geno5 wrote:
Evajager,
I got the right answer but I am abit unsure on statement 2. Could you solve the question. I understand if you waiting for others to post first.
I am abit unclear on this part of the statement (2) My age can be written as the product of a two digit integer and the sum of its digits.
You guys, just being too polite, don't want to reveal my age. Well, it seems that I have no choice, I have to do it...
(1) Obviously not sufficient. Too many options: 4 + 25 = 29, 9 + 25 = 34, 4 + 36 = 40... (wishful thinking)
(2) My age is (A + B)AB, where AB is a two digit number, A and B are distinct, and A + B is a perfect square.
Possible solutions: AB = 10, (1 + 0)*10 = 10.
4*13 =52 (4*31 = 124 > 100)
Next perfect square is 9. But any two digits with sum 9, when multiplied by 9, will give a number greater than 100. 9*18 is the smallest and already greater than 100.
So, we are left with two possibilities: 10 and 52.
(1) and (2) together: 10 = 1 + 9 and 52 = 16 + 36, both are sums of two perfect squares.
So, the answer should be E. If we take into account that I am an adult, then B should be the answer.
I cannot full you anymore...I am 52 years old.
Just a short summary of the properties of the number 52:
\(52 = 4*13\) \(,\,\,\,4=2^2\) and \(4 = 1 + 3.\)
\(52 = 16 + 36 = 4^2+6^2\), sum of two consecutive even squares.
\(13 = 4 + 9 = 2^2+3^2\), sum of two consecutive squares.
Can you find some more?
Next year is going to be 53. Prime number. Until now, I just found that \(53=6\cdot{9}-1=(2\cdot{3})\cdot{3^2}-1.\)