Understanding the Number Pattern

The question asks us to identify the pattern in the given sets of numbers and find the missing number in the third set. We are given three sets of numbers in the format (a, b, c).

• Set 1: (4, 2, 18)
• Set 2: (1, 7, 24)
• Set 3: (5, 4, ?)

We need to find a mathematical relationship between the first two numbers (a and b) in each set that results in the third number (c).

Analysing the Pattern with Given Sets

Let's examine the first two sets to find a consistent rule. We are looking for an operation involving the first number (a) and the second number (b) that produces the third number (c).

Consider Set 1: (4, 2, 18). Let a=4 and b=2. We need an operation to get c=18.

• Maybe addition and multiplication: $(a+b) \times \text{constant} = c$? Let's try: $(4+2) \times k = 18 \implies 6 \times k = 18 \implies k = 3$.
• Let's test this rule $(a+b) \times 3 = c$ on the second set.

Consider Set 2: (1, 7, 24). Let a=1 and b=7. According to our potential rule, $(a+b) \times 3 = c$.

• Let's calculate: $(1+7) \times 3 = 8 \times 3 = 24$.
• This matches the third number in the second set (24).

The pattern appears to be: (First Number + Second Number) $\times$ 3 = Third Number or $(a+b) \times 3 = c$.

Applying the Pattern to Find the Missing Number

Now we apply this rule to the third set: (5, 4, ?).

• Here, a = 5 and b = 4.
• Using the rule $(a+b) \times 3 = c$, we substitute the values:
• $(5 + 4) \times 3 = ?$
• $9 \times 3 = ?$
• $27 = ?$

So, the missing number is 27.

Conclusion

Based on the identified pattern, the number that replaces the question mark is 27.

Revision Table: Key Learnings

Additional Information: Solving Number Patterns

Solving number pattern questions often involves trial and error with different mathematical operations. Here are some common approaches:

• Look for relationships between adjacent numbers (addition, subtraction, multiplication, division).
• Look for relationships between numbers at fixed positions (e.g., first and third, first and last).
• Consider operations involving squaring, cubing, or roots.
• Think about combinations of operations (like addition followed by multiplication).
• Test a potential rule on all given examples before applying it to find the missing value.
• Pay attention to any notes, like the one provided here stating operations must be on whole numbers, not individual digits.