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Math

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* 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

  • Math -

    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

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

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