pascal questions: 5-digit numbers, filling tub, perfect sqrs

[ejkaminsky]

1) a five-digit number is created using each of the digits 1,3,5,7, and 9 once. Each of the digits in the tens and thousands positions is larger that its eighboring digits. The number of such five-digits numbers is:
a) 16 b)12 c)10 d)8 e)6

2) a bathtub with 2 taps can be filled in 20 minutes using only the cold water tap. It can be filled in 30 minutes using onl the hot water tap. The flow of each tap isn't changed when both taps are turned on. It takes 24 minutes to drain the full tub. Starting with an empty tub and the drain plug in place, the cold water is turned on. Five minutes later the hot water is also turned on, and five minutes after that, the drain plug is removed. How many additional minutes, after the plug is removed, would it take to fill the tub?

A) 8 B) 11 C) 18 D) 20 E) 26

3) There are exactly k perfect squares which are divisors of 1996 to the power of 1996. The sum of the digits in the number k is:

A) 29 B) 26 C) 30 D) 22 E) 27[/img][/i]

 

[pka]

Yes, so what?
This is a homework help site, not a homework done site.
So what have you tried?

 

[ejkaminsky]

this actually isn't homework... i'm a mother and my son needed help with this and i didn't know the answers so what i wanted was somebody to do this step-by-step so i could help my son with it

 

[stapel]

this actually isn't homework... i'm a mother and my son needed help with this and i didn't know the answers so what i wanted was somebody to do this step-by-step so i could help my son with it

Unfortunately, trying to tutor through a "translator" who doesn't "speak the language" does not generally end happily. :shock:

Please have the student reply with his thoughts, showing everything he has tried so far. It would also help if he provided his current level of study (elementary-school "gifted" class? college-level algebra class? etc) and current topic(s) of study that generated these exercises.

Thank you!

Eliz.