i want to earn a symbol in the battle factory it says on the guide here i need to won there 20 times so i can battle their boss.can i done it w/saving and turning off the game??

Yes, provided you save the proper way, IE in between matches when the guy says "would you like to take a break or continue with the challenge?"

but if i do that i think i will be disqualified wen i turn off the game..or if i save between the matches and turn on the game again will my character will be in the battle room or in the ..lets say counter of the battle factory wer i will select to battle in lvl 50 or open lvl????

Your streak will end if you turn off the game any time you are in the Battle Factory itself. You must be out at the front desk of the building (or elsewhere, that's not in the Battle Factory) to turn off the game.

Here's how it works:
If you want to rest, just tell the guy and he'll save your game. After that, this screen:

2005 Pokemon
1995-2005 Nintendo
1995-2005 Creatures
1995-2005 Game Freak

or something like that will pop up. Now turn off your GBA/DS. When you want to continue, turn it back on and load the game as normal. The guy will say "We've been waiting for you!", save your game, and lead you back in again with the same team.

Doing this in the original Battle Tower, in Crystal version, would cause a disqualification. This was an unfortunate glitch in the game, and has been remedied in RS.

- DNA

r u saying that wen i choose to rest in between batles do the game will restart only?if thats wat will happen then i need is..for example im playing in around8:00 pm and im going to sleep in 9:00 so i need to turn off my game boy and open it again tomorrow wat answer should i select to the guy that will ask me(would u like to take a break or continue w/the challenge)wat should i select?retire or rest? if i select one of these i want my character should be inside the battle factory and not on the outside and the guy in glasses will say to me that(ur disqualified)......

Retire means you forfeit the challenge entirely.
Rest is when you want to take a break. It will save your game and then soft reset itself so you can come back to it later.

So yes. Select Rest, wait for the entry screen to come on, then turn off your system, and come back to battle when you feel like it.
- DNA

ok i understand now THANK U ALL OF U!!!!!!!!