Finding the Odd Number Pair

This question asks us to identify the number pair that is different from the others based on a certain pattern or rule followed by the numbers in the pairs. We are given four number pairs:

1. 14 : 33
2. 8 : 25
3. 5 : 15
4. 9 : 23

We need to analyze each pair to find a mathematical relationship between the first number and the second number.

Analyzing Number Pairs for Patterns

Let's examine each number pair:

Pair 1: 14 : 33

Let the first number be $N_1$ and the second number be $N_2$. Here, $N_1 = 14$ and $N_2 = 33$. We can try different simple arithmetic operations. For example, multiplying the first number by a constant and adding or subtracting another constant to get the second number.

Let's try multiplying by 2:

$14 \times 2 = 28$

To get 33 from 28, we need to add 5:

$28 + 5 = 33$

So, the potential pattern for this pair is $N_1 \times 2 + 5 = N_2$. Let's check if this pattern holds for other pairs.

Pair 3: 5 : 15

Here, $N_1 = 5$ and $N_2 = 15$. Let's apply the pattern $N_1 \times 2 + 5$:

$5 \times 2 = 10$

$10 + 5 = 15$

This matches the second number in the pair. So, Pair 3 follows the pattern $N_1 \times 2 + 5 = N_2$.

Pair 4: 9 : 23

Here, $N_1 = 9$ and $N_2 = 23$. Let's apply the pattern $N_1 \times 2 + 5$:

$9 \times 2 = 18$

$18 + 5 = 23$

This also matches the second number in the pair. So, Pair 4 follows the pattern $N_1 \times 2 + 5 = N_2$.

Pair 2: 8 : 25

Here, $N_1 = 8$ and $N_2 = 25$. Let's apply the pattern $N_1 \times 2 + 5$:

$8 \times 2 = 16$

$16 + 5 = 21$

The result is 21, but the second number in the pair is 25. This pair does not follow the pattern $N_1 \times 2 + 5 = N_2$.

Identifying the Odd Pair

Based on our analysis, three of the number pairs (14:33, 5:15, and 9:23) follow the pattern where the second number is obtained by multiplying the first number by 2 and adding 5. The number pair 8:25 does not follow this pattern.

• Pair 1: $14 \times 2 + 5 = 28 + 5 = 33$ (Follows pattern)
• Pair 2: $8 \times 2 + 5 = 16 + 5 = 21$ (Does not follow pattern)
• Pair 3: $5 \times 2 + 5 = 10 + 5 = 15$ (Follows pattern)
• Pair 4: $9 \times 2 + 5 = 18 + 5 = 23$ (Follows pattern)

Therefore, the number pair 8 : 25 is the odd one out.

Revision Table: Pattern Application

Additional Information: Number Series Patterns

Odd one out questions based on number pairs or series often involve identifying a rule. Common patterns include:

• Arithmetic Progression: Adding or subtracting a constant value.
• Geometric Progression: Multiplying or dividing by a constant value.
• Differences/Ratios: Looking at the differences or ratios between consecutive terms.
• Multiplication/Division with Addition/Subtraction: A combination like $N \times a \pm b$.
• Squares or Cubes: $N^2$, $N^3$, $N^2 \pm a$, $N^3 \pm a$.
• Prime Numbers: Identifying pairs or numbers that are prime or based on prime numbers.
• Digit Operations: Sum or product of digits.
• Specific sequences like Fibonacci.

To solve these problems, it's helpful to test simple patterns first and then move to more complex ones if needed. Comparing the results for all given options helps confirm the identified pattern and find the number pair that deviates.