What is my age (expressed as a positive integer)? Although

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 \(53=6\cdot{9}-1=(2\cdot{3})\cdot{3^2}-1.\)

Welcome to the Club!
This is not a real GMAT test question, I was just trying to fool the club members...

I guess you didn't consider 10 as a possible solution for (2).
But you are right, I am 52. And as formulated, the answer to the question is either B or E, depending on whether we regard 10 as a possible solution or not.

Thanks Evajager,
Yes I did not consider 10, I don't know how come I counted only till 9.
So what's the answer then...is it (E) or (C).

I am just understanding how data sufficiency works, as my math concepts are good but this part is new to me.

The answer should be E. Both 10 and 52 fulfill the conditions in statements (1) and (2).

But taking into account the given piece of information that Although not young anymore, my age is still a two digit integer.,
only 52 is an answer.

Therefore, C and not E.

Very nice to see you back, Eva! Looking forward to your beautiful questions and solutions!

Eva thanks for clearing that up !

EvaJager is 52.

Answer would be E.

1) a lot of options...so not sufficient.

2) sum of digits of any 2 digit number can be at max = 18.
so, we need to consider squares < 18 ie 1,4,9 and 16.
let the age be ab
=> (10a+b)(a+b) = age.
where a+b = perfect square.

for a+b=1 ; ab=10
for a+b=4 ; ab = 13 and 31 (since digits are distinct)
for a+b=9 ; ab = 18,27,... (but we can ignore 9 and 16 coz as soon as we multiply the sum of digits with the number, it would become a 3 digit number)

we are left with:
10*1 = 10
13*4 = 52
31*4 = a three digit number (ignore)

so, B alone is insufficient.

combine both statements.

age is a sum of 2 distinct prfct sq. and age can either be 10 or 52.
10 = 1^2 + 3^2
52 = 6^2+4^2

hence, the age can be 52 or 10. So E.

\(10=1^2+3^2\)

missed that. damn.

thanks!!