Solving the Number Analogy Question

This question asks us to find a relationship between the first pair of numbers (13 and 1331) and apply that same relationship to the third number (17) to find the fourth number. This type of problem is known as a numerical analogy or number series problem, requiring pattern recognition.

Understanding the Number Relationship

Let's examine the first pair of numbers: 13 and 1331. We need to figure out how 13 is related to 1331. Let's consider different mathematical operations:

• Addition/Subtraction: $1331 - 13 = 1318$. Adding 1318 is the difference, but this usually isn't the pattern in such analogies.
• Multiplication/Division: $1331 / 13 = 102.38...$. Not a simple whole number multiplication.
• Powers: Let's consider powers of 13 or numbers related to 13.
• $13^2 = 169$ (Too small)
• $13^3 = 2197$ (Too large)
• What about powers of a number slightly different from 13? Let's try subtracting a small number from 13.
• Consider $(13 - 1)^3 = 12^3 = 1728$ (Close, but not 1331)
• Consider $(13 - 2)^3 = 11^3$.
• Let's calculate $11^3$:

$\qquad 11^2 = 11 \times 11 = 121$

$\qquad 11^3 = 121 \times 11$

We can calculate $121 \times 11$ as:

So, $11^3 = 1331$. This matches the second number in the first pair!

The relationship is: the second number is the cube of (the first number minus 2).

In mathematical terms, if the first number is $n$, the second number is $(n-2)^3$.

Applying the Relationship to the Third Number

Now we apply the same rule to the third number, which is 17. According to the pattern, the missing number should be $(17 - 2)^3$.

First, calculate $17 - 2$: $17 - 2 = 15$.

Next, calculate $15^3$.

$\qquad 15^2 = 15 \times 15 = 225$

$\qquad 15^3 = 225 \times 15$

Let's calculate $225 \times 15$:

So, $15^3 = 3375$.

Finding the Missing Number

Based on the established pattern from the first pair (13 and 1331), the missing number related to 17 is 3375.

Checking the Options for the Number Analogy

We found the missing number to be 3375. Let's look at the given options:

1. 1453
2. 3375
3. 1829
4. 2642

Our calculated number, 3375, matches option 2.

Therefore, the correct answer related to 17 in the same way as 13 is related to 1331 is 3375.

Revision Table: Number Analogy Pattern

This table summarizes the relationship found in the number analogy question.

Additional Information on Number Series and Analogies

Number series and analogy problems are common in aptitude tests. They test your ability to identify patterns in sequences of numbers. Common patterns include:

• Arithmetic progressions (adding or subtracting a constant number).
• Geometric progressions (multiplying or dividing by a constant number).
• Square or cube series (numbers are squares or cubes of consecutive or related numbers).
• Combinations of operations (e.g., multiply and then add).
• Patterns based on digits of the number.
• Alternating patterns (different rules apply to alternate numbers).
• Difference/sum of consecutive numbers following a pattern.

To solve these problems, look for the simplest pattern first, such as constant differences or ratios, and then consider squares, cubes, or more complex combinations. Practice is key to quickly identifying different types of number patterns.