Question

The probability that $4^{th}$ power of a positive integer ends in the digit 6 is

• A. $10$ %
• B. $20$ %
• C. $25$ %
• D. $40$ %

Answer 1

The correct option is D $40$ %

The final digit of any power of an integer relies solely on the final digit of the original integer itself.

We have the following:

Original Last Digit 0 1 2 3 4 5 6 7 8 9

last digit of the 4th power 0 1 6 1 6 5 6 1 6 1

Since each final digit of the original integer is equally likely, the probability that the fourth power of a randomly selected integer being 6 will be

$\frac{\text{\#of choices that lead to final digit being 6}}{\text{\#of choices regardless}}=\frac{4}{10}=40\%$