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

It is currently 28 Aug 2015, 19:20
GMAT Club Tests

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

The sum of the digits of [(10^x)^y]-64=279. What is the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 277
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 48 [2] , given: 282

The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] New post 28 Oct 2012, 09:18
2
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (02:35) correct 53% (02:19) wrong based on 145 sessions
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy ?

A. 28
B. 29
C. 30
D. 31
E. 32
[Reveal] Spoiler: OA

_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+


Last edited by Bunuel on 29 Oct 2012, 00:59, edited 2 times in total.
Renamed the topic and edited the question.
Manager
Manager
User avatar
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 72
GMAT Date: 10-01-2012
Followers: 2

Kudos [?]: 34 [0], given: 84

Re: The Sum of the digits of(10^x)^y [#permalink] New post 28 Oct 2012, 10:13
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.
_________________

I will rather do nothing than be busy doing nothing - Zen saying

Senior Manager
Senior Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 277
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 48 [0], given: 282

Re: The Sum of the digits of(10^x)^y [#permalink] New post 28 Oct 2012, 10:22
Pansi wrote:
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.


Well, It is a multiple of 9. How will you arrive at xy with that approach?

Try finding patterns. (thats the clue)
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

1 KUDOS received
Current Student
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 648
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 40

Kudos [?]: 424 [1] , given: 23

GMAT ToolKit User Premium Member
Re: The Sum of the digits of(10^x)^y [#permalink] New post 28 Oct 2012, 18:44
1
This post received
KUDOS
Pansi wrote:
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.


Well, simple reason is that the question is incorrect.

rajathpanta wrote:
Well, It is a multiple of 9. How will you arrive at xy with that approach?

Try finding patterns. (thats the clue)


Question is:
10^xy -64 = N,
where sum of digits of N=79

The pattern is like this:

100 -64 = 36
1000 -64 = 936
10000 -64 =9936

or,
1 followed by (n times 0) = (n-2)times 9 followed by 36

Therefore sumof digits on right side is always a multiple of 9 [9s and 6+3 =9]

However in question stem RHS is 79, which is not divisible by 9. And therefore you can not arrive at any of the answer choices given.

Rajathpanta- on a lighter note - if this too is from Aristotle, I'd suggest please change the source of questions. :D

Hope it helps!
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Manager
Manager
avatar
Joined: 29 Jul 2012
Posts: 189
GMAT Date: 11-18-2012
Followers: 0

Kudos [?]: 53 [0], given: 23

Re: The Sum of the digits of(10^x)^y [#permalink] New post 28 Oct 2012, 19:40
still confuse with question
any more explanation
_________________

Thriving for CHANGE

Senior Manager
Senior Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 277
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 48 [0], given: 282

Re: The Sum of the digits of(10^x)^y [#permalink] New post 28 Oct 2012, 19:42
Vips0000 wrote:
Pansi wrote:
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.


Well, simple reason is that the question is incorrect.

rajathpanta wrote:
Well, It is a multiple of 9. How will you arrive at xy with that approach?

Try finding patterns. (thats the clue)


Question is:
10^xy -64 = N,
where sum of digits of N=79

The pattern is like this:

100 -64 = 36
1000 -64 = 936
10000 -64 =9936

or,
1 followed by (n times 0) = (n-2)times 9 followed by 36

Therefore sumof digits on right side is always a multiple of 9 [9s and 6+3 =9]

However in question stem RHS is 79, which is not divisible by 9. And therefore you can not arrive at any of the answer choices given.

Rajathpanta- on a lighter note - if this too is from Aristotle, I'd suggest please change the source of questions. :D

Hope it helps!



Hi Vips00,

This is from the veritas prep questions set!

Thanks.
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Current Student
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 648
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 40

Kudos [?]: 424 [0], given: 23

GMAT ToolKit User Premium Member
Re: The Sum of the digits of(10^x)^y [#permalink] New post 28 Oct 2012, 20:47
rajathpanta wrote:
Vips0000 wrote:
Pansi wrote:
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.


Well, simple reason is that the question is incorrect.

rajathpanta wrote:
Well, It is a multiple of 9. How will you arrive at xy with that approach?

Try finding patterns. (thats the clue)


Question is:
10^xy -64 = N,
where sum of digits of N=79

The pattern is like this:

100 -64 = 36
1000 -64 = 936
10000 -64 =9936

or,
1 followed by (n times 0) = (n-2)times 9 followed by 36

Therefore sumof digits on right side is always a multiple of 9 [9s and 6+3 =9]

However in question stem RHS is 79, which is not divisible by 9. And therefore you can not arrive at any of the answer choices given.

Rajathpanta- on a lighter note - if this too is from Aristotle, I'd suggest please change the source of questions. :D

Hope it helps!



Hi Vips00,

This is from the veritas prep questions set!

Thanks.


Hmmm, but you get that the question is incorrect and why?
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Current Student
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 648
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 40

Kudos [?]: 424 [0], given: 23

GMAT ToolKit User Premium Member
Re: The Sum of the digits of(10^x)^y [#permalink] New post 28 Oct 2012, 20:49
Aristocrat wrote:
still confuse with question
any more explanation

What is confusing? I already explained it in detail. If there is any particular thing you could not understand let me know, would try to explain further.
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49665 [3] , given: 7400

Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink] New post 29 Oct 2012, 00:59
3
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
rajathpanta wrote:
The sum of the digits of [(10^x)^y]-64=79. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32


The question should read:
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32

Also, it should be mentioned that xy is a positive integers.

First of all \((10^x)^y=10^{xy}\).

\(10^{xy}\) has \(xy+1\) digits: 1 and \(xy\) zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of \(10^{xy}-64\) is 279 --> \(9(xy-2)+3+6=279\) --> \(9(xy-2)=270\) --> \(xy=32\).

Answer: E.

Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope it's clear.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Intern
Intern
User avatar
Status: Active
Joined: 30 Jun 2012
Posts: 38
Location: India
Followers: 4

Kudos [?]: 60 [1] , given: 36

Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] New post 29 Oct 2012, 01:26
1
This post received
KUDOS
As

Question is \((10^x)^y - 64\) . Let say \((10^x)^y\) as Number1
Say Number1 - 64 = Number2 ==>
100 - 64 = 36 [ Number1: No. of zeroes = 2 , Number2: No. of 9's = zero ] and Sum of digits of Number 2 : 9*0 + (3+6) = 1*9 = 9
1000 - 64 = 936 [ Number1: No. of zeroes = 3 , Number2: No. of 9's = 1] and Sum of digits of Number 2 : 9*1 + (3+6) = 9 + 9 = 2*9 = 18
10000 - 64 = 9936 [ Number1: No. of zeroes = 4 , Number2: No. of 9's = 2] and Sum of digits of Number 2 : 9*2 + (3+6) = 18 + 9 = 3*9= 27
100000 - 64 = 99936 [ Number1: No. of zeroes = 5 , Number2: No. of 9's = 3] and Sum of digits of Number 2 : 9*3 + (3+6) = 27 + 9 =4*9= 36


so lets go from right to left for the sum of digits of number2 i.e given as 279
so 279 = 31*9 = 9*30 + (3+6) => Number2: Number of 9's = 30 ==> Number1: Number of zeros = 32

So the Number1 i.e. \((10^x)^y = 10000.....(32 zeroes)\)

Now, as we now, \(10^1\) = 10 (1 zero)
\(10^2\) = 100 (2 zeroes)
\(10^3\) = 1000 (3 zeroes)

same way, 10000.....(32 zeroes) = \(10^32\)

\((10^x)^y = 10^(xy) = 10^32\)
==> xy = 32
_________________

Thanks and Regards!

P.S. +Kudos Please! in case you like my post. :)

Intern
Intern
avatar
Joined: 04 Aug 2013
Posts: 10
Followers: 0

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

Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink] New post 24 Nov 2013, 18:36
Hi Bunuel,

Could you please xplain the last bit oft he equations which takes us to a 279?

Thanks


quote="Bunuel"]
rajathpanta wrote:
The sum of the digits of [(10^x)^y]-64=79. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32


The question should read:
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32

Also, it should be mentioned that xy is a positive integers.

First of all \((10^x)^y=10^{xy}\).

\(10^{xy}\) has \(xy+1\) digits: 1 and \(xy\) zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of \(10^{xy}-64\) is 279 --> \(9(xy-2)+3+6=279\) --> \(9(xy-2)=270\) --> \(xy=32\).

Answer: E.

Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope it's clear.[/quote]
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49665 [1] , given: 7400

Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink] New post 25 Nov 2013, 01:52
1
This post received
KUDOS
Expert's post
Shibs wrote:
Hi Bunuel,

Could you please xplain the last bit oft he equations which takes us to a 279?

Thanks


quote="Bunuel"]
rajathpanta wrote:
The sum of the digits of [(10^x)^y]-64=79. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32


The question should read:
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32

Also, it should be mentioned that xy is a positive integers.

First of all \((10^x)^y=10^{xy}\).

\(10^{xy}\) has \(xy+1\) digits: 1 and \(xy\) zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of \(10^{xy}-64\) is 279 --> \(9(xy-2)+3+6=279\) --> \(9(xy-2)=270\) --> \(xy=32\).

Answer: E.

Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope it's clear.


\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. Threfore the sum of the digits is \(9(xy-2)+3+6=279\).

Hope it's clear.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Senior Manager
Senior Manager
avatar
Status: Student
Joined: 26 Aug 2013
Posts: 266
Location: France
Concentration: Finance, General Management
GMAT 1: 650 Q47 V32
GPA: 3.44
Followers: 2

Kudos [?]: 45 [1] , given: 401

Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] New post 08 Jan 2014, 03:19
1
This post received
KUDOS
Hi,

this is my process (edited to be the most efficient possible):

\(1000-64= 936\). Whatever XY is you finish with \(36 ==> 3+6=9\)

Therefore, \(279-9=270\) and \(270/9=30\)

Now you add the last two digits (3 and 6)

Answer is \(30+2=32\)

Hope it helps
_________________

Think outside the box

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6096
Followers: 340

Kudos [?]: 68 [0], given: 0

Premium Member
Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] New post 21 Jan 2015, 22:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: The sum of the digits of [(10^x)^y]-64=279. What is the   [#permalink] 21 Jan 2015, 22:41
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic What is the tens' digit of the sum of the first 40 terms of LM 5 26 Jan 2012, 06:28
12 Experts publish their posts in the topic What is the sum of digits of number 10^28 – 28? arjtryarjtry 11 22 Jul 2008, 18:09
6 Experts publish their posts in the topic What is the sum of all possible 3-digit numbers that can be Bunuel 4 07 Jan 2010, 04:07
26 Experts publish their posts in the topic What is the sum of all 3 digit numbers that leave a remainde joyseychow 16 06 Aug 2009, 19:33
68 Experts publish their posts in the topic What is the sum of all 3 digit positive integers that can be asimov 18 29 Apr 2009, 00:06
Display posts from previous: Sort by

The sum of the digits of [(10^x)^y]-64=279. What is the

  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®.