To determine the value that the placeholder "" can take in the number [tex]\( 25215 \)[/tex] so that it is divisible by 3, follow these steps:
1. Understanding divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
2. Calculate the sum of given digits:
Consider the number [tex]\( 25*215 \)[/tex]. The sum of the known digits is:
[tex]\[
2 + 5 + 2 + 1 + 5 = 15
\][/tex]
We add an unknown digit [tex]\( x \)[/tex] in the position of "*":
[tex]\[
\text{Sum of the digits} = 15 + x
\][/tex]
3. Determine the value of [tex]\( x \)[/tex]:
To make the entire number divisible by 3, the sum of the digits [tex]\( 15 + x \)[/tex] must be divisible by 3. We will test each option:
- (a) If [tex]\( x = 1 \)[/tex]:
[tex]\[
15 + 1 = 16 \quad \text{(not divisible by 3)}
\][/tex]
- (b) If [tex]\( x = 3 \)[/tex]:
[tex]\[
15 + 3 = 18 \quad \text{(divisible by 3)}
\][/tex]
- (c) If [tex]\( x = 4 \)[/tex]:
[tex]\[
15 + 4 = 19 \quad \text{(not divisible by 3)}
\][/tex]
- (d) If [tex]\( x = 5 \)[/tex]:
[tex]\[
15 + 5 = 20 \quad \text{(not divisible by 3)}
\][/tex]
4. Conclusion:
Out of the provided options, only [tex]\( x = 3 \)[/tex] makes the sum [tex]\( 15 + x \)[/tex] divisible by 3. Therefore, the value that "" can take to make the number [tex]\( 25215 \)[/tex] divisible by 3 is:
[tex]\[
\boxed{3}
\][/tex]
