Understanding the Number Pattern

The given sequence of numbers appears to form a grid pattern. We can arrange the numbers into a 3x3 grid based on how such problems are typically presented:

We need to find the pattern relating the numbers in this grid to replace the question mark (?). Let's examine the rows and columns for logical relationships.

Discovering the Pattern Logic in Rows

Let's look at the relationship between the numbers in each row:

• Row 1: 26, 19, 12

Let's check the differences: $26 - 19 = 7$ and $19 - 12 = 7$. This is an arithmetic progression with a common difference of 7.

Alternatively, let's see if the middle number is related to the first and third numbers. Is 19 the average of 26 and 12?

$\frac{26 + 12}{2} = \frac{38}{2} = 19$. Yes, the middle number is the average of the first and third numbers in Row 1.

• Row 3: 23, 20, 17

Let's check the differences: $23 - 20 = 3$ and $20 - 17 = 3$. This is an arithmetic progression with a common difference of 3.

Let's check if the middle number is the average of the first and third numbers. Is 20 the average of 23 and 17?

$\frac{23 + 17}{2} = \frac{40}{2} = 20$. Yes, the middle number is the average of the first and third numbers in Row 3.

Based on Row 1 and Row 3, the pattern seems to be that the middle number in each row is the average of the first and the third number in that row.

Applying the Pattern to Find the Missing Number

Now let's apply this pattern to Row 2, which is: 32, ?, 16.

According to the pattern, the missing number (?) should be the average of 32 and 16.

Missing Number $= \frac{\text{First Number} + \text{Third Number}}{2}$

Missing Number $= \frac{32 + 16}{2}$

Missing Number $= \frac{48}{2}$

Missing Number $= 24$

Why 24 is the Correct Answer

The number that replaces the question mark (?) is 24. This is because, following the established pattern observed in the other rows, the number in the middle of the row is the average of the numbers at the ends of the row.

• Row 1: $\frac{26+12}{2} = \frac{38}{2} = 19$
• Row 3: $\frac{23+17}{2} = \frac{40}{2} = 20$
• Row 2: $\frac{32+16}{2} = \frac{48}{2} = 24$

Therefore, 24 is the number that logically completes the pattern in the grid.

Revision Table: Number Pattern Summary

Additional Information: Types of Number Patterns

Number pattern questions are common in logic and reasoning tests. While this question used the average pattern, other types of number patterns include:

• Arithmetic Progressions: Adding or subtracting a constant number (like Row 1 and Row 3 also showed a constant difference).
• Geometric Progressions: Multiplying or dividing by a constant number.
• Square or Cube Patterns: Numbers related to squares or cubes of integers.
• Triangular Numbers, Fibonacci Sequence, etc.
• Mixed Operations: A pattern involving a combination of operations across terms or positions.

Identifying the relationship between numbers, whether in rows, columns, or diagonally, is key to solving such pattern recognition problems.