Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 27 May 2017, 19:36

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 260
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 97 [2] , given: 282

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

### Show Tags

28 Oct 2012, 10:18
2
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:27) correct 48% (02:12) wrong based on 233 sessions

### HideShow timer Statistics

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, 01:59, edited 2 times in total.
Renamed the topic and edited the question.
Manager
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 69
GMAT Date: 10-01-2012
Followers: 3

Kudos [?]: 70 [0], given: 84

Re: The Sum of the digits of(10^x)^y [#permalink]

### Show Tags

28 Oct 2012, 11:13
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
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 260
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 97 [0], given: 282

Re: The Sum of the digits of(10^x)^y [#permalink]

### Show Tags

28 Oct 2012, 11:22
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+

Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 641
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 49

Kudos [?]: 589 [1] , given: 23

Re: The Sum of the digits of(10^x)^y [#permalink]

### Show Tags

28 Oct 2012, 19:44
1
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
Joined: 29 Jul 2012
Posts: 186
GMAT Date: 11-18-2012
Followers: 0

Kudos [?]: 98 [0], given: 23

Re: The Sum of the digits of(10^x)^y [#permalink]

### Show Tags

28 Oct 2012, 20:40
still confuse with question
any more explanation
_________________

Thriving for CHANGE

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 260
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 97 [0], given: 282

Re: The Sum of the digits of(10^x)^y [#permalink]

### Show Tags

28 Oct 2012, 20:42
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+

Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 641
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 49

Kudos [?]: 589 [0], given: 23

Re: The Sum of the digits of(10^x)^y [#permalink]

### Show Tags

28 Oct 2012, 21:47
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

Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 641
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 49

Kudos [?]: 589 [1] , given: 23

Re: The Sum of the digits of(10^x)^y [#permalink]

### Show Tags

28 Oct 2012, 21:49
1
KUDOS
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

Math Expert
Joined: 02 Sep 2009
Posts: 38921
Followers: 7744

Kudos [?]: 106366 [5] , given: 11622

Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink]

### Show Tags

29 Oct 2012, 01:59
5
KUDOS
Expert's post
11
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 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 --> $$9(xy-2)+3+6=279$$ --> $$9(xy-2)=270$$ --> $$xy=32$$.

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.
_________________
Intern
Status: Active
Joined: 30 Jun 2012
Posts: 37
Location: India
Followers: 5

Kudos [?]: 84 [3] , given: 36

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

### Show Tags

29 Oct 2012, 02:26
3
KUDOS
1
This post was
BOOKMARKED
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
Joined: 04 Aug 2013
Posts: 9
Followers: 0

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

Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink]

### Show Tags

24 Nov 2013, 19:36
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 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 --> $$9(xy-2)+3+6=279$$ --> $$9(xy-2)=270$$ --> $$xy=32$$.

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]
Math Expert
Joined: 02 Sep 2009
Posts: 38921
Followers: 7744

Kudos [?]: 106366 [1] , given: 11622

Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink]

### Show Tags

25 Nov 2013, 02:52
1
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 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 --> $$9(xy-2)+3+6=279$$ --> $$9(xy-2)=270$$ --> $$xy=32$$.

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.
_________________
Senior Manager
Status: Student
Joined: 26 Aug 2013
Posts: 259
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Followers: 2

Kudos [?]: 63 [1] , given: 401

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

### Show Tags

08 Jan 2014, 04:19
1
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
Joined: 09 Sep 2013
Posts: 15493
Followers: 651

Kudos [?]: 210 [0], given: 0

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

### Show Tags

21 Jan 2015, 23:41
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 Club Legend
Joined: 09 Sep 2013
Posts: 15493
Followers: 651

Kudos [?]: 210 [0], given: 0

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

### Show Tags

30 Jan 2016, 02:40
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.
_________________
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2644
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 128

Kudos [?]: 1477 [0], given: 789

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

### Show Tags

30 Jan 2016, 07:00
rajathpanta wrote:
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

Sum of the digits of (10^x)^y - 64 = 279.

We know that (X^a)^b = X^(ab)

Thus, the given form becomes = 10^(xy) - 64.

Now start with xy=2, 10^2 - 64 = 36, sum of the digits = 6+3=9 (realize that the sum of digits is 9*(xy-1))
xy=3 ---> 1000-64=936 = 18 (realize that the sum of digits is 9*(xy-1))
xy=4 ---> 10000-64=9936 = 27 (realize that the sum of digits is 9*(xy-1))
xy=5 ---> 100000-64 = 99936 (realize that the sum of digits is 9*(xy-1))... etc so this is your pattern. The sum of the digits = 9*(xy-1)

Now sum of the digits given = 279.

Thus, based on the pattern above, the sum of the digits must be ---> 9*(xy-1) = 279 ---> xy = 32.

E is thus the correct answer.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

CEO
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (D)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 26

Kudos [?]: 344 [0], given: 169

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

### Show Tags

24 Feb 2016, 18:32
gosh..the structure of the question is hideous...
i solved it this way..
the sum is 279. the last 2 digits must be 3 and 6, or 9. so the rest will be a bunch of 9's. how many 9's? 30.
now, 30 of nines + 36 -> 32 digits +1 since we need to round up - 33 in total, we thus must have 10^32.
Re: The sum of the digits of [(10^x)^y]-64=279. What is the   [#permalink] 24 Feb 2016, 18:32
Similar topics Replies Last post
Similar
Topics:
17 What is the sum of all four digit integers formed using the digits 1, 7 17 Nov 2016, 11:13
12 What is the tens' digit of the sum of the first 40 terms of 7 20 Nov 2015, 17:25
12 What is the sum of digits of number 10^28 – 28? 11 24 Feb 2015, 04:41
53 What is the sum of all 3 digit positive integers that can be formed 21 24 Aug 2016, 19:51
125 What is the sum of all 3 digit positive integers that can be 20 07 Nov 2016, 01:29
Display posts from previous: Sort by