Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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:

 292 students sent a solution. 6 points: 79 students. 5 points: 49 students. 4 points: 62 students. 3 points: 65 students. 2 points: 14 students. 1 point: 19 students. 0 point: 3 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, September 2011