Finding Your Age in Year x2: Answers & Solutions

[Cr4X]

I am faced with a problem at school, which I strongly believe 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.

 

[Gokul43201]

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.

 

[Muzza]

I think he means $$x^2$$. Assume the person's year of birth is a, then $$x^2 - a = x$$, or equivalently, $$a = x^2 - x$$. But $$1900 \leq a \leq 1999$$, so $$1900 \leq x^2 - x \leq 1999$$. Solving for x and disregarding negative values gives $$44.09 \leq x \leq 45.21$$, 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.

 

[Gokul43201]

I think he means $$x^2$$.

Of course, he does !