Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Jul 2014, 17:27

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 479 [0], given: 43

GMAT Tests User
What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 11:25
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

28% (03:10) correct 72% (01:28) wrong based on 25 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

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Manager
avatar
Joined: 05 Dec 2011
Posts: 78
Location: Canada
Concentration: Accounting, Finance
GMAT Date: 09-08-2012
GPA: 3
Followers: 0

Kudos [?]: 19 [0], given: 2

Reviews Badge
Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 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.
_________________

Thanks = +1 Kudos

Study from reliable sources!!

Thursdays with Ron: http://www.manhattangmat.com/thursdays-with-ron.cfm

Gmat Prep Questions:
CR gmatprepsc-105446.html
SC gmatprepsc-105446.html

Intern
Intern
avatar
Joined: 08 Oct 2012
Posts: 19
Followers: 0

Kudos [?]: 1 [0], given: 0

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

so the answer is C
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 479 [0], given: 43

GMAT Tests User
Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 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.

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 479 [0], given: 43

GMAT Tests User
Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 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.

Intern
Intern
avatar
Joined: 08 Oct 2012
Posts: 19
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 10 Oct 2012, 15:28
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
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 479 [0], given: 43

GMAT Tests User
Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 11 Oct 2012, 01:22
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).
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

2 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 479 [2] , given: 43

GMAT Tests User
Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 26 Feb 2014, 06:37
2
This post received
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.,
only 52 is an answer.

Therefore, C and not E.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18832
Followers: 3267

Kudos [?]: 22816 [0], given: 2651

Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 26 Feb 2014, 06:43
Expert's post
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.,
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!
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 27 May 2012
Posts: 213
Followers: 0

Kudos [?]: 46 [0], given: 111

Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 26 Feb 2014, 06:45
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.,
only 52 is an answer.

Therefore, C and not E.


Eva thanks for clearing that up !
_________________

- Stne

Intern
Intern
avatar
Joined: 22 Jan 2014
Posts: 29
Followers: 0

Kudos [?]: 7 [0], given: 22

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


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.

Last edited by thefibonacci on 26 Feb 2014, 13:16, edited 1 time in total.
1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 479 [1] , given: 43

GMAT Tests User
Re: What is my age (expressed as a positive integer)? Although [#permalink] New post 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 :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.


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.

Intern
Intern
avatar
Joined: 22 Jan 2014
Posts: 29
Followers: 0

Kudos [?]: 7 [0], given: 22

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


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. :cry:

thanks!!
Re: What is my age (expressed as a positive integer)? Although   [#permalink] 26 Feb 2014, 13:15
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic For positive integer k, is the expression (k + jeeteshsingh 10 21 Feb 2010, 13:40
For positive integer k, is the expression (k + dancinggeometry 6 16 Sep 2008, 06:38
Can the positive integer p be expressed as the product of alimad 4 30 Jun 2008, 06:10
Can the positive integer x be expressed as the product of tarek99 2 01 Feb 2008, 02:39
Can the positive integer p be expressed as the product of circkit 3 14 Nov 2007, 04:05
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.