Problem K. 299. (September 2011)

K. 299. There are 2011 pairs of twins living in a city. Among the 4022 people, there are 1900 males, and the number of pairs of twin sisters is 11 greater than the number of sister-brother pairs. How many pairs of twin brothers are there?

(6 pont)

Deadline expired on October 10, 2011.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A lány ikerpárok száma legyen \(\displaystyle l\), akkor a vegyes ikerpárok száma \(\displaystyle l-11\). A városban lakó lányok szám \(\displaystyle 4022-1900=2122\), másrészről \(\displaystyle 2l+l-11=3l-11\). A kettőt összevetve \(\displaystyle l=711\), azaz a vegyes ikerpárok száma 700, a fiúkból állóké pedig \(\displaystyle 2011-711-700={\mathbf 600}\).

Statistics:

291 students sent a solution.
6 points:	79 students.
5 points:	49 students.
4 points:	62 students.
3 points:	64 students.
2 points:	14 students.
1 point:	19 students.
0 point:	3 students.
Unfair, not evaluated:	1 solutions.

Problems in Mathematics of KöMaL, September 2011