Finding the Odd Set Out in Number Patterns

The question asks us to identify the set that does not follow the same pattern as the others in the given group. The given sets are:

• (2, 14, 16)
• (6, 30, 36)
• (5, 35, 40)
• (3, 21, 24)

We need to examine the relationship between the numbers within each set to find a common rule or pattern that applies to most of them, and then identify the one set that deviates from this pattern.

Analyzing the Relationships within Each Set

Let's look at how the numbers in each set are related. We can explore different arithmetic operations:

Set 1: (2, 14, 16)

• Is there a relationship between 2 and 14? $14 = 2 \times 7$.
• Is there a relationship between 14 and 16? $16 = 14 + 2$.
• Let's check if the third number is the sum of the first two: $2 + 14 = 16$. Yes, it is.

Pattern observed: Second number = First number $\times$ 7, and Third number = First number + Second number.

Set 2: (6, 30, 36)

• Is there a relationship between 6 and 30? $30 = 6 \times 5$.
• Is there a relationship between 30 and 36? $36 = 30 + 6$.
• Let's check if the third number is the sum of the first two: $6 + 30 = 36$. Yes, it is.

Pattern observed: Second number = First number $\times$ 5, and Third number = First number + Second number.

Set 3: (5, 35, 40)

• Is there a relationship between 5 and 35? $35 = 5 \times 7$.
• Is there a relationship between 35 and 40? $40 = 35 + 5$.
• Let's check if the third number is the sum of the first two: $5 + 35 = 40$. Yes, it is.

Pattern observed: Second number = First number $\times$ 7, and Third number = First number + Second number.

Set 4: (3, 21, 24)

• Is there a relationship between 3 and 21? $21 = 3 \times 7$.
• Is there a relationship between 21 and 24? $24 = 21 + 3$.
• Let's check if the third number is the sum of the first two: $3 + 21 = 24$. Yes, it is.

Pattern observed: Second number = First number $\times$ 7, and Third number = First number + Second number.

Comparing the Patterns

We can see a consistent pattern where the third number in each set is the sum of the first two numbers. Let's represent the set as (a, b, c). The pattern $c = a + b$ holds for all sets.

Now let's look at the relationship between the first and second numbers. We found that the second number is the first number multiplied by an integer. Let's call this integer the 'multiplier'. So, $b = a \times \text{multiplier}$.

From the table, we can clearly see that for the sets (2, 14, 16), (5, 35, 40), and (3, 21, 24), the multiplier used to get the second number from the first is 7.

However, for the set (6, 30, 36), the multiplier used is 5.

Since three of the sets follow the pattern where the second number is 7 times the first number (in addition to the third number being the sum of the first two), the set that uses a different multiplier (5) does not belong to this group.

Conclusion

The set that does NOT belong in the group is (6, 30, 36) because the relationship between its first two numbers is multiplication by 5, whereas in the other three sets, the relationship is multiplication by 7.

Revision Table: Analyzing Set Patterns

This table confirms that the multiplier 5 is unique to the set (6, 30, 36).

Additional Information: Number Reasoning and Patterns

Questions involving finding the 'odd one out' from a group of numbers or sets are common in logical and quantitative reasoning tests. These questions assess your ability to identify underlying patterns and rules. The patterns can involve various arithmetic operations (addition, subtraction, multiplication, division), sequences, squares, cubes, prime numbers, or a combination of these. To solve such problems, it's helpful to:

• Look for relationships between adjacent numbers.
• Look for relationships between the first and last numbers.
• Check for sums, differences, products, or quotients.
• Consider squares, cubes, or other powers.
• Test for common differences or ratios.
• Look for prime or composite numbers.
• Examine digit properties (sum of digits, etc.).

Applying these techniques systematically helps in uncovering the hidden pattern and identifying the element that does not conform.