional Information: Solving Number Pattern Problems

Number pattern problems require careful observation and systematic testing of possible relationships between the given numbers. Common relationships often involve basic arithmetic operations (addition, subtraction, multiplication, division), powers, roots, or combinations of these operations. It's important to test a potential rule against all provided examples to ensure its consistency before applying it to find the missing value. The constraint about not breaking down numbers into constituent digits is crucial and simplifies the approach by limiting the types of operations to consider.