Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

What is my age (expressed as a positive integer)? Although [#permalink]
10 Oct 2012, 11:25

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

31% (03:20) correct
69% (01:36) wrong based on 29 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 )

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.

Re: What is my age (expressed as a positive integer)? Although [#permalink]
10 Oct 2012, 13:11

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. _________________

Re: What is my age (expressed as a positive integer)? Although [#permalink]
10 Oct 2012, 13:53

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.

Re: What is my age (expressed as a positive integer)? Although [#permalink]
10 Oct 2012, 13:59

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

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: What is my age (expressed as a positive integer)? Although [#permalink]
10 Oct 2012, 14:42

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. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: What is my age (expressed as a positive integer)? Although [#permalink]
26 Feb 2014, 10:36

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.

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. _________________

Illegitimi non carborundum.

Last edited by thefibonacci on 26 Feb 2014, 13:16, edited 1 time in total.

Re: What is my age (expressed as a positive integer)? Although [#permalink]
26 Feb 2014, 11:20

1

This post received 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.

Answer would be C.

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.

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

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: What is my age (expressed as a positive integer)? Although [#permalink]
26 Feb 2014, 13:15

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.

Answer would be C.

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.

gmatclubot

Re: What is my age (expressed as a positive integer)? Although
[#permalink]
26 Feb 2014, 13:15

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...