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

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Director
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What is my age (expressed as a positive integer)? Although [#permalink]

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10 Oct 2012, 12:25
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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 )

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]

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26 Feb 2014, 07:37
2
KUDOS
EvaJager wrote:
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).

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

Therefore, C and not E.
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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 12:20
1
KUDOS
thefibonacci wrote:
EvaJager wrote:
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 )

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.

EvaJager is 52.

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 cannot be expressed in the form of x^2+y^2
52 = 6^2+4^2

hence, the age is 52....which can be found by combining both the fact statements.

$$10=1^2+3^2$$
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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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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]

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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.

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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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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]

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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.

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]

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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.
Director
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Followers: 90

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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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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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Love GMAT Quant questions and running.

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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 07:43
EvaJager wrote:
EvaJager wrote:
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).

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

Therefore, C and not E.

Very nice to see you back, Eva! Looking forward to your beautiful questions and solutions!
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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 07:45
EvaJager wrote:
EvaJager wrote:
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).

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

Therefore, C and not E.

Eva thanks for clearing that up !
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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 11:36
EvaJager wrote:
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 )

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.

EvaJager is 52.

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.
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Last edited by thefibonacci on 26 Feb 2014, 14:16, edited 1 time in total.
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Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 14:15
EvaJager wrote:
thefibonacci wrote:
EvaJager wrote:
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 )

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.

EvaJager is 52.

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 cannot be expressed in the form of x^2+y^2
52 = 6^2+4^2

hence, the age is 52....which can be found by combining both the fact statements.

$$10=1^2+3^2$$

missed that. damn.

thanks!!
_________________

Illegitimi non carborundum.

Re: What is my age (expressed as a positive integer)? Although   [#permalink] 26 Feb 2014, 14:15
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