Question

* How many different odd 3-digit numbers can be formed using the digits 1,2,3,4,5 if none the numbes have repeating digits?

* A bus having a seating capacity of 45 people is 80% occupied. When the bus stops one -third of the people get off and 3 people get on the bus. The bus is now______ % occupied?

* If x-1 is a prime number greater than 3, which of the following could be a prime number?
a)x^2 b)x c)x-2 d)x+1 e)x+2

Answer 1

1. To be odd, it must end in an odd number, so the number of possible odds is
4x3x3 = 36

2. number of people on bus = .8(45) = 36
1/3 or 12 leave leaving 24, now 3 get on
number of people on bus = 15
percentage: 15/45 = 1/3 or 33 1/3 %

3. consider each choice:
--x^2: clearly any square is not prime
--x : since the original x-1 is a prime greater than 3, it must clearly be odd, so x must be even, thus not a prime
-- x+1: mmmmhhh, suppose x-1 = 11, then
x+1 = 13 ,which is prime
as a matter of fact , there would be many such choices and they would fall under the category of "twin Primes", that is, they are 2 units apart.
e.g. of other twin primes: 17,19 or 59,61

<b>so x+1 is a possibility</b> , which of course rules out x+2 , since it would be even.