Question

The three-digit number \[3x1\] is divisible by 9. Find the value of \[x\].
A. 1
B. 2
C. 5
D. 6

Answer 1

Hint: First, we will use the divisibility rule of 9 for 3 or more digits, that is the sum of its digits should be divisible by 9. Then we will find the sum of the given number and take it equal to 9 or 18 to find the required value.

Complete step by step answer:

We are given that the number \[3x1\] is divisible by 9.
We know that the divisibility rule of 9 for 3 or more digits is the sum of its digits should be divisible by 9.
Finding the sum of the given number, we get
\[
   \Rightarrow 3 + x + 1 \\
   \Rightarrow 4 + x \\
 \]
So here \[4 + x\] must be divisible by 9.
This is possible when \[4 + x = 9\] or 18.
Since \[x\] is a single-digit number, so we have
\[ \Rightarrow 4 + x = 9\]
Subtracting the above equation by 4 on both sides, we get
\[
   \Rightarrow 4 + x - 4 = 9 - 4 \\
   \Rightarrow x = 5 \\
 \]
Hence, option C is correct.

Note: Students must know that the divisibility test of 9 to easily find the solution. In solving these types of questions, students must consider that if a number with 3 or more digits is divisible by 9 if the sum of its digits should be divisible by 9, else they can get confused. One should be really careful while using the divisibility tests and avoid calculation mistakes.