Understanding Number Pair Relationships

In this question, we are given a pair of numbers, 27 and 8, and we need to find another pair from the given options that shares the same relationship. This type of problem tests our ability to identify patterns and logical connections between numbers.

Analyzing the Given Number Pair: 27 : 8

Let's examine the relationship between the two numbers, 27 and 8. We need to think about various mathematical operations or patterns that could connect 27 and 8. Some possibilities include:

• Arithmetic operations (addition, subtraction, multiplication, division).
• Relationship based on digits.
• Relationship based on squares, cubes, or other powers.
• A combination of operations.

Let's try to find a simple relationship. If we divide the first number, 27, by a small integer, say 3, we get 9. How can we get 8 from 9? By subtracting 1. So, let's test the relationship:

Second Number = (First Number / 3) - 1

Let's apply this to the given pair 27 : 8:

\( (27 \div 3) - 1 = 9 - 1 = 8 \)

This relationship holds true for the given number pair 27 : 8.

Applying the Relationship to the Options

Now, we will apply this identified relationship to each of the given options to see which pair satisfies the same rule: Second Number = (First Number / 3) - 1.

Option 1: 12 : 3

Let's apply the relationship to the first number, 12:

\( (12 \div 3) - 1 = 4 - 1 = 3 \)

The result is 3, which is the second number in the pair 12 : 3. This option fits the relationship.

Option 2: 39 : 14

Let's apply the relationship to the first number, 39:

\( (39 \div 3) - 1 = 13 - 1 = 12 \)

The result is 12, which is not equal to the second number in the pair (14). This option does not fit the relationship.

Option 3: 19 : 5

Let's apply the relationship to the first number, 19:

The first number, 19, is not divisible by 3. So, this option cannot fit the relationship (First Number / 3) - 1, which requires the first number to be divisible by 3.

Option 4: 33 : 9

Let's apply the relationship to the first number, 33:

\( (33 \div 3) - 1 = 11 - 1 = 10 \)

The result is 10, which is not equal to the second number in the pair (9). This option does not fit the relationship.

Identifying the Correct Pair

Based on our analysis, only Option 1 (12 : 3) follows the same relationship as the given pair 27 : 8.

The relationship is: The second number is obtained by dividing the first number by 3 and then subtracting 1.

Therefore, the number pair that is related in the same way as 27 : 8 is 12 : 3.

Revision Table: Number Analogy Concepts

Understanding number analogies involves recognizing various types of relationships. Here's a quick revision:

Additional Information: Problem Solving Strategy for Number Analogies

When approaching number analogy problems like 27 : 8, it's helpful to follow a systematic approach:

• Look for simple arithmetic operations first (addition, subtraction, multiplication, division).
• Consider relationships involving squares, cubes, or roots.
• Examine the digits of the number – sometimes the relationship is based on the sum, product, or difference of digits.
• Look for multi-step operations or combinations of the above.
• Test your identified relationship thoroughly with the given pair before applying it to the options.
• Apply the relationship to each option systematically and check if it holds true.
• Be open to different types of relationships; sometimes they can be unconventional.

Practicing with various types of number analogies helps in quickly recognizing patterns during exams.