Number Analogy Pattern Explanation

This question tests your ability to identify patterns in number sequences. We are given a relationship between two numbers ($14825$ and $36047$) and need to apply the same pattern to find the missing number related to $27416$. The goal is to find the missing number in the second pair ($27416 : ?$).

Pair 1 Digit Transformation ($14825 \rightarrow 36047$)

Let's break down the first pair and compare the digits at each position:

• The first digit of $14825$ is $1$, and the first digit of $36047$ is $3$.
• The second digit of $14825$ is $4$, and the second digit of $36047$ is $6$.
• The third digit of $14825$ is $8$, and the third digit of $36047$ is $0$.
• The fourth digit of $14825$ is $2$, and the fourth digit of $36047$ is $4$.
• The fifth digit of $14825$ is $5$, and the fifth digit of $36047$ is $7$.

Pattern Discovery: Add 2 Modulo 10

We observe the change for each digit:

• $1 \rightarrow 3$ (Increase of 2)
• $4 \rightarrow 6$ (Increase of 2)
• $8 \rightarrow 0$ (This looks like $(8 + 2) \pmod{10}$, which equals $10 \pmod{10} = 0$)
• $2 \rightarrow 4$ (Increase of 2)
• $5 \rightarrow 7$ (Increase of 2)

The consistent logical pattern is that each digit in the first number is transformed by adding 2 to it. For the digit 8, the result $8+2=10$ becomes 0, following the rule of addition modulo 10.

Applying Pattern to $27416$

Now, we apply this discovered pattern (add 2 to each digit, taking the result modulo 10) to the number $27416$:

• First digit: $2$. Applying the rule: $(2 + 2) \pmod{10} = 4$.
• Second digit: $7$. Applying the rule: $(7 + 2) \pmod{10} = 9$.
• Third digit: $4$. Applying the rule: $(4 + 2) \pmod{10} = 6$.
• Fourth digit: $1$. Applying the rule: $(1 + 2) \pmod{10} = 3$.
• Fifth digit: $6$. Applying the rule: $(6 + 2) \pmod{10} = 8$.

Combining these resulting digits gives us the number $49638$.

Solution Derivation and Option Match

The missing number derived using the identified pattern is $49638$. This result matches Option 1.