Finding the Different Number Pair in Reasoning Questions

This question asks us to identify the number pair that is different from the other three. We need to look for a pattern or rule that applies to three of the pairs and find the one that doesn't follow that rule. Let's examine each number pair provided.

Analyzing Each Number Pair

We will look at the relationship between the numbers in each pair.

1. 16 : 36

   Let's see if these numbers are perfect squares or have any other obvious relationship.

   • The first number is $16$. $16 = 4 \times 4 = 4^2$.
   • The second number is $36$. $36 = 6 \times 6 = 6^2$.
   • In this pair, both numbers are perfect squares. The base numbers are $4$ and $6$. The difference between these base numbers is $6 - 4 = 2$.
2. 25 : 49

   Let's analyze this pair similarly.

   • The first number is $25$. $25 = 5 \times 5 = 5^2$.
   • The second number is $49$. $49 = 7 \times 7 = 7^2$.
   • Here also, both numbers are perfect squares. The base numbers are $5$ and $7$. The difference between these base numbers is $7 - 5 = 2$.
3. 48 : 81

   Let's look at the third pair.

   • The first number is $48$. Is $48$ a perfect square? $6^2 = 36$, $7^2 = 49$. No, $48$ is not a perfect square.
   • The second number is $81$. Is $81$ a perfect square? $9 \times 9 = 81$. Yes, $81 = 9^2$.
   • In this pair, only the second number is a perfect square.
4. 64 : 100

   Finally, let's check the fourth pair.

   • The first number is $64$. $64 = 8 \times 8 = 8^2$.
   • The second number is $100$. $100 = 10 \times 10 = 10^2$.
   • Again, both numbers are perfect squares. The base numbers are $8$ and $10$. The difference between these base numbers is $10 - 8 = 2$.

Identifying the Pattern and the Different Pair

Let's summarize our findings in a table to see the pattern clearly.

From the table, we can observe a clear pattern in the first, second, and fourth pairs: both numbers in the pair are perfect squares, and the base numbers (the numbers that are squared) have a difference of $2$.

• For 16 : 36, the base numbers are 4 and 6 ($6-4=2$).
• For 25 : 49, the base numbers are 5 and 7 ($7-5=2$).
• For 64 : 100, the base numbers are 8 and 10 ($10-8=2$).

The third pair, 48 : 81, does not follow this pattern because $48$ is not a perfect square.

Therefore, the number pair 48 : 81 is different from the other three.

Revision Table: Key Concepts in Reasoning

Additional Information: Recognizing Number Patterns

Reasoning questions often involve recognizing patterns in numbers. Here are some common types of patterns to look for:

• Arithmetic Progression: Numbers increasing or decreasing by a constant difference (e.g., 2, 5, 8, 11...).
• Geometric Progression: Numbers increasing or decreasing by a constant ratio (e.g., 2, 4, 8, 16...).
• Squares and Cubes: Numbers are perfect squares ($1, 4, 9, 16, ...$) or perfect cubes ($1, 8, 27, 64, ...$).
• Prime Numbers: Numbers greater than 1 that have only two divisors: 1 and themselves (2, 3, 5, 7, 11, ...).
• Fibonacci Series: Each number is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, ...).
• Differences/Sums: The pattern might be in the differences or sums between consecutive numbers or pairs.
• Combined Patterns: Sometimes, a pattern might involve a combination of operations (e.g., multiply by 2, then add 1).

For number pair questions, look for relationships within the pair (like in this question - squares of numbers with a difference) or relationships between consecutive pairs.