Understanding Number Analogy and Patterns

Number analogy questions test your ability to find the relationship between a pair of numbers and apply that same relationship to another number to find a missing term. In the given analogy, we have:

11 : 123 :: 12 : ?

This means we need to figure out the pattern or operation that transforms 11 into 123 and then apply that same pattern to 12 to find the corresponding number.

Analyzing the Relationship between 11 and 123

Let's examine the numbers 11 and 123. How can we get from 11 to something close to 123? We can try common mathematical operations:

• Addition/Subtraction: Adding a large number to 11. Not a typical pattern for analogies involving squares or cubes.
• Multiplication: $11 \times 10 = 110$, $11 \times 11 = 121$, $11 \times 12 = 132$. 121 is close to 123.
• Squaring: $11^2 = 11 \times 11 = 121$. This is very close to 123.
• Cubing: $11^3 = 1331$. Too large.

The value 121, which is $11^2$, is only 2 less than 123. This suggests a possible pattern:

\begin{equation*} \text{Number} \rightarrow (\text{Number})^2 + 2 \end{equation*}

Let's test this pattern with the first pair:

\begin{equation*} 11 \rightarrow 11^2 + 2 = 121 + 2 = 123 \end{equation*}

This pattern holds true for the first pair of numbers.

Applying the Pattern to Find the Missing Number

Now, we apply the same pattern to the number 12 to find the missing term in the analogy $12 : ?$.

Using the pattern $(\text{Number})^2 + 2$:

\begin{equation*} 12 \rightarrow 12^2 + 2 \end{equation*}

Calculate the square of 12:

\begin{equation*} 12^2 = 12 \times 12 = 144 \end{equation*}

Now add 2 to the result:

\begin{equation*} 144 + 2 = 146 \end{equation*}

So, according to the pattern, the missing number is 146.

Verifying with Options

Let's compare our result, 146, with the given options:

• Option 1: 144
• Option 2: 146
• Option 3: 148
• Option 4: 150

Our calculated number, 146, matches Option 2.

The relationship in this number analogy is squaring the first number and adding 2 to get the second number.

\begin{itemize} \item 11 : $11^2 + 2 = 121 + 2 = 123$ \item 12 : $12^2 + 2 = 144 + 2 = 146$ \end{itemize}

Revision Table: Number Analogy Key Concepts

Additional Information: Common Number Patterns in Analogies

Number analogy questions often use common mathematical patterns. Understanding these can help solve problems faster. Some frequent patterns include:

• Squaring or Cubing the number ($n^2$, $n^3$).
• Adding or subtracting a constant ($n+k$, $n-k$).
• Multiplying or dividing by a constant ($n \times k$, $n / k$).
• Combinations of operations, like squaring and adding/subtracting ($n^2+k$, $n^2-k$).
• Operations involving the digits of the number.
• Sequences based on prime numbers, odd/even numbers, etc.

Practice with various types of number patterns will improve your ability to solve number analogy and reasoning questions quickly.