Solving Number Analogy Problems

This question asks us to find the missing term in an analogy based on the relationship between the first pair of numbers. The analogy is given as 11 : 169 :: 18 : ....... We need to understand how 11 is related to 169 and apply that same relationship to find the number that relates to 18.

Identifying the Pattern in the Analogy

Let's look at the first pair of numbers: 11 and 169. We need to find a mathematical operation or pattern that connects 11 to 169.

• Consider basic arithmetic operations: $11 + X = 169$, $11 \times X = 169$. These don't immediately seem simple.
• Consider squares or cubes. We know that $13^2 = 169$.
• How can we get 13 from 11? By adding 2: $11 + 2 = 13$.

So, the pattern seems to be: Take the first number, add 2 to it, and then square the result. Let's verify this pattern with the first pair:

Applying the pattern to the first term (11):

Step 1: Add 2 to the first term: $11 + 2 = 13$

Step 2: Square the result: $13^2 = 13 \times 13 = 169$

This result (169) matches the second term in the analogy. Therefore, the identified pattern is likely correct.

Applying the Pattern to the Third Term

Now, we apply the same pattern to the third term, which is 18, to find the missing fourth term.

Applying the pattern to the third term (18):

Step 1: Add 2 to the third term: $18 + 2 = 20$

Step 2: Square the result: $20^2 = 20 \times 20 = 400$

So, the missing term in the analogy is 400.

Checking the Options

Let's compare our result with the given options:

• Option 1: 396 (Does not match 400)
• Option 2: 256 (Does not match 400; $16^2 = 256$)
• Option 3: 361 (Does not match 400; $19^2 = 361$)
• Option 4: 400 (Matches our calculated result)

The calculated value, 400, is present as Option 4.

Conclusion on the Number Analogy

The relationship between 11 and 169 is that 169 is the square of (11 + 2). Applying this same relationship to 18, we find that the missing term is the square of (18 + 2), which is $20^2 = 400$. Thus, the analogy is 11 : 169 :: 18 : 400.

Revision Table: Key Concepts for Number Analogies

Additional Information on Number Analogies and Reasoning

Number analogy questions are a common type of question in logical reasoning tests. They assess your ability to identify patterns and relationships between numbers. These patterns can be based on various mathematical concepts, including:

• Basic arithmetic operations (addition, subtraction, multiplication, division)
• Squares and cubes
• Prime numbers, composite numbers, odd/even numbers
• Series involving differences, ratios, or alternating operations
• Digit-based logic (sum of digits, product of digits)

To solve number analogy problems effectively, it is helpful to:

• Be familiar with squares and cubes of numbers up to a reasonable limit.
• Practice identifying different types of patterns.
• Test simple patterns first before looking for complex ones.
• Carefully apply the identified pattern to the third term.
• Check if the result matches any of the given options.

Regular practice with different types of reasoning questions, including number analogies, helps improve problem-solving speed and accuracy.