Understanding the Pattern Recognition Question

This question asks us to carefully study a given pattern of numbers and determine the number that should replace the question mark (?). The pattern is presented in a way that suggests a relationship exists between the numbers.

The numbers are given as: 13 16 52 15 24 90 23 36 ?

Let's arrange these numbers into what seems like a logical structure, possibly rows or groups, based on the flow provided in the question.

Analyzing the Numerical Pattern

The numbers appear to be presented in groups of three. Let's represent them as three rows:

Now, let's try to find a relationship between the numbers in each row that results in the third number. We can explore common mathematical operations like addition, subtraction, multiplication, division, or combinations thereof.

Consider the first row: 13, 16, 52.

• Sum: $13 + 16 = 29$. $29$ is not $52$.
• Difference: $|16 - 13| = 3$. $3$ is not $52$.
• Product: $13 \times 16 = 208$. Can we get $52$ from $208$? $208 / 4 = 52$. This looks promising.

Let's test this relationship with the second row: 15, 24, 90.

• Product of the first two numbers: $15 \times 24$.
• Calculation: $15 \times 24 = 360$.
• Now, divide the product by 4, as observed in the first row: $360 / 4 = 90$.

The relationship holds true for the second row as well. The pattern seems to be: (First Number $\times$ Second Number) / 4 = Third Number.

Applying the Pattern to Find the Missing Number

We will now apply the identified pattern to the third row: 23, 36, ?

Using the pattern: (First Number $\times$ Second Number) / 4 = ?

Substitute the numbers from the third row:

• First Number = 23
• Second Number = 36

Calculation:

$(23 \times 36) / 4 = ?$

First, calculate the product of 23 and 36:

$23 \times 36$

• $23 \times 30 = 690$
• $23 \times 6 = 138$
• $690 + 138 = 828$

So, $23 \times 36 = 828$.

Now, divide the product by 4:

$828 / 4 = ?$

Calculation:

• $800 / 4 = 200$
• $28 / 4 = 7$
• $200 + 7 = 207$

The missing number is 207.

Comparing with Options

Let's check the given options:

• Option 1: 108
• Option 2: 207
• Option 3: 117
• Option 4: 81

Our calculated missing number, 207, matches Option 2.

Conclusion

The pattern in the given sequence is that the third number in each row is the product of the first two numbers divided by 4. Applying this rule to the third row (23, 36, ?) gives us (23 $\times$ 36) / 4 = 828 / 4 = 207. Therefore, the missing number is 207.

Revision Table: Pattern Analysis Summary

Additional Information on Pattern Recognition in Reasoning

Pattern recognition questions are common in reasoning and aptitude tests. They require you to identify the underlying rule or relationship in a series of numbers, letters, or figures.

Key strategies for solving numerical pattern questions:

• Look for simple arithmetic progressions (addition, subtraction).
• Look for geometric progressions (multiplication, division).
• Consider differences between consecutive terms. Sometimes the differences themselves form a pattern.
• Consider ratios between consecutive terms.
• Look for patterns involving alternating operations.
• Consider relationships between numbers in different positions (e.g., first and third, second and fourth).
• In grid or row/column patterns, look for relationships within rows, within columns, or diagonally.
• Try squaring or cubing numbers, or taking square roots or cube roots.
• Consider digit sums or other properties of the numbers.

Practice is key to improving your ability to quickly identify patterns.