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Simple question

  1. Jun 7, 2004 #1
    I am faced with a problem at school, which I strongly belive i answered correctly to, but I have still gotten it as an error, so I would like to know what you would reply to this:

    I am x years in year x2. I am born in the 20. century.

    A: When am I born?
    B: How old am I in year x2?


    Thanks in advance.
     
  2. jcsd
  3. Jun 7, 2004 #2

    Gokul43201

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    Does x2 refer to a 2-digit number whose unit digit is "2" and ten's digit is "x" ?

    If this is true, then the year of birth depends on x (there is no constant answer). Simply, the year of birth is :10x+2-x = 9x+2 (assuming you TURNED x years old in year x2)

    If you want the individual digits of the 2-digit year in terms of x, then for x=[2..9] you have :
    ten's digit = x-1 and unit's digit =12 - x
    and for x=[0,1,2], ten's digit = x, unit's digit = 2-x

    Perhaps you should clarify "I am x years in year x2" before anyone speculates any further.
     
    Last edited: Jun 7, 2004
  4. Jun 7, 2004 #3
    I think he means [tex]x^2[/tex]. Assume the person's year of birth is a, then [tex]x^2 - a = x[/tex], or equivalently, [tex]a = x^2 - x[/tex]. But [tex]1900 \leq a \leq 1999[/tex], so [tex]1900 \leq x^2 - x \leq 1999[/tex]. Solving for x and disregarding negative values gives [tex]44.09 \leq x \leq 45.21[/tex], so x must be 45 (well, that's not really true, but I'm assuming we're working with only natural numbers here). This gives a = 1980. And yes, a person born in 1980 is indeed 45 years old in the year 45^2 = 2025.
     
    Last edited: Jun 7, 2004
  5. Jun 7, 2004 #4

    Gokul43201

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    Of course, he does !
     
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