Understanding the Number Analogy

This question involves a number analogy, where we need to identify a pattern between the first pair of numbers ($32654$ and $54876$) and apply that same pattern to the second pair ($51763$ and the unknown number).

Analyzing the First Pair: $32654 \rightarrow 54876$

Let's look at the digits of the first number ($32654$) and how they relate to the digits of the second number ($54876$).

• The first digit of $32654$ is $3$, and the first digit of $54876$ is $5$. The difference is $5 - 3 = 2$.
• The second digit of $32654$ is $2$, and the second digit of $54876$ is $4$. The difference is $4 - 2 = 2$.
• The third digit of $32654$ is $6$, and the third digit of $54876$ is $8$. The difference is $8 - 6 = 2$.
• The fourth digit of $32654$ is $5$, and the fourth digit of $54876$ is $7$. The difference is $7 - 5 = 2$.
• The fifth digit of $32654$ is $4$, and the fifth digit of $54876$ is $6$. The difference is $6 - 4 = 2$.

The pattern identified is that each digit in the number $32654$ is increased by $2$ to get the corresponding digit in $54876$. This can be shown as:

• $3 + 2 = 5$
• $2 + 2 = 4$
• $6 + 2 = 8$
• $5 + 2 = 7$
• $4 + 2 = 6$

Combining these results ($5, 4, 8, 7, 6$) gives us $54876$.

Applying the Pattern to the Second Pair: $51763 \rightarrow ?$

We will now apply the same rule (adding $2$ to each digit) to the number $51763$ to find the missing number.

• First digit: $5 + 2 = 7$
• Second digit: $1 + 2 = 3$
• Third digit: $7 + 2 = 9$
• Fourth digit: $6 + 2 = 8$
• Fifth digit: $3 + 2 = 5$

Combining these digits ($7, 3, 9, 8, 5$) gives us the number $73985$.

Choosing the Correct Option

Based on the established pattern of adding $2$ to each digit, the missing number is calculated as $73985$. Let's compare this with the given options:

• Option 1: $73986$
• Option 2: $74986$
• Option 3: $72985$
• Option 4: $73985$

Our calculated result $73985$ corresponds to Option 4. The provided correct answer is Option 1 ($73986$).