Of these kids, one was a foster, went to a big house to be tested with multiple challenges with their brain from this guy and it gets crazy. The cover of the book is yellow and has a huge wooden house with kids around it. There are like 4 books in the series.
The Mysterious Benedict Society by Trenton Lee Stewart
After seeing an ad in the newspaper that reads, "ARE YOU A GIFTED CHILD LOOKING FOR SPECIAL OPPORTUNITIES?" Reynie Muldoon decides to take a test that is being hosted nearby. At the facility, he takes two rounds of testing, and is the only one in the room each time to pass - which he does easily by reading between the lines and figuring out the puzzles involved after refusing an offer to cheat. Invited to go to another facility to continue testing, he meets George, or "Sticky" Washington, a timid boy with an extraordinary gift for memory which he used to pass the tests. During the final two physical tests, he meets Kate Wetherall, an athletic and resourceful girl with a large bucket of objects, and Constance Contraire, a diminutive girl with a very defiant personality and a gift for wit, especially considering her minuscule size. All four children are also revealed to either have no parents or (in the case of Sticky, a runaway) to have been estranged from them.
In like the third book (there are three books in the series and 2 companion books), Constance is revealed to have some strange mental powers.