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

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What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 12:25
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33% (00:00) correct 66% (01:15) wrong based on 0 sessions
I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes...
Contemplating my age, I just realized that the integer number that represents my age has some very nice properties :o)

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares.
(2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.
[Reveal] Spoiler: OA

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Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 14:11
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.
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Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 14:53
I am posting here for the first time as I joined GMAT club recently.

If we take statement (2) then according to that i took two digit integer as 13 and the sum of it's digits is 4( which is a perfect square) so the product of 13 and 4 = 52.

now according to statement first 16( which is a perfect square)+ 36( which is also a perfect square) = 52 which is the age in two digits.

so the answer is C
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Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 14:59
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.
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Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 15:42
aah123 wrote:
I am posting here for the first time as I joined GMAT club recently.

If we take statement (2) then according to that i took two digit integer as 13 and the sum of it's digits is 4( which is a perfect square) so the product of 13 and 4 = 52.

now according to statement first 16( which is a perfect square)+ 36( which is also a perfect square) = 52 which is the age in two digits.

so the answer is C


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.
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Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 16:28
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.
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Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 11 Oct 2012, 02:22
aah123 wrote:
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).
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Re: What is my age (expressed as a positive integer)? Although   [#permalink] 11 Oct 2012, 02:22
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