• Welcome! The new FreeMathHelp.com forum is live. We've moved from VB4 to Xenforo 2.1 as our underlying software. Hopefully you find the upgrade to be a positive change. Please feel free to reach out as issues arise -- things will be a little different, and minor issues will no doubt crop up.

how old am I

bekah24h

New member
Joined
Feb 3, 2011
Messages
3
How old am I? My age is a perfect square number of years greater than a perfect square number; it is also a perfect square number of years less than a perfect square. Next year, my age will be a prime number less than 50
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,091
bekah24h said:
How old am I? My age is a perfect square number of years greater than a perfect square number; it is also a perfect square number of years less than a perfect square. Next year, my age will be a prime number less than 50
Next year, my age will be a prime number less than 50

Does the sentence above mean:

Next year, my age will be a prime number - less than 50

Next year, my age will be - a prime number less than 50

In either case:

Start defining your variable:

Let my age = A

Now continue.....

Please show us your work/thoughts, indicating exactly where you are stuck - so that we may know where to begin to help you.
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, bekah24h!

How old am I?
My age is a perfect square number of years greater than a perfect square number.
It is also a perfect square number of years less than a perfect square.
Next year, my age will be a prime number less than 50.

There is no formula for this type of problem.
. . We must resort to intelligent guesswork.


Let \(\displaystyle A\) = my age.

\(\displaystyle \text{Then: }\;\begin{array}{ccccc}A\text{ is the sum of two squares:} & A &=& a^2+b^2 \\ A\text{ is the difference of two squares:} & A &=& c^2-d^2 \end{array}\)


Consider the square numbers:

. . \(\displaystyle \begin{array}{ccccccccccccccc}1 & \boxed{4} & 9 & 16 & 25 & \boxed{36} & 49 & 64 & \boxed{81} & 100 & \boxed{121} & 144 & 169 & \hdots\)
. . . .. \(\displaystyle \underbrace{\qquad\qquad\qquad\qquad\quad}_{\text{sum of 40}} \qquad\qquad\quad \underbrace{\qquad\qquad\qquad\quad}_{\text{difference of 40}}\)


Therefore, my age is 40.

 
Top