## Subject IV. (20 points)

Amaya and Keiko are two girls from Osaka. They live on the same floor in a building with two staircases, each with 5 apartments per floor. At the ground floor of the building are shops.

The apartments are numbered in ascending order, starting from the first floor. Amaya lives in apartment 28, and Keiko in apartment 164. How many floors does the building have?

Prof. Sorin Borodi, "Alexandru Papiu Ilarian" Theoretical High School, Dej

All subjects are mandatory. 10 points are awarded by default.

Effective working time - 2 hours.

## Grading Scale for Grade 5 (OLM 2013 - Local Stage)

## Of. $10 \mathrm{p}$
## Subject IV.

Obviously, the girls live on different staircases.

(5 points)

On the first staircase, apartment 28 is on the 6th floor.

On the second staircase, the first apartment on the 6th floor is 161.

(5 points)

It follows that on the second staircase, the first apartment is $161-25=136$.

This means that on the first staircase, the last apartment is 135.

(5 points)

$135 \div 5 = 27$ floors

(5 points)