Analyzing Number Pairs to Find the Odd One Out

This question asks us to identify the number pair that is different from the other three given pairs. This is a common type of logical reasoning problem where we need to find a pattern or rule that applies to most of the given options and then find the one that doesn't follow that rule.

Finding the Pattern in Number Pairs

We are given four number pairs:

• 17 : 60
• 13 : 90
• 23 : 84
• 19 : 68

Let's examine the relationship between the first number and the second number in each pair. We look for a consistent mathematical operation or set of operations that connects the two numbers in at least three of the pairs.

Let the first number be \(x\) and the second number be \(y\). We need to find a rule like \(y = f(x)\) that holds true for most pairs.

Testing Potential Patterns

Let's try multiplying the first number by a small integer and adding or subtracting a constant to see if we can arrive at the second number.

Analyzing Pair 1: 17 : 60

Let's try multiplying 17 by different numbers:

• $17 \times 3 = 51$. To get 60, we add $60 - 51 = 9$. So, $17 \times 3 + 9 = 60$.
• $17 \times 4 = 68$. To get 60, we subtract $68 - 60 = 8$. So, $17 \times 4 - 8 = 60$.

Let's test if either of these patterns works for other pairs.

Analyzing Pair 2: 13 : 90

Let's test the patterns found from Pair 1:

• Using $x \times 3 + 9$: $13 \times 3 + 9 = 39 + 9 = 48$. This is not 90.
• Using $x \times 4 - 8$: $13 \times 4 - 8 = 52 - 8 = 44$. This is not 90.

This pair might be the different one, but let's check the other two pairs first.

Analyzing Pair 3: 23 : 84

Let's test the patterns again:

• Using $x \times 3 + 9$: $23 \times 3 + 9 = 69 + 9 = 78$. This is not 84.
• Using $x \times 4 - 8$: $23 \times 4 - 8 = 92 - 8 = 84$. This matches the second number!

So, Pair 3 (23 : 84) follows the pattern \(y = x \times 4 - 8\).

Analyzing Pair 4: 19 : 68

Let's test the pattern \(y = x \times 4 - 8\):

• Using $x \times 4 - 8$: $19 \times 4 - 8 = 76 - 8 = 68$. This matches the second number!

So, Pair 4 (19 : 68) also follows the pattern \(y = x \times 4 - 8\).

Identifying the Different Number Pair

We found that:

• Pair 1 (17 : 60) follows the pattern $17 \times 4 - 8 = 60$.
• Pair 3 (23 : 84) follows the pattern $23 \times 4 - 8 = 84$.
• Pair 4 (19 : 68) follows the pattern $19 \times 4 - 8 = 68$.

However, Pair 2 (13 : 90) does not follow this pattern, as $13 \times 4 - 8 = 44$, which is not 90.

Therefore, the number pair that is different from the others is 13 : 90.

Summary of Findings

The table clearly shows that the pair 13 : 90 is the one that does not fit the pattern \(y = x \times 4 - 8\) that the other three pairs follow.

Revision Table - Number Pair Reasoning

Additional Information - Logical Reasoning Tips

When tackling logical reasoning questions involving number pairs or series, consider the following strategies:

• Look for basic arithmetic operations: Addition, subtraction, multiplication, division between the numbers.
• Consider squares and cubes: The numbers might be related to squares or cubes of the first number or related to numbers near squares/cubes.
• Combine operations: The pattern could involve multiplication/division followed by addition/subtraction (like in this problem).
• Check digit properties: Sometimes the pattern involves the sum or product of the digits of the numbers.
• Prime and composite numbers: The pattern might relate to whether the numbers are prime or composite.
• Difference or ratio: Look at the difference or ratio between the numbers. Is it constant or following a pattern?

Always test your potential pattern against all the given options to confirm it works for the majority before concluding which one is the odd one out.