Finding the Pattern in Number Analogy

The question asks us to find the number that is related to the fifth number (18) in the same way as the second number (189) is related to the first number (17), and the fourth number (69) is related to the third number (13).

This type of problem requires identifying the mathematical or logical relationship between the numbers in the given pairs and applying that relationship to the third pair.

Analyzing the First Pair: 17 ∶ 189

Let's examine the relationship between 17 and 189. We need to find an operation or a series of operations that transforms 17 into 189.

Consider potential operations:

• Multiplication: $17 \times \text{something} = 189$. $189 / 17 \approx 11.1$. Not a simple integer multiplier.
• Squaring: \(17^2 = 289\). This is larger than 189. Let's see the difference: \(289 - 189 = 100\).

This suggests a possible relationship: The second number might be the square of the first number minus 100.

Let's test this hypothesis:

\(17^2 - 100 = 289 - 100 = 189\)

This relationship holds for the first pair.

Analyzing the Second Pair: 13 ∶ 69

Now, let's check if the same relationship holds for the second pair, 13 and 69. The proposed relationship is: The second number is the square of the first number minus 100.

Let's apply this to the pair (13, 69):

\(13^2 - 100 = 169 - 100 = 69\)

This relationship also holds for the second pair.

Identifying the Consistent Pattern

The pattern observed in both the first and second pairs is consistent. The relationship between the two numbers in each pair ($N_1$ ∶ $N_2$) is:

\(N_2 = N_1^2 - 100\)

Applying the Pattern to the Third Pair: 18 ∶ ?

We need to use the identified pattern to find the number related to 18. The first number in this pair is 18.

Using the pattern \(N_2 = N_1^2 - 100\), where \(N_1 = 18\):

\(N_2 = 18^2 - 100\)

Calculate \(18^2\):

\(18 \times 18 = 324\)

Now, subtract 100:

\(N_2 = 324 - 100 = 224\)

Comparing with Options

The calculated number is 224. Let's compare this with the given options:

Our calculated value, 224, matches Option 1.

Conclusion

The relationship governing the number pairs is that the second number is obtained by squaring the first number and subtracting 100. Applying this pattern to 18 gives us 224. Thus, 18 ∶ 224.

Revision Table: Key Concepts

Additional Information: Solving Number Series and Analogies

Number series and analogy questions are common in logical reasoning tests. They assess your ability to identify patterns and relationships. Here are some common types of patterns to look for:

• Arithmetic Operations: Addition, subtraction, multiplication, division, or a combination of these.
• Squares and Cubes: Relationships involving squares (\(N^2\)) or cubes (\(N^3\)) of numbers.
• Powers: Numbers raised to various powers (\(N^x\)).
• Digit Operations: Sum, difference, product, or other operations involving the digits of the numbers.
• Prime Numbers: The series or analogy might involve prime numbers.
• Fibonacci Sequence: Each number is the sum of the two preceding ones.
• Alternating Patterns: Different patterns might apply to alternate numbers or pairs.

Solving these questions effectively requires practice and a systematic approach to testing different possible relationships.