Salah has collected more than $$20$$ football cards.  When he puts his cards in piles of four, he has three cards left over.  When he puts the cards in piles of five, he has four cards left over.  Which of the following could be the number of cards he has in total? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem
The number of Salah\textquotesingle s cards is $$3$$ more than a multiple of $$4$$, and $$4$$ more than a multiple of $$5$$. Of the two-digit options given, the only one that satisfies both criteria is $$39(=9\times4+3 =7\times5+4)$$. 