Question

Kaleb defined a $\emph{clever integer}$ as an even integer that is greater than 20, less than 120, and such that the sum of its digits is 9. What fraction of all clever integers is divisible by 27

Answer 1

Using proportions, it is found that $\mathbf{\frac{2}{5}}$ are divisible by 27.

According to the description given in the problem, the clever integers are: 27, 36, 45, 54, 63, 72, 81, 90, 108, 117.

From these numbers, we have that:

• There are 10 clever integers.

• Of those, 4, which are 27, 54, 81 and 108, are divisible by 27.

Then:

$f = \frac{4}{10} = \frac{2}{5}$

$\mathbf{\frac{2}{5}}$ are divisible by 27.

To learn more about proportions, you can take a look at https://brainly.com/question/24372153